Quotients of triangle groups acting on surfaces of genus 2 to 101 ----------------------------------------------------------------- Below is a list of all quotients of ordinary hyperbolic triangle groups that act on a compact Riemann surface of 2 to 101, up to isomorphism, duality/triality and reflection. The notation "Tg.n" is used for the nth quotient of genus g. The "Triangle type" indicates the three positive integers p, q and r in the defining presentation < x,y,z | xyz = x^p = y^q = z^r = 1 > for the ordinary (p,q,r) triangle group. Such a triangle group is spherical (genus 0) if 1/p + 1/q + 1/r > 1, Euclidean (genus 1) if 1/p + 1/q + 1/r = 1, or hyperbolic (genus > 1) if 1/p + 1/q + 1/r < 1. In particular, by the Riemann-Hurwitz formula, this list includes all "large" groups of orientation-preserving automorphisms of compact Riemann surfaces of genus 2 to 101, where "large" means that |G| > 12(g-1) where g is the genus and G is the conformal automorphism group. The action is labelled "Reflexible" if there exists an involutory automorphism of the quotient that inverts the images of two of the three generators x, y and z, and otherwise "Chiral" (if no such reflection exists). These were found by Marston Conder (University of Auckland) with the help of the "LowIndexNormalSubgroups" routine in Magma, in August 2006. Total number of quotient groups in list below: 20810 Genus 2 T2.1 : Triangle type {2,3,8} Group order 48 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y^-1 * z^-1 * x * z ] T2.2 : Triangle type {2,4,6} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^6 ] T2.3 : Triangle type {2,4,8} Group order 16 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-1 * x * y^-1 * z^-2 ] T2.4 : Triangle type {2,5,10} Group order 10 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-5 ] T2.5 : Triangle type {2,6,6} Group order 12 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^6 ] T2.6 : Triangle type {2,8,8} Group order 8 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^3 * z^-1 ] T2.7 : Triangle type {3,3,4} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y^-1 * x ] T2.8 : Triangle type {3,4,4} Group order 12 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^4 ] T2.9 : Triangle type {3,6,6} Group order 6 Reflexible action Defining relators: [ x^3, y^-1 * x^-1 * y^-1, y * z^-1 ] T2.10 : Triangle type {4,4,4} Group order 8 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * x^-1 * y ] T2.11 : Triangle type {5,5,5} Group order 5 Reflexible action Defining relators: [ x^-2 * y^-1, y * x^-1 * y, x * z^-1 ] Genus 3 T3.1 : Triangle type {2,3,7} Group order 168 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * z ] T3.2 : Triangle type {2,3,8} Group order 96 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-3, z * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T3.3 : Triangle type {2,3,12} Group order 48 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y^-1 * z^-3 ] T3.4 : Triangle type {2,4,6} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^6 ] T3.5 : Triangle type {2,4,8} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z^-2 ] T3.6 : Triangle type {2,4,8} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-4 * x * y * z^-3 ] T3.7 : Triangle type {2,4,12} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-2 * x * y^-1 * z^-3 ] T3.8 : Triangle type {2,6,6} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^6 ] T3.9 : Triangle type {2,7,14} Group order 14 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-7 ] T3.10 : Triangle type {2,8,8} Group order 16 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^2 * z^-1 ] T3.11 : Triangle type {2,8,8} Group order 16 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-8 ] T3.12 : Triangle type {2,12,12} Group order 12 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^5 * z^-1 ] T3.13 : Triangle type {3,3,4} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * y^-1 * x * y^-1 * x ] T3.14 : Triangle type {3,3,6} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * z ] T3.15 : Triangle type {3,3,7} Group order 21 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * y * x * z ] T3.16 : Triangle type {3,4,4} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^4 ] T3.17 : Triangle type {3,4,12} Group order 12 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^4 ] T3.18 : Triangle type {3,9,9} Group order 9 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z ] T3.19 : Triangle type {4,4,4} Group order 16 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 ] T3.20 : Triangle type {4,4,4} Group order 16 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^4 ] T3.21 : Triangle type {4,4,6} Group order 12 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z * y^-1 * x * z ] T3.22 : Triangle type {4,8,8} Group order 8 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^4, y * z^-1 ] T3.23 : Triangle type {4,8,8} Group order 8 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z * x^-1 * z ] T3.24 : Triangle type {7,7,7} Group order 7 Reflexible action Defining relators: [ x^-2 * y^-1, y^-2 * x * y^-1, x * z^-1 ] T3.25 : Triangle type {7,7,7} Group order 7 Reflexible action Defining relators: [ x^-2 * y, x * y * z, z * x^-1 * z ] Genus 4 T4.1 : Triangle type {2,3,12} Group order 72 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * y^-1 * z^-1, x * z^3 * y^2 * z^-4 ] T4.2 : Triangle type {2,4,5} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T4.3 : Triangle type {2,4,6} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^6 ] T4.4 : Triangle type {2,4,10} Group order 40 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * y * z^-3 ] T4.5 : Triangle type {2,4,16} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-4 * x * y^-1 * z^-3 ] T4.6 : Triangle type {2,5,5} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (z^-1 * y)^3 ] T4.7 : Triangle type {2,6,6} Group order 36 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^6 ] T4.8 : Triangle type {2,6,6} Group order 36 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 ] T4.9 : Triangle type {2,6,12} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^6 ] T4.10 : Triangle type {2,9,18} Group order 18 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-9 ] T4.11 : Triangle type {2,10,10} Group order 20 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z * y^-7 * z ] T4.12 : Triangle type {2,16,16} Group order 16 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-7 * z ] T4.13 : Triangle type {3,3,6} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T4.14 : Triangle type {3,4,4} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^4 ] T4.15 : Triangle type {3,4,6} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * y * x^-1 * z ] T4.16 : Triangle type {3,5,15} Group order 15 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-5 ] T4.17 : Triangle type {3,6,6} Group order 18 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-6 ] T4.18 : Triangle type {3,6,6} Group order 18 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1 ] T4.19 : Triangle type {3,6,6} Group order 18 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-6 ] T4.20 : Triangle type {3,12,12} Group order 12 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, z^-1 * y^2 * z^-1 ] T4.21 : Triangle type {4,4,5} Group order 20 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-1 * y * x * z^-1 ] T4.22 : Triangle type {4,4,5} Group order 20 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y^-1 * x^-1 * z^2 ] T4.23 : Triangle type {4,4,8} Group order 16 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z * y * x^-1 * z^2 ] T4.24 : Triangle type {4,6,12} Group order 12 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * x^-1 * z ] T4.25 : Triangle type {5,10,10} Group order 10 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-1 * x^2 * z^-1 ] T4.26 : Triangle type {5,10,10} Group order 10 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-5, y * z^-1 ] T4.27 : Triangle type {6,6,6} Group order 12 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-1 * x^2 * z^-1 ] T4.28 : Triangle type {9,9,9} Group order 9 Reflexible action Defining relators: [ x^-2 * y^-1, y^2 * x^-1 * y^2, x * z^-1 ] Genus 5 T5.1 : Triangle type {2,3,8} Group order 192 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z^3 * y * z^-1 * x * z * y^-1 * x * y^-1 * z^-2 * x ] T5.2 : Triangle type {2,3,10} Group order 120 Reflexible action Defining relators: [ x^2, y^3, x * y * z, (y * z^-2 * x * z)^2 ] T5.3 : Triangle type {2,4,5} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^4 ] T5.4 : Triangle type {2,4,6} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * x * y^-1 * z^-2 * x ] T5.5 : Triangle type {2,4,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4 ] T5.6 : Triangle type {2,4,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^8 ] T5.7 : Triangle type {2,4,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-12 ] T5.8 : Triangle type {2,4,20} Group order 40 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * y^-1 * z^-3 ] T5.9 : Triangle type {2,5,5} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^-2 * x * y * z^-2 ] T5.10 : Triangle type {2,6,6} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * y^-1 * z^-1 * x ] T5.11 : Triangle type {2,6,15} Group order 30 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * y^-1 * z^-2 ] T5.12 : Triangle type {2,8,8} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * y^-1 * z^-1 * x ] T5.13 : Triangle type {2,8,8} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^8 ] T5.14 : Triangle type {2,11,22} Group order 22 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-8 ] T5.15 : Triangle type {2,12,12} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-7 * z ] T5.16 : Triangle type {2,20,20} Group order 20 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z * y^-8 ] T5.17 : Triangle type {3,3,4} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * y^-1 * z^-1 * x^-1 * z * y * x ] T5.18 : Triangle type {3,3,5} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * y^-1 * x * z^2, z^2 * y^-1 * x^-1 * z^2 ] T5.19 : Triangle type {3,4,4} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * z^-1 * x^-1 * y * z^-1 ] T5.20 : Triangle type {3,4,4} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * z^-1 * x^-1 * y^-1 * z ] T5.21 : Triangle type {3,6,6} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2 ] T5.22 : Triangle type {3,15,15} Group order 15 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z ] T5.23 : Triangle type {4,4,4} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4, z^-2 * x^-1 * z * y^-1 ] T5.24 : Triangle type {4,4,4} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2 ] T5.25 : Triangle type {4,4,6} Group order 24 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 ] T5.26 : Triangle type {4,4,10} Group order 20 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y^-1 * x * z^2 ] T5.27 : Triangle type {4,8,8} Group order 16 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y * z^-1)^2 ] T5.28 : Triangle type {4,8,8} Group order 16 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^2 * z^-1 ] T5.29 : Triangle type {6,12,12} Group order 12 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^6, y * z^-1 ] T5.30 : Triangle type {11,11,11} Group order 11 Reflexible action Defining relators: [ x^-2 * y^-1, y^-3 * x * y^-2, x * z^-1 ] T5.31 : Triangle type {11,11,11} Group order 11 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-2 * x * y^-1 ] Genus 6 T6.1 : Triangle type {2,3,10} Group order 150 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-5 * x * y^-2 * z^-4 ] T6.2 : Triangle type {2,4,6} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^6 ] T6.3 : Triangle type {2,4,9} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-4 * x * y * z^-4 ] T6.4 : Triangle type {2,4,14} Group order 56 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y * z^-4 ] T6.5 : Triangle type {2,4,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-8 * x * y^-1 * z^-3 ] T6.6 : Triangle type {2,5,10} Group order 50 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-1 * z^-2 ] T6.7 : Triangle type {2,6,8} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^8 ] T6.8 : Triangle type {2,6,8} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^2 * y^2 * x * z ] T6.9 : Triangle type {2,9,9} Group order 36 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^9 ] T6.10 : Triangle type {2,10,15} Group order 30 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-2 * z^2 ] T6.11 : Triangle type {2,13,26} Group order 26 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^13 ] T6.12 : Triangle type {2,14,14} Group order 28 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^14 ] T6.13 : Triangle type {2,24,24} Group order 24 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-8 ] T6.14 : Triangle type {3,3,5} Group order 75 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * x^-1 * z^2 ] T6.15 : Triangle type {3,3,13} Group order 39 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * y^-1 * z^-1 ] T6.16 : Triangle type {3,7,21} Group order 21 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-1 * z * y^-3 * z^2 ] T6.17 : Triangle type {3,8,8} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-8 ] T6.18 : Triangle type {3,18,18} Group order 18 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z ] T6.19 : Triangle type {4,4,7} Group order 28 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^3 * y * x * z^3 ] T6.20 : Triangle type {4,4,12} Group order 24 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y * x^-1 * z^3 ] T6.21 : Triangle type {4,5,20} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-5 ] T6.22 : Triangle type {4,6,6} Group order 24 Reflexible action Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^2 * x * z^-1 ] T6.23 : Triangle type {4,6,6} Group order 24 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^6 ] T6.24 : Triangle type {4,16,16} Group order 16 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-2 * y * z^-1 ] T6.25 : Triangle type {5,5,5} Group order 25 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 ] T6.26 : Triangle type {5,15,15} Group order 15 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-2 * x * z^-1 ] T6.27 : Triangle type {5,15,15} Group order 15 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-5 ] T6.28 : Triangle type {7,14,14} Group order 14 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-2 * y * z^-1 ] T6.29 : Triangle type {7,14,14} Group order 14 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^2 * x^-1 * z^2 ] T6.30 : Triangle type {7,14,14} Group order 14 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-7, y * z^-1 ] T6.31 : Triangle type {13,13,13} Group order 13 Reflexible action Defining relators: [ x^-2 * y^-1, y^-4 * x * y^-2, x * z^-1 ] T6.32 : Triangle type {13,13,13} Group order 13 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y * x^-2 * y^2 ] T6.33 : Triangle type {13,13,13} Group order 13 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-1, y^3 * z^-1 ] Genus 7 T7.1 : Triangle type {2,3,7} Group order 504 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, y * z^-1 * x * z * y * z^-1 * x * z^2 * y * z^-2 * y * z^-2 * x * z^2 ] T7.2 : Triangle type {2,3,12} Group order 144 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z^2 * y * x * y^-1 * z^-2 * x * z ] T7.3 : Triangle type {2,4,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-2 * x * z * y^-1 * z^-4 ] T7.4 : Triangle type {2,4,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * z^5 * y^-1 * z^-4 ] T7.5 : Triangle type {2,4,28} Group order 56 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y^-1 * z^-4 ] T7.6 : Triangle type {2,6,9} Group order 54 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y^2 * x * z ] T7.7 : Triangle type {2,6,9} Group order 54 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-4 * x * y * z^-4 ] T7.8 : Triangle type {2,6,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, y * z^-1 * x * y^-1 * z^-2 ] T7.9 : Triangle type {2,6,21} Group order 42 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^2 * y * z^-1 * x * z^3 ] T7.10 : Triangle type {2,7,7} Group order 56 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, x * y^-3 * z^-1 * y * z^-1 ] T7.11 : Triangle type {2,15,30} Group order 30 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^15 ] T7.12 : Triangle type {2,16,16} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^16 ] T7.13 : Triangle type {2,16,16} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^6 * z^-2 ] T7.14 : Triangle type {2,28,28} Group order 28 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^13 * z^-1 ] T7.15 : Triangle type {3,3,6} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T7.16 : Triangle type {3,4,6} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1 ] T7.17 : Triangle type {3,4,12} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1 ] T7.18 : Triangle type {3,8,24} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z * y^-3 * z^2 ] T7.19 : Triangle type {3,9,9} Group order 27 Chiral action Defining relators: [ x^3, x * y * z, y^-2 * x * z ] T7.20 : Triangle type {3,9,9} Group order 27 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^4 * z^-2 ] T7.21 : Triangle type {3,21,21} Group order 21 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-1 * z * y^-4 * z ] T7.22 : Triangle type {4,4,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T7.23 : Triangle type {4,4,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T7.24 : Triangle type {4,4,8} Group order 32 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * x^-1 * z^3 ] T7.25 : Triangle type {4,4,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-1 * z^2 ] T7.26 : Triangle type {4,4,14} Group order 28 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^3 * y * x^-1 * z^3 ] T7.27 : Triangle type {4,6,12} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^6 ] T7.28 : Triangle type {4,10,20} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-3 * z^2 ] T7.29 : Triangle type {6,6,6} Group order 24 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y * x * y^-1 ] T7.30 : Triangle type {6,9,18} Group order 18 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-2 * y^2 ] T7.31 : Triangle type {6,9,18} Group order 18 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^6 ] T7.32 : Triangle type {8,16,16} Group order 16 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-8, y * z^-1 ] T7.33 : Triangle type {8,16,16} Group order 16 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-3 * y^2 ] T7.34 : Triangle type {8,16,16} Group order 16 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^2 * x^-2 * z^2 ] T7.35 : Triangle type {15,15,15} Group order 15 Reflexible action Defining relators: [ x^-2 * y^-1, y^-5 * x * y^-2, x * z^-1 ] Genus 8 T8.1 : Triangle type {2,3,8} Group order 336 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T8.2 : Triangle type {2,3,8} Group order 336 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * z^-2 * x * z * y * x * y^-1 * z^-3 * x * z ] T8.3 : Triangle type {2,4,18} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-13 * x * y * z^-4 ] T8.4 : Triangle type {2,4,32} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * z^5 * y^-1 * x * y^-1 * z^-3 ] T8.5 : Triangle type {2,6,6} Group order 84 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-1 * z * y^2 * x * y^-1 * z^-1 ] T8.6 : Triangle type {2,6,10} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T8.7 : Triangle type {2,6,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-3 * x * y^-1 * z^-4 ] T8.8 : Triangle type {2,8,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z * y * x * y^-1 * z^-3 ] T8.9 : Triangle type {2,10,20} Group order 40 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^10 ] T8.10 : Triangle type {2,17,34} Group order 34 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^17 ] T8.11 : Triangle type {2,18,18} Group order 36 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^18 ] T8.12 : Triangle type {2,32,32} Group order 32 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-1 ] T8.13 : Triangle type {3,3,4} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, (x * z * y^-1 * z^-1)^2 ] T8.14 : Triangle type {3,3,4} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T8.15 : Triangle type {3,4,8} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T8.16 : Triangle type {3,6,6} Group order 42 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-2 * y^2 * z^-1 * y ] T8.17 : Triangle type {3,6,6} Group order 42 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * z^-1 * x^-1 * y^-1 * z^-1 ] T8.18 : Triangle type {3,10,10} Group order 30 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y * z^-1 * y^6 * z^-1 * y ] T8.19 : Triangle type {3,24,24} Group order 24 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z * y^-5 ] T8.20 : Triangle type {4,4,9} Group order 36 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x^-1 * z^3 ] T8.21 : Triangle type {4,4,16} Group order 32 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * x * z^3 ] T8.22 : Triangle type {4,12,12} Group order 24 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^3 * z^-1 * y ] T8.23 : Triangle type {5,6,6} Group order 30 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^6 ] T8.24 : Triangle type {5,20,20} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-5 ] T8.25 : Triangle type {5,20,20} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-5 ] T8.26 : Triangle type {6,6,12} Group order 24 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z * y * x^-1 * z^2 ] T8.27 : Triangle type {6,8,8} Group order 24 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * x^-1 * y * z^-1 ] T8.28 : Triangle type {9,18,18} Group order 18 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-9, y * z^-1 ] T8.29 : Triangle type {9,18,18} Group order 18 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^2 * x^-1 * z^2 ] T8.30 : Triangle type {10,10,10} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-2 * x^2 * z^-2 ] T8.31 : Triangle type {17,17,17} Group order 17 Reflexible action Defining relators: [ x^-2 * y^-1, y^5 * x^-1 * y^3, x * z^-1 ] T8.32 : Triangle type {17,17,17} Group order 17 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-3 * x * y^-2 ] T8.33 : Triangle type {17,17,17} Group order 17 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-3 * y^2 ] Genus 9 T9.1 : Triangle type {2,3,12} Group order 192 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * z, z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 ] T9.2 : Triangle type {2,4,5} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, z * y^-1 * z^2 * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T9.3 : Triangle type {2,4,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z ] T9.4 : Triangle type {2,4,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T9.5 : Triangle type {2,4,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y^-1 * z * y^-2 * z^-2 * x * z ] T9.6 : Triangle type {2,4,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^8 ] T9.7 : Triangle type {2,4,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^8 ] T9.8 : Triangle type {2,4,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T9.9 : Triangle type {2,4,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z^-3, (y * z^-1)^4 ] T9.10 : Triangle type {2,4,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * y^-1 * z^-4 ] T9.11 : Triangle type {2,4,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-3 * x * z^2 * y * z^-1 * x * y * x * y^-1 * z^-3 ] T9.12 : Triangle type {2,4,20} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-15 * x * y * z^-4 ] T9.13 : Triangle type {2,4,36} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-13 * x * y^-1 * z^-4 ] T9.14 : Triangle type {2,5,5} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T9.15 : Triangle type {2,5,6} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-2)^2 ] T9.16 : Triangle type {2,5,6} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^6 ] T9.17 : Triangle type {2,6,6} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1 ] T9.18 : Triangle type {2,6,6} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3 ] T9.19 : Triangle type {2,8,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^8 ] T9.20 : Triangle type {2,8,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^8 ] T9.21 : Triangle type {2,8,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-3 * z^-1 * x * z, y * x * y^-2 * z^3 ] T9.22 : Triangle type {2,8,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^8 ] T9.23 : Triangle type {2,8,8} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z * y^-1 * z^-1 ] T9.24 : Triangle type {2,8,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * y^-1 * z^-3 ] T9.25 : Triangle type {2,8,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^8 ] T9.26 : Triangle type {2,12,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^3 * z^-2, z * y * x * y^-1 * z^-1 * x ] T9.27 : Triangle type {2,12,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-12 ] T9.28 : Triangle type {2,12,12} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-2 * z^2 * y^-6 * z^2 ] T9.29 : Triangle type {2,14,21} Group order 42 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^3 ] T9.30 : Triangle type {2,19,38} Group order 38 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^8 * y^-10 ] T9.31 : Triangle type {2,20,20} Group order 40 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-9 * z ] T9.32 : Triangle type {2,36,36} Group order 36 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-1 ] T9.33 : Triangle type {3,3,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T9.34 : Triangle type {3,3,19} Group order 57 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-1 * x * z^2 ] T9.35 : Triangle type {3,4,4} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T9.36 : Triangle type {3,4,4} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T9.37 : Triangle type {3,4,12} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y ] T9.38 : Triangle type {3,5,5} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-5 ] T9.39 : Triangle type {3,5,5} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z * x^-1 * y^-1 * x * y^-1 * x, y^-5 ] T9.40 : Triangle type {3,6,6} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1 ] T9.41 : Triangle type {3,10,30} Group order 30 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^4 * z^-2 ] T9.42 : Triangle type {3,27,27} Group order 27 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^6 ] T9.43 : Triangle type {4,4,4} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * z * y ] T9.44 : Triangle type {4,4,4} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T9.45 : Triangle type {4,4,4} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y ] T9.46 : Triangle type {4,4,4} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4 ] T9.47 : Triangle type {4,4,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^6 ] T9.48 : Triangle type {4,4,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x * z, (y^-1 * x)^3 ] T9.49 : Triangle type {4,4,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^4 ] T9.50 : Triangle type {4,4,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^6 ] T9.51 : Triangle type {4,4,10} Group order 40 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, y^-1 * z^-1 * x^-1 * z^2 ] T9.52 : Triangle type {4,4,10} Group order 40 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y * x * z^3 ] T9.53 : Triangle type {4,4,18} Group order 36 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x * z^3 ] T9.54 : Triangle type {4,7,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-7 ] T9.55 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z^2 * y^-5 ] T9.56 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1 ] T9.57 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-1 * z^2 ] T9.58 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1 ] T9.59 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-2 * z^3 ] T9.60 : Triangle type {4,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y * z^-1 ] T9.61 : Triangle type {4,24,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-1 ] T9.62 : Triangle type {4,24,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^3 * z^-2 ] T9.63 : Triangle type {6,8,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^6 ] T9.64 : Triangle type {6,12,12} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^6 ] T9.65 : Triangle type {7,21,21} Group order 21 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 ] T9.66 : Triangle type {7,21,21} Group order 21 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-7 ] T9.67 : Triangle type {7,21,21} Group order 21 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z * x^-2 * z^2 ] T9.68 : Triangle type {8,8,12} Group order 24 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y^-1 * x * z ] T9.69 : Triangle type {8,8,12} Group order 24 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z * x^-2 * z^2 ] T9.70 : Triangle type {10,20,20} Group order 20 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-10, y * z^-1 ] T9.71 : Triangle type {10,20,20} Group order 20 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^3 * x^-1 * y^3 ] T9.72 : Triangle type {19,19,19} Group order 19 Reflexible action Defining relators: [ x^-2 * y^-1, y^6 * x^-1 * y^3, x * z^-1 ] T9.73 : Triangle type {19,19,19} Group order 19 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^2 * x^-2 * y^3 ] T9.74 : Triangle type {19,19,19} Group order 19 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-1 * y^2 ] T9.75 : Triangle type {19,19,19} Group order 19 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y * x^-2 * y^2 ] Genus 10 T10.1 : Triangle type {2,3,8} Group order 432 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z^2 * y * x * z * y * z^-1 * x * y^-1 * z^-2 * x * z ] T10.2 : Triangle type {2,3,9} Group order 324 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^2 * y * z^-1 * x * z * y * x * y * x * z * y^-1 * z^-1 * x ] T10.3 : Triangle type {2,3,12} Group order 216 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^7 * y^-1 * x * z^4 ] T10.4 : Triangle type {2,3,15} Group order 180 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z^2, z^-4 * x * z * y^-1 * x * z^2 * y^-1 * z^-1 ] T10.5 : Triangle type {2,3,18} Group order 162 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^6 * y * z^-5 * x ] T10.6 : Triangle type {2,3,24} Group order 144 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y^-1 * z^-4 ] T10.7 : Triangle type {2,4,5} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (z^-1 * y)^5 ] T10.8 : Triangle type {2,4,6} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2 * y * z^-1)^2 ] T10.9 : Triangle type {2,4,6} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T10.10 : Triangle type {2,4,7} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x * y * z^-3 ] T10.11 : Triangle type {2,4,8} Group order 144 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, y * z^-2 * x * y^-1 * z^-2 * y * z^-1 ] T10.12 : Triangle type {2,4,12} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T10.13 : Triangle type {2,4,22} Group order 88 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-17 * x * y * z^-4 ] T10.14 : Triangle type {2,4,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-15 * x * y^-1 * z^-4 ] T10.15 : Triangle type {2,6,6} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-2 * z^-2 * y ] T10.16 : Triangle type {2,6,6} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T10.17 : Triangle type {2,6,6} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z ] T10.18 : Triangle type {2,6,12} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^6 ] T10.19 : Triangle type {2,6,12} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z * y * x * z^4 * y^-1 * x * y^-1 * z^-3 * x * z ] T10.20 : Triangle type {2,6,12} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * z^2 * y * z^-1 * x * y^-1 * z^-5 ] T10.21 : Triangle type {2,6,30} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^4 * y^-1 * z^-5 ] T10.22 : Triangle type {2,8,8} Group order 72 Chiral action Defining relators: [ x^2, x * y * z, z * y^-3 * z^-1 * x * y^-1 ] T10.23 : Triangle type {2,9,18} Group order 54 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-9 ] T10.24 : Triangle type {2,12,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * y^2 * z^-2 ] T10.25 : Triangle type {2,21,42} Group order 42 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^10 * y^-10 ] T10.26 : Triangle type {2,22,22} Group order 44 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-9 * z ] T10.27 : Triangle type {2,40,40} Group order 40 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-10 ] T10.28 : Triangle type {3,3,4} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y^-1 * z^-1 * x * z^2 * y * x ] T10.29 : Triangle type {3,3,4} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y * x^-1 * z * y * z^-1 * x^-1 ] T10.30 : Triangle type {3,3,6} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^6 ] T10.31 : Triangle type {3,3,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * y^-1 * x * z * y ] T10.32 : Triangle type {3,3,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z^2 * y^-1 ] T10.33 : Triangle type {3,3,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * z * y^-1 ] T10.34 : Triangle type {3,3,21} Group order 63 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x^-1 * z^2 ] T10.35 : Triangle type {3,4,4} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * y * x * y^-1 * z^-1 ] T10.36 : Triangle type {3,4,4} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * x^-1 * y * x^-1 * y^-1 * x * z ] T10.37 : Triangle type {3,4,6} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3 ] T10.38 : Triangle type {3,6,6} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T10.39 : Triangle type {3,6,6} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T10.40 : Triangle type {3,6,6} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (z^-1 * y)^3 ] T10.41 : Triangle type {3,6,6} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T10.42 : Triangle type {3,6,14} Group order 42 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y * z^-1, y * z^-1 * x^-1 * z * y ] T10.43 : Triangle type {3,11,33} Group order 33 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^11 ] T10.44 : Triangle type {3,12,12} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z * y^-1 * z * y^-4 * z ] T10.45 : Triangle type {3,12,12} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * z^-1 ] T10.46 : Triangle type {3,12,12} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^2 * y^-3 * z * y^-4 * z ] T10.47 : Triangle type {3,30,30} Group order 30 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^5 * z^-1 ] T10.48 : Triangle type {4,4,4} Group order 72 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * x * y^-1 * x * z * y^-1, y^-1 * z * y^-1 * x * z * x^-1 ] T10.49 : Triangle type {4,4,4} Group order 72 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^2 ] T10.50 : Triangle type {4,4,11} Group order 44 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^11 ] T10.51 : Triangle type {4,4,20} Group order 40 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y * x^-1 * z^3 ] T10.52 : Triangle type {4,6,12} Group order 36 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1 ] T10.53 : Triangle type {4,14,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-5 * z^2 ] T10.54 : Triangle type {5,6,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^6 ] T10.55 : Triangle type {5,25,25} Group order 25 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z ] T10.56 : Triangle type {5,25,25} Group order 25 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-3 * x^-1 * z^2 ] T10.57 : Triangle type {6,6,6} Group order 36 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^6 ] T10.58 : Triangle type {6,6,6} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^6 ] T10.59 : Triangle type {6,6,6} Group order 36 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, (x * y^-1)^2, y^6 ] T10.60 : Triangle type {6,6,15} Group order 30 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * x * z^2 ] T10.61 : Triangle type {6,24,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^2 * x^-1 * z^2 ] T10.62 : Triangle type {8,12,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 ] T10.63 : Triangle type {8,12,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-1 * x^3 * z^-2 ] T10.64 : Triangle type {9,9,9} Group order 27 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, z * y^-1 * x * y^-1 ] T10.65 : Triangle type {9,9,9} Group order 27 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2 ] T10.66 : Triangle type {11,22,22} Group order 22 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^4 * y^-2 ] T10.67 : Triangle type {11,22,22} Group order 22 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * x^-1 * y^2 ] T10.68 : Triangle type {11,22,22} Group order 22 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^5 * z^-1 ] T10.69 : Triangle type {11,22,22} Group order 22 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-4 * x^2 * z^-2 ] T10.70 : Triangle type {11,22,22} Group order 22 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-11, y * z^-1 ] T10.71 : Triangle type {12,12,12} Group order 24 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * x^2 * z^-1 ] T10.72 : Triangle type {21,21,21} Group order 21 Reflexible action Defining relators: [ x^-2 * y^-1, y^7 * x^-1 * y^3, x * z^-1 ] T10.73 : Triangle type {21,21,21} Group order 21 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z, y^2 * x^-1 * y^2 ] Genus 11 T11.1 : Triangle type {2,4,6} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T11.2 : Triangle type {2,4,8} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T11.3 : Triangle type {2,4,8} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1 ] T11.4 : Triangle type {2,4,12} Group order 120 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T11.5 : Triangle type {2,4,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * z^2 * y^-1 * z^-2 ] T11.6 : Triangle type {2,4,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-19 * x * y * z^-4 ] T11.7 : Triangle type {2,4,44} Group order 88 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-17 * x * y^-1 * z^-4 ] T11.8 : Triangle type {2,6,6} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-2 * y)^2, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T11.9 : Triangle type {2,6,8} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * z^-1 * x * y^-1 * z^-2 * x ] T11.10 : Triangle type {2,6,8} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y^-1 * z * y^-2 * z^-2 * x ] T11.11 : Triangle type {2,6,33} Group order 66 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y^-1 * z^-4 * x ] T11.12 : Triangle type {2,8,8} Group order 80 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^-1 * z * y^-2 * z^-1 * x * z ] T11.13 : Triangle type {2,8,8} Group order 80 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^8 ] T11.14 : Triangle type {2,8,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z * y * x * z * y * z^-4 ] T11.15 : Triangle type {2,8,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z * y^-1 * z^-4 ] T11.16 : Triangle type {2,12,12} Group order 60 Chiral action Defining relators: [ x^2, x * y * z, z^-2 * y^2 * z^-1 * y ] T11.17 : Triangle type {2,23,46} Group order 46 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^12 * y^-10 ] T11.18 : Triangle type {2,24,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-9 * z ] T11.19 : Triangle type {2,24,24} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-2 * z^2 * y^-8 ] T11.20 : Triangle type {2,44,44} Group order 44 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-10 ] T11.21 : Triangle type {3,4,4} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x * z * y)^2, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T11.22 : Triangle type {3,8,8} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, z * y * x^-1 * y^-2, z^-2 * x^-1 * z * y ] T11.23 : Triangle type {3,8,8} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1 * y)^2 ] T11.24 : Triangle type {3,33,33} Group order 33 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^10 * z^-1 ] T11.25 : Triangle type {4,4,4} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T11.26 : Triangle type {4,4,4} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T11.27 : Triangle type {4,4,6} Group order 60 Chiral action Defining relators: [ x * y * z, x^4, y^4, z * y * x^-1 * y * x ] T11.28 : Triangle type {4,4,12} Group order 48 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^12 ] T11.29 : Triangle type {4,4,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y^-1 * z^-1 * x^-1 * z^3 ] T11.30 : Triangle type {4,4,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3 ] T11.31 : Triangle type {4,4,22} Group order 44 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * z^-3 * x * z^3 ] T11.32 : Triangle type {4,6,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^6, y * z^-1 * y * x * y^-1 * z^-1 ] T11.33 : Triangle type {4,6,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^6 ] T11.34 : Triangle type {4,6,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^6 ] T11.35 : Triangle type {4,8,8} Group order 40 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y * x^-1 * z * y^-1 ] T11.36 : Triangle type {4,8,8} Group order 40 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * x^-1 * z * y^-1 ] T11.37 : Triangle type {4,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z^2 * y^-2 * z * y^-1 * z ] T11.38 : Triangle type {4,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-4 * z ] T11.39 : Triangle type {6,10,15} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-3 * x^-1 * z^2 ] T11.40 : Triangle type {8,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * x^2 * z * y^-1 ] T11.41 : Triangle type {8,8,8} Group order 32 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-3 * y^-1 * z^-1 ] T11.42 : Triangle type {12,24,24} Group order 24 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^12, y * z^-1 ] T11.43 : Triangle type {12,24,24} Group order 24 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-5 * y^2 ] T11.44 : Triangle type {23,23,23} Group order 23 Reflexible action Defining relators: [ x^-2 * y^-1, y^8 * x^-1 * y^3, x * z^-1 ] T11.45 : Triangle type {23,23,23} Group order 23 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-4 * x * y^-3 ] T11.46 : Triangle type {23,23,23} Group order 23 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-3 * x * y^-2 ] T11.47 : Triangle type {23,23,23} Group order 23 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^2 * x^-1 * z^2 ] Genus 12 T12.1 : Triangle type {2,4,15} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-1 * x * z^8 * y * x * z * y^-1 * z^-3 ] T12.2 : Triangle type {2,4,26} Group order 104 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-20 * x * y * z^-5 ] T12.3 : Triangle type {2,4,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-19 * x * y^-1 * z^-4 ] T12.4 : Triangle type {2,5,10} Group order 110 Chiral action Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-2 * z^-1 * y * z^-1 ] T12.5 : Triangle type {2,5,10} Group order 110 Chiral action Defining relators: [ x^2, x * y * z, y^-5, y^2 * z^-1 * y^2 * z^-1 * x * z ] T12.6 : Triangle type {2,6,14} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-4 * x * z^4 * y^-1 * x * y^-1 * z^-4 ] T12.7 : Triangle type {2,8,10} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T12.8 : Triangle type {2,10,30} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^10 ] T12.9 : Triangle type {2,14,28} Group order 56 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-4 * z * y^-7 * z * y^-1 ] T12.10 : Triangle type {2,15,15} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-11 * z * y^-1 ] T12.11 : Triangle type {2,25,50} Group order 50 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^14 * y^-10 ] T12.12 : Triangle type {2,26,26} Group order 52 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-9 * z ] T12.13 : Triangle type {2,48,48} Group order 48 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-10 ] T12.14 : Triangle type {3,3,14} Group order 84 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-2 * x^-1 * z^3 ] T12.15 : Triangle type {3,13,39} Group order 39 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z * y^-5 * z^2 ] T12.16 : Triangle type {3,14,14} Group order 42 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^4 * y^-9 ] T12.17 : Triangle type {3,36,36} Group order 36 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z * y^-1 * z * y^-3 * z^2 ] T12.18 : Triangle type {4,4,13} Group order 52 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z * y * z^-1 * x * z^2 ] T12.19 : Triangle type {4,4,13} Group order 52 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x^-1 * z^7 ] T12.20 : Triangle type {4,4,24} Group order 48 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * z^-3 * x * z^3 ] T12.21 : Triangle type {4,6,8} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-2 * x^-1 * y * z^-1 ] T12.22 : Triangle type {4,6,8} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-1 * z^2, y^6 ] T12.23 : Triangle type {4,9,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y^4 * z^-3 ] T12.24 : Triangle type {4,10,10} Group order 40 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y^3 * z^-1 * y)^2 ] T12.25 : Triangle type {4,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-3 * z^2 ] T12.26 : Triangle type {5,5,5} Group order 55 Chiral action Defining relators: [ x * y * z, x^-5, y * x^-2 * z * y, y^-1 * z * x^-1 * z * y^-1 ] T12.27 : Triangle type {5,5,5} Group order 55 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * z * y, x * z^-1 * x^-1 * y^2 ] T12.28 : Triangle type {5,7,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-2 * x * y^-3 ] T12.29 : Triangle type {5,8,8} Group order 40 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, y^8 ] T12.30 : Triangle type {5,8,8} Group order 40 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^6 * z^-2 ] T12.31 : Triangle type {5,30,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^3 * z^-2 ] T12.32 : Triangle type {5,30,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-2 ] T12.33 : Triangle type {6,6,7} Group order 42 Chiral action Defining relators: [ x * y * z, z * y * x * z, z * x^-2 * y^-2, x^6 ] T12.34 : Triangle type {6,6,7} Group order 42 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, z * y * x^-1 * y^-1 * x, x^6 ] T12.35 : Triangle type {6,6,7} Group order 42 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^3 * y^-1 * x^-1 * z^3 ] T12.36 : Triangle type {6,9,9} Group order 36 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z ] T12.37 : Triangle type {6,15,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-2 * x^-1 * z^2 ] T12.38 : Triangle type {7,28,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-7 ] T12.39 : Triangle type {7,28,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T12.40 : Triangle type {7,28,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-7 ] T12.41 : Triangle type {9,27,27} Group order 27 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^9 ] T12.42 : Triangle type {9,27,27} Group order 27 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * y * z^-2 ] T12.43 : Triangle type {9,27,27} Group order 27 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^3 * x^-1 * y^3 ] T12.44 : Triangle type {10,10,15} Group order 30 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, (x * z^-1)^2 ] T12.45 : Triangle type {10,10,15} Group order 30 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-2 * y * x * z^-2 ] T12.46 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-5 * y^2 ] T12.47 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-2 * y^2 * z^-2 ] T12.48 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^3 ] T12.49 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^4 * y^-2 ] T12.50 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-2 * x * z^-2 * x^3 * z^-2 ] T12.51 : Triangle type {13,26,26} Group order 26 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^13, y * z^-1 ] T12.52 : Triangle type {14,14,14} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-3 * x^2 * z^-3 ] T12.53 : Triangle type {14,14,14} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-2 * x^2 * y^-2 ] T12.54 : Triangle type {25,25,25} Group order 25 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-5 * x^2 * z^-2 ] T12.55 : Triangle type {25,25,25} Group order 25 Reflexible action Defining relators: [ x^-2 * y^-1, y^9 * x^-1 * y^3, x * z^-1 ] T12.56 : Triangle type {25,25,25} Group order 25 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-6 * z ] Genus 13 T13.1 : Triangle type {2,3,10} Group order 360 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, x * z * y * x * z * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T13.2 : Triangle type {2,3,12} Group order 288 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^-12 ] T13.3 : Triangle type {2,4,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, y * z^-3 * y * z^-1 * y * z^-1 * y * z^-3 ] T13.4 : Triangle type {2,4,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-5 * x * z^5 * y^-1 * x * z * y^-1 * z^-3 ] T13.5 : Triangle type {2,4,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T13.6 : Triangle type {2,4,28} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-22 * x * y * z^-5 ] T13.7 : Triangle type {2,4,52} Group order 104 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-20 * x * y^-1 * z^-5 ] T13.8 : Triangle type {2,5,10} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-1 * y^2 * z^-1 * x * y^-1 ] T13.9 : Triangle type {2,6,6} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T13.10 : Triangle type {2,6,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-2)^2 ] T13.11 : Triangle type {2,6,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y^-1 * z^-3 ] T13.12 : Triangle type {2,6,15} Group order 90 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^9 * y * z^-5 ] T13.13 : Triangle type {2,6,39} Group order 78 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-3 * x * z^4 * y^-1 * z^-5 ] T13.14 : Triangle type {2,9,18} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-9 ] T13.15 : Triangle type {2,12,12} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T13.16 : Triangle type {2,12,12} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-3 * z^2 * y^-5 * z^2 ] T13.17 : Triangle type {2,16,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * y^4 * z^-3 ] T13.18 : Triangle type {2,16,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^5 * z^-1 * y * z^-1 ] T13.19 : Triangle type {2,16,16} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-1 * y^8 * z^-2 * y^2 * z^-1 * y ] T13.20 : Triangle type {2,27,54} Group order 54 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^16 * y^-10 ] T13.21 : Triangle type {2,28,28} Group order 56 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-9 * z ] T13.22 : Triangle type {2,52,52} Group order 52 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-10 ] T13.23 : Triangle type {3,3,5} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (x * z^2 * y)^2 ] T13.24 : Triangle type {3,3,6} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z * y)^2, z^6 ] T13.25 : Triangle type {3,4,6} Group order 96 Chiral action Defining relators: [ x^3, x * y * z, y^4, x * z * y^-1 * x * z * y, (z^-1 * y)^3 ] T13.26 : Triangle type {3,4,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3 ] T13.27 : Triangle type {3,4,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x * z * y^-1 ] T13.28 : Triangle type {3,4,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (x * z * y)^2, (z^-1 * y)^3 ] T13.29 : Triangle type {3,4,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y ] T13.30 : Triangle type {3,6,6} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T13.31 : Triangle type {3,6,6} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (x * z * y)^2 ] T13.32 : Triangle type {3,6,6} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (y * z^-2 * y)^2 ] T13.33 : Triangle type {3,12,12} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^2 * x^-1 * z^2 ] T13.34 : Triangle type {3,12,12} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2 ] T13.35 : Triangle type {3,14,42} Group order 42 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-6 * z * y^-5 * z^2 ] T13.36 : Triangle type {3,15,15} Group order 45 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-7 * z * y^-5 * z^2 ] T13.37 : Triangle type {3,39,39} Group order 39 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z * y^-6 * z ] T13.38 : Triangle type {4,4,6} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T13.39 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^8 ] T13.40 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1 ] T13.41 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * z * y ] T13.42 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y ] T13.43 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^8 ] T13.44 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y, z * y * x^2 * z * y^-1 ] T13.45 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, y * x * y^-1 * x * z^2 ] T13.46 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y^-1 ] T13.47 : Triangle type {4,4,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y ] T13.48 : Triangle type {4,4,14} Group order 56 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y^-1 * x^-1 * z^7 ] T13.49 : Triangle type {4,4,26} Group order 52 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y * x^-1 * z^7 ] T13.50 : Triangle type {4,6,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T13.51 : Triangle type {4,6,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T13.52 : Triangle type {4,10,20} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^4 * z^-1 * y ] T13.53 : Triangle type {4,18,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y^5 * z^-1 * y ] T13.54 : Triangle type {5,5,5} Group order 60 Reflexible action Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * x, x * z^-1 * x^-1 * z * y ] T13.55 : Triangle type {6,6,6} Group order 48 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, y^2 * x^-1 * z^2 ] T13.56 : Triangle type {6,6,6} Group order 48 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, (y * z^-1)^2, x^6 ] T13.57 : Triangle type {6,12,12} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^3 * z^-2 ] T13.58 : Triangle type {6,12,12} Group order 36 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^6 ] T13.59 : Triangle type {6,12,12} Group order 36 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, (z^-1 * y)^3 ] T13.60 : Triangle type {8,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^8 ] T13.61 : Triangle type {8,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x ] T13.62 : Triangle type {8,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T13.63 : Triangle type {8,16,16} Group order 32 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-3 * z * y ] T13.64 : Triangle type {9,9,9} Group order 36 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-1 * x^3 * y^-2 ] T13.65 : Triangle type {10,15,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-3 * x^2 * y^-3 ] T13.66 : Triangle type {10,15,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^4 * z^-2 ] T13.67 : Triangle type {10,15,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-1 * z * x^-7 * y * x^-1 ] T13.68 : Triangle type {14,28,28} Group order 28 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^14, y * z^-1 ] T13.69 : Triangle type {14,28,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-5 * x^2 * y^-3 ] T13.70 : Triangle type {14,28,28} Group order 28 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-1 ] T13.71 : Triangle type {27,27,27} Group order 27 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-1 * x^3 * z^-2 ] T13.72 : Triangle type {27,27,27} Group order 27 Reflexible action Defining relators: [ x^-2 * y^-1, y^10 * x^-1 * y^3, x * z^-1 ] Genus 14 T14.1 : Triangle type {2,3,7} Group order 1092 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T14.2 : Triangle type {2,3,7} Group order 1092 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, z * y * x * z * y * x * z^2 * y * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T14.3 : Triangle type {2,3,7} Group order 1092 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T14.4 : Triangle type {2,4,30} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-24 * x * y * z^-5 ] T14.5 : Triangle type {2,4,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-22 * x * y^-1 * z^-5 ] T14.6 : Triangle type {2,6,6} Group order 156 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z^-1 * x * y^-1 * z * y^2 * x * y^-1 * z^-1 * x ] T14.7 : Triangle type {2,6,16} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^5 * y * x * z * y * x * y^-1 * z^-3 * x * z^4 ] T14.8 : Triangle type {2,6,42} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^5 * y * z^-1 * x * z * y^-1 * z^-2 * x * z^3 ] T14.9 : Triangle type {2,8,20} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-1 * x * z * y * x * z * y * z^-5 ] T14.10 : Triangle type {2,10,35} Group order 70 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * y^-1 * z^-3 ] T14.11 : Triangle type {2,29,58} Group order 58 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-10 ] T14.12 : Triangle type {2,30,30} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-11 ] T14.13 : Triangle type {2,56,56} Group order 56 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-10 ] T14.14 : Triangle type {3,4,5} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * x^-1 * z^2 ] T14.15 : Triangle type {3,6,6} Group order 78 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y^2 * z^-1 * y * z^-1 ] T14.16 : Triangle type {3,6,6} Group order 78 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T14.17 : Triangle type {3,16,16} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^6 * y^-9 ] T14.18 : Triangle type {3,42,42} Group order 42 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-6 * z * y^-7 ] T14.19 : Triangle type {4,4,15} Group order 60 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^-1 * z ] T14.20 : Triangle type {4,4,15} Group order 60 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 ] T14.21 : Triangle type {4,4,28} Group order 56 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y^-1 * x * z^7 ] T14.22 : Triangle type {4,6,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^6 ] T14.23 : Triangle type {4,8,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3 ] T14.24 : Triangle type {4,20,20} Group order 40 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^3 * z^-1 * y^5 * z^-1 ] T14.25 : Triangle type {5,8,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^8 ] T14.26 : Triangle type {5,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-2 * z^3 ] T14.27 : Triangle type {5,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-5 ] T14.28 : Triangle type {6,6,8} Group order 48 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^4 * y * x * z^3 ] T14.29 : Triangle type {6,6,21} Group order 42 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^3 * y^-1 * x * z^3 ] T14.30 : Triangle type {6,18,18} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^4 * z^-2 ] T14.31 : Triangle type {8,8,10} Group order 40 Chiral action Defining relators: [ x * y * z, y * x^-2 * y * z^-1, z * x^-2 * y^-1 * x ] T14.32 : Triangle type {8,8,10} Group order 40 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, y * x^-1 * y * x^-1 * z^3 ] T14.33 : Triangle type {8,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z * x^-3 * z^3 ] T14.34 : Triangle type {8,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^8 ] T14.35 : Triangle type {15,30,30} Group order 30 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^15, y * z^-1 ] T14.36 : Triangle type {15,30,30} Group order 30 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^3 * x^-3 * z^3 ] T14.37 : Triangle type {29,29,29} Group order 29 Reflexible action Defining relators: [ x^-2 * y^-1, y^11 * x^-1 * y^3, x * z^-1 ] T14.38 : Triangle type {29,29,29} Group order 29 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-6 * x * y^-3 ] T14.39 : Triangle type {29,29,29} Group order 29 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^3 * y^-3 ] T14.40 : Triangle type {29,29,29} Group order 29 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-3 * x * y^-2 ] T14.41 : Triangle type {29,29,29} Group order 29 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-5 * y^2 ] Genus 15 T15.1 : Triangle type {2,3,9} Group order 504 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^-2 * x * z * y * x * z * y * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T15.2 : Triangle type {2,3,12} Group order 336 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * z * y * x * y * z^-2 * x * y^-1 * z^-1, y * z^-1 * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T15.3 : Triangle type {2,3,14} Group order 294 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^9 * y * x * z^-1 * x * z^4 ] T15.4 : Triangle type {2,3,20} Group order 240 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * z * y^2 * x * z^2 * y^-1 * z^-1, z^2 * y * x * z * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 * x ] T15.5 : Triangle type {2,4,6} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (z * y^-1 * z)^3 ] T15.6 : Triangle type {2,4,18} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-5 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T15.7 : Triangle type {2,4,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-5 * x * z^5 * y^-1 * z^-5 ] T15.8 : Triangle type {2,4,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-18 * x * z^7 * y^-1 * z^-6 ] T15.9 : Triangle type {2,4,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-24 * x * y^-1 * z^-5 ] T15.10 : Triangle type {2,6,10} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-1 * x * y^-2 * z^-3 ] T15.11 : Triangle type {2,7,14} Group order 98 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-7 ] T15.12 : Triangle type {2,8,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^2 * y^-1 * z^-3 ] T15.13 : Triangle type {2,8,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x ] T15.14 : Triangle type {2,8,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^6 * y * x * y^-1 * x * y^-1 * z^-3 * x ] T15.15 : Triangle type {2,8,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z^2 * y * z^-2 * x * z * y^-1 * z^-3 ] T15.16 : Triangle type {2,8,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-5 * x * z^2 * y^-1 * z^-2 ] T15.17 : Triangle type {2,8,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^5 * y^-1 * x * z^2 * y^-1 * z^-1 * x ] T15.18 : Triangle type {2,14,35} Group order 70 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-2 * z^3 ] T15.19 : Triangle type {2,18,18} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-14 * z * y^-1 ] T15.20 : Triangle type {2,22,33} Group order 66 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-2 * z^2 * y^-6 * z ] T15.21 : Triangle type {2,31,62} Group order 62 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^19 * y^-10 * z ] T15.22 : Triangle type {2,32,32} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-11 ] T15.23 : Triangle type {2,32,32} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-1 * y^8 * z^-2 * y^3 * z^-1 ] T15.24 : Triangle type {2,60,60} Group order 60 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-10 * z ] T15.25 : Triangle type {3,3,6} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z * y * z^-1 * x^-1 * y * x * z ] T15.26 : Triangle type {3,3,6} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z * x^-1 * y^-1 * x * z * y * x * z ] T15.27 : Triangle type {3,3,7} Group order 147 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y^-1 * x^-1 * z^3 ] T15.28 : Triangle type {3,3,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-2 * x * z^2, z * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x ] T15.29 : Triangle type {3,3,31} Group order 93 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x^-1 * z^3 ] T15.30 : Triangle type {3,4,4} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z * x^-1 * y^-1 * x * y^-1 * x ] T15.31 : Triangle type {3,4,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3 ] T15.32 : Triangle type {3,4,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T15.33 : Triangle type {3,4,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T15.34 : Triangle type {3,4,12} Group order 84 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 ] T15.35 : Triangle type {3,16,48} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-8 * z * y^-5 * z^2 ] T15.36 : Triangle type {3,45,45} Group order 45 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-7 * z * y^-6 * z ] T15.37 : Triangle type {4,4,9} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-5 * x * y * z^-3 ] T15.38 : Triangle type {4,4,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^4 ] T15.39 : Triangle type {4,4,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^4 ] T15.40 : Triangle type {4,4,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-16 ] T15.41 : Triangle type {4,4,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T15.42 : Triangle type {4,4,30} Group order 60 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-8 * x * y^-1 * z^-6 ] T15.43 : Triangle type {4,8,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T15.44 : Triangle type {4,8,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3 ] T15.45 : Triangle type {4,11,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-4 * y^5 ] T15.46 : Triangle type {4,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, (y * z^-1 * y)^2 ] T15.47 : Triangle type {4,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, z^-1 * y^3 * z^-2 ] T15.48 : Triangle type {4,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2 ] T15.49 : Triangle type {4,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^2 * z^-3 ] T15.50 : Triangle type {4,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^5 * z^-1 * y^4 * z^-1 * y ] T15.51 : Triangle type {4,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^4 * z^-2 ] T15.52 : Triangle type {4,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^6 ] T15.53 : Triangle type {5,5,11} Group order 55 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1 ] T15.54 : Triangle type {5,5,11} Group order 55 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^-5, y^-1 * z^-1 * x^2 * y^-2 ] T15.55 : Triangle type {6,7,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-2 * x * y^-3 ] T15.56 : Triangle type {6,8,8} Group order 48 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, y * z^-1 * x^-1 * y^-1 * z ] T15.57 : Triangle type {6,8,8} Group order 48 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z * y * x^-1 * y^-2 ] T15.58 : Triangle type {6,8,8} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^8 ] T15.59 : Triangle type {6,8,8} Group order 48 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1, x^6 ] T15.60 : Triangle type {6,36,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-3 * y * z^-2 ] T15.61 : Triangle type {7,7,7} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-7 ] T15.62 : Triangle type {7,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-7 ] T15.63 : Triangle type {7,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-7 ] T15.64 : Triangle type {7,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, z^-3 * x * z^-2 ] T15.65 : Triangle type {8,8,20} Group order 40 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * x * z^2 ] T15.66 : Triangle type {8,8,20} Group order 40 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x * z^2 ] T15.67 : Triangle type {9,12,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-9 ] T15.68 : Triangle type {9,12,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y * x^-3 * y^3 ] T15.69 : Triangle type {11,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^5 * z^-1 ] T15.70 : Triangle type {11,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, x^-1 * z^3 * x^-2 * z^3 ] T15.71 : Triangle type {11,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x * z^-1 * x^7 * y^-1 * x^2 ] T15.72 : Triangle type {11,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^3 * x^-1 * z^3 ] T15.73 : Triangle type {11,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-1 * y^3 * z^-2 ] T15.74 : Triangle type {16,32,32} Group order 32 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^16, y * z^-1 ] T15.75 : Triangle type {16,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x * y^-2 * x^6 ] T15.76 : Triangle type {16,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^3 * x^-1 * y^3 ] T15.77 : Triangle type {16,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-8 * x * z^-2 ] T15.78 : Triangle type {16,32,32} Group order 32 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-3 * y * z^-2 ] T15.79 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x^-2 * y^-1, y^12 * x^-1 * y^3, x * z^-1 ] T15.80 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^4 * x^-1 * y^3 * x^-1 * y^2 ] T15.81 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-4 * x * y^-3 ] T15.82 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-4 * y^3 ] T15.83 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y^5 * z^-1 ] T15.84 : Triangle type {31,31,31} Group order 31 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-2 * x^3 * y^-3 ] Genus 16 T16.1 : Triangle type {2,3,8} Group order 720 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z^2 * y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-2 * x * z^3 ] T16.2 : Triangle type {2,4,5} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^6, y^-1 * z^2 * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z ] T16.3 : Triangle type {2,4,10} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^10 ] T16.4 : Triangle type {2,4,34} Group order 136 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-27 * x * y * z^-6 ] T16.5 : Triangle type {2,4,64} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-25 * x * y^-1 * z^-6 ] T16.6 : Triangle type {2,5,5} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T16.7 : Triangle type {2,6,8} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^8 ] T16.8 : Triangle type {2,6,18} Group order 108 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T16.9 : Triangle type {2,6,18} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^6 * y * x * z^3 * y * x * y * x * y^-1 * z^-3 * x * z^2 ] T16.10 : Triangle type {2,6,18} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^11 * y * x * y^-1 * z^-5 ] T16.11 : Triangle type {2,6,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^10 * y * x * y^-1 * z^-4 ] T16.12 : Triangle type {2,10,10} Group order 100 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^10, (y * z^-1 * y^3)^2 ] T16.13 : Triangle type {2,10,10} Group order 100 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T16.14 : Triangle type {2,10,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^10 ] T16.15 : Triangle type {2,18,36} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-2 * y^8 * z^-2 * y^6 ] T16.16 : Triangle type {2,33,66} Group order 66 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^21 * y^-10 * z ] T16.17 : Triangle type {2,34,34} Group order 68 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-11 ] T16.18 : Triangle type {2,64,64} Group order 64 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-10 * z ] T16.19 : Triangle type {3,3,4} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x, x^-1 * z * y * z^-1 * x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T16.20 : Triangle type {3,4,6} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, (y * z^-2)^2 ] T16.21 : Triangle type {3,4,6} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^6 ] T16.22 : Triangle type {3,6,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T16.23 : Triangle type {3,6,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6 ] T16.24 : Triangle type {3,6,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^6 ] T16.25 : Triangle type {3,8,8} Group order 72 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T16.26 : Triangle type {3,8,8} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T16.27 : Triangle type {3,10,15} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2 ] T16.28 : Triangle type {3,17,51} Group order 51 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-9 * z * y^-5 * z^2 ] T16.29 : Triangle type {3,18,18} Group order 54 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-1 * y ] T16.30 : Triangle type {3,18,18} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-10 * z * y^-5 * z^2 ] T16.31 : Triangle type {3,18,18} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2 ] T16.32 : Triangle type {3,18,18} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^8 * y^-9 ] T16.33 : Triangle type {3,48,48} Group order 48 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-8 * z * y^-6 * z ] T16.34 : Triangle type {4,4,5} Group order 100 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1 ] T16.35 : Triangle type {4,4,5} Group order 100 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * x^-1 * z^2 ] T16.36 : Triangle type {4,4,17} Group order 68 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-2 * y * x * z^-2 ] T16.37 : Triangle type {4,4,17} Group order 68 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y * x * z^7 ] T16.38 : Triangle type {4,4,32} Group order 64 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-9 * x * y^-1 * z^-6 ] T16.39 : Triangle type {4,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z * y^2 * x * z^-1 * x ] T16.40 : Triangle type {4,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^6 ] T16.41 : Triangle type {4,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6, (y * z^-1 * y)^2 ] T16.42 : Triangle type {4,6,12} Group order 60 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^-1 * y * z^-1 ] T16.43 : Triangle type {4,12,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * z^-1 * y ] T16.44 : Triangle type {4,22,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-4 * y^3 * z^-2 ] T16.45 : Triangle type {5,9,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-3 * y^3 * z^-2 ] T16.46 : Triangle type {5,10,10} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^4 * z^-1 ] T16.47 : Triangle type {5,10,10} Group order 50 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, z^-1 * y * x^-1 * y^-2 ] T16.48 : Triangle type {5,10,10} Group order 50 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, (y^-3 * z * y^-1)^2 ] T16.49 : Triangle type {5,10,10} Group order 50 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-5, x^-1 * y^-1 * x^2 * z * x^-1 ] T16.50 : Triangle type {5,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^6 * z^-1 * y ] T16.51 : Triangle type {5,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^4 * z^-3 ] T16.52 : Triangle type {6,6,9} Group order 54 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^-1 * y * x^-1 * y^-1 * z^-1 ] T16.53 : Triangle type {6,6,9} Group order 54 Chiral action Defining relators: [ x * y * z, z * y * x * z, x^6, (x * y^-1 * x)^2 ] T16.54 : Triangle type {6,6,9} Group order 54 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^9 ] T16.55 : Triangle type {6,6,9} Group order 54 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 ] T16.56 : Triangle type {6,6,24} Group order 48 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^3 * y^-1 * z^-1 * x^-1 * z^3 ] T16.57 : Triangle type {6,8,12} Group order 48 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * y^-1 * z^-1, x^6 ] T16.58 : Triangle type {6,14,21} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-3 * z^2 ] T16.59 : Triangle type {8,10,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^8 ] T16.60 : Triangle type {9,36,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-9 ] T16.61 : Triangle type {9,36,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T16.62 : Triangle type {10,10,20} Group order 40 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T16.63 : Triangle type {10,10,20} Group order 40 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2 ] T16.64 : Triangle type {12,18,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-12 ] T16.65 : Triangle type {12,18,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * x^2 * z^-3 ] T16.66 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-1 * y^2 * x^-6 ] T16.67 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-5 * z^2 ] T16.68 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x^2 * z^-3 ] T16.69 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^3 * x^-1 * z^3 ] T16.70 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^4 * x^-1 * y^4 ] T16.71 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^5 * z^-1 ] T16.72 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-8 * x^2 * z^-2 ] T16.73 : Triangle type {17,34,34} Group order 34 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^17, y * z^-1 ] T16.74 : Triangle type {18,18,18} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, (x^-1 * y^4)^2 ] T16.75 : Triangle type {33,33,33} Group order 33 Reflexible action Defining relators: [ x^-2 * y^-1, y^12 * x^-1 * y^4, x * z^-1 ] T16.76 : Triangle type {33,33,33} Group order 33 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y, y^-1 * z * y^-2 * x^-1 * z^3 ] Genus 17 T17.1 : Triangle type {2,3,7} Group order 1344 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z ] T17.2 : Triangle type {2,3,8} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T17.3 : Triangle type {2,3,14} Group order 336 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-4 * x * z * y * x * y * z^-3 * x * z ] T17.4 : Triangle type {2,4,6} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, x * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y ] T17.5 : Triangle type {2,4,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T17.6 : Triangle type {2,4,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2)^4 ] T17.7 : Triangle type {2,4,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, (y^-1 * z^2)^4 ] T17.8 : Triangle type {2,4,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T17.9 : Triangle type {2,4,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x ] T17.10 : Triangle type {2,4,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T17.11 : Triangle type {2,4,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T17.12 : Triangle type {2,4,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^5 * y^-1 * z^-2 ] T17.13 : Triangle type {2,4,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * y^-1 * z^-2 * x ] T17.14 : Triangle type {2,4,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-12 ] T17.15 : Triangle type {2,4,20} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-14 * x * y * z^-5 ] T17.16 : Triangle type {2,4,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-29 * x * y * z^-6 ] T17.17 : Triangle type {2,4,68} Group order 136 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-27 * x * y^-1 * z^-6 ] T17.18 : Triangle type {2,5,6} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, y^-1 * z * y^-1 * z * y^2 * z^-1 * x * z^2 ] T17.19 : Triangle type {2,5,10} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, y * x * z * y^2 * z^-3 ] T17.20 : Triangle type {2,5,10} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T17.21 : Triangle type {2,6,6} Group order 192 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * x * z * y^2 * x * z * y^-1 * z ] T17.22 : Triangle type {2,6,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z * y * x * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z ] T17.23 : Triangle type {2,6,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T17.24 : Triangle type {2,6,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y^-1 * z * y^-3 * z^-1 * x * z^2, z^-1 * y * x * y^-2 * z * y^-1 * z^-2 ] T17.25 : Triangle type {2,6,6} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T17.26 : Triangle type {2,6,15} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * z^-1 * y^2 * z^-1 * x * z ] T17.27 : Triangle type {2,6,51} Group order 102 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-1 * x * z^9 * y * x * y^-1 * z^-5 ] T17.28 : Triangle type {2,7,14} Group order 112 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^2 * y^-2 * z * y^-1 * z ] T17.29 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^8 ] T17.30 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^8 ] T17.31 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T17.32 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, (y * z^-1)^4 ] T17.33 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z ] T17.34 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^8, y^-1 * z * y^-3 * z^-2 * x * y^-1 ] T17.35 : Triangle type {2,8,8} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T17.36 : Triangle type {2,8,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-2 * x * z^3 * y * x * y^-1 * z^-5 ] T17.37 : Triangle type {2,8,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z^2 * y * z^-7 ] T17.38 : Triangle type {2,12,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-12 ] T17.39 : Triangle type {2,12,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2 ] T17.40 : Triangle type {2,12,12} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-12 ] T17.41 : Triangle type {2,20,20} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, (y * z^-1 * y^8)^2 ] T17.42 : Triangle type {2,35,70} Group order 70 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^23 * y^-10 * z ] T17.43 : Triangle type {2,36,36} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-11 ] T17.44 : Triangle type {2,68,68} Group order 68 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-10 * z ] T17.45 : Triangle type {3,3,4} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z ] T17.46 : Triangle type {3,3,7} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^3, x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T17.47 : Triangle type {3,3,7} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z^2 * y^-1 * x * z^3 ] T17.48 : Triangle type {3,4,4} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T17.49 : Triangle type {3,4,4} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.50 : Triangle type {3,4,4} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.51 : Triangle type {3,4,4} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.52 : Triangle type {3,4,4} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.53 : Triangle type {3,4,12} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y^-1 ] T17.54 : Triangle type {3,5,5} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * z * y^-2 ] T17.55 : Triangle type {3,6,6} Group order 96 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^2 * z^-1 * x^-1 * y^-2 * z^-1 ] T17.56 : Triangle type {3,6,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T17.57 : Triangle type {3,6,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (y^-1 * z)^4 ] T17.58 : Triangle type {3,6,6} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, (x * z * y)^2 ] T17.59 : Triangle type {3,15,15} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-2 * x * y^-1 * z ] T17.60 : Triangle type {3,51,51} Group order 51 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-9 * z * y^-7 ] T17.61 : Triangle type {4,4,4} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T17.62 : Triangle type {4,4,4} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T17.63 : Triangle type {4,4,4} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z^-1 * x^-1 ] T17.64 : Triangle type {4,4,4} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T17.65 : Triangle type {4,4,4} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1 ] T17.66 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T17.67 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^6 ] T17.68 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^-1 * y^-1 * x ] T17.69 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^6 ] T17.70 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z ] T17.71 : Triangle type {4,4,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^6 ] T17.72 : Triangle type {4,4,10} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, y^-1 * z^-2 * x^-1 * z^3 ] T17.73 : Triangle type {4,4,10} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 ] T17.74 : Triangle type {4,4,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y^-1 * x^-1 * z^8 ] T17.75 : Triangle type {4,4,34} Group order 68 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y * x^-1 * z^7 ] T17.76 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1 ] T17.77 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x ] T17.78 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T17.79 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^8 ] T17.80 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T17.81 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * y * z^-1 ] T17.82 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T17.83 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y ] T17.84 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y ] T17.85 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^8 ] T17.86 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^8 ] T17.87 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T17.88 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * z * y ] T17.89 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1 ] T17.90 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T17.91 : Triangle type {4,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z ] T17.92 : Triangle type {4,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y^5 * z^-1)^2 ] T17.93 : Triangle type {4,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^4 * z^-1 ] T17.94 : Triangle type {5,5,5} Group order 80 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (x * y^-2)^2, y^-5 ] T17.95 : Triangle type {6,8,24} Group order 48 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * y * z^-1, x^6 ] T17.96 : Triangle type {6,8,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 ] T17.97 : Triangle type {6,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, y^2 * x^-1 * z^2 ] T17.98 : Triangle type {6,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^6 ] T17.99 : Triangle type {6,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^6 ] T17.100 : Triangle type {6,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-4 * z ] T17.101 : Triangle type {7,7,7} Group order 56 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, y * x^-2 * y * z^-1, z^-2 * x^-1 * y^2 ] T17.102 : Triangle type {7,7,7} Group order 56 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y * x, z * y * x^-1 * z * y^-1 ] T17.103 : Triangle type {8,8,12} Group order 48 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T17.104 : Triangle type {8,8,12} Group order 48 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T17.105 : Triangle type {8,20,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^8 ] T17.106 : Triangle type {8,20,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-2 * y^3 ] T17.107 : Triangle type {10,20,20} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-1 * x^4 * z^-3 ] T17.108 : Triangle type {10,20,20} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-1 * y * x^-6 * z * x^-2 ] T17.109 : Triangle type {18,36,36} Group order 36 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-18, y * z^-1 ] T17.110 : Triangle type {18,36,36} Group order 36 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-5 * z^2 ] T17.111 : Triangle type {35,35,35} Group order 35 Reflexible action Defining relators: [ x^-2 * y^-1, y^-14 * x * y^-3, x * z^-1 ] T17.112 : Triangle type {35,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^2 * x^-5 * y * x^-1 ] T17.113 : Triangle type {35,35,35} Group order 35 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-11 * z ] Genus 18 T18.1 : Triangle type {2,4,21} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-8 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T18.2 : Triangle type {2,4,38} Group order 152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y * z^-6 ] T18.3 : Triangle type {2,4,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-29 * x * y^-1 * z^-6 ] T18.4 : Triangle type {2,6,20} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^7 * y^-1 * x * z^12 ] T18.5 : Triangle type {2,8,8} Group order 136 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z^-3 ] T18.6 : Triangle type {2,8,14} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-4 * x * z^3 * y * x * y * x * y^-1 * z^-4 ] T18.7 : Triangle type {2,10,45} Group order 90 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y^-1 * z^-3 ] T18.8 : Triangle type {2,12,16} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z^3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T18.9 : Triangle type {2,14,42} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-4 * z * y^-7 * z * y^-1 ] T18.10 : Triangle type {2,20,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^6 * z^-4 ] T18.11 : Triangle type {2,21,21} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-10 * y^8 * z^-1 ] T18.12 : Triangle type {2,26,39} Group order 78 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-3 * z^2 * y^-6 * z * y^-1 ] T18.13 : Triangle type {2,37,74} Group order 74 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^25 * y^-10 * z ] T18.14 : Triangle type {2,38,38} Group order 76 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^38 ] T18.15 : Triangle type {2,72,72} Group order 72 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-10 * z ] T18.16 : Triangle type {3,3,37} Group order 111 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-3 * x^-1 * z^3 ] T18.17 : Triangle type {3,19,57} Group order 57 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-11 * z * y^-5 * z^2 ] T18.18 : Triangle type {3,20,20} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^10 * y^-9 ] T18.19 : Triangle type {3,54,54} Group order 54 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-10 * z * y^-7 ] T18.20 : Triangle type {4,4,19} Group order 76 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^10 * y^-1 * x * y^-1 * z^-3 * x * z^4 ] T18.21 : Triangle type {4,4,36} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y^-1 * x * z^8 ] T18.22 : Triangle type {4,13,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z^4 * y^-2 * z^3 ] T18.23 : Triangle type {4,14,14} Group order 56 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-3 * y * z^-1 * y^2 * z^-1 * y * z^-3 * y ] T18.24 : Triangle type {4,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^3 * z^-2 ] T18.25 : Triangle type {5,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-3 * y^5 ] T18.26 : Triangle type {5,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-4 * y^2 * z^-3 ] T18.27 : Triangle type {6,6,10} Group order 60 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-4 * x^-1 * y * x^-1 * y * x^-1 * y * z^-3 ] T18.28 : Triangle type {6,12,24} Group order 48 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2 ] T18.29 : Triangle type {6,16,16} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T18.30 : Triangle type {7,8,8} Group order 56 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^8 ] T18.31 : Triangle type {7,42,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-7 ] T18.32 : Triangle type {7,42,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-7 ] T18.33 : Triangle type {7,42,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-7 ] T18.34 : Triangle type {8,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T18.35 : Triangle type {10,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-10 ] T18.36 : Triangle type {10,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z * x^-3 * z^3 ] T18.37 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^9 ] T18.38 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^3 * x^-1 * z^3 ] T18.39 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, x * z^-3 * x^2 * z^-3 ] T18.40 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-13 ] T18.41 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^5 * y^-3 ] T18.42 : Triangle type {13,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-4 * z^3 ] T18.43 : Triangle type {14,14,21} Group order 42 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x^-1 * y * x^-1 * y * z^-1 ] T18.44 : Triangle type {14,14,21} Group order 42 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^4 * y^-2 ] T18.45 : Triangle type {14,14,21} Group order 42 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-3 * x^2 * z^-3 ] T18.46 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^2 * z^-1 * y^7 ] T18.47 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-1 ] T18.48 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-3 * x^2 * z^-3 ] T18.49 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * y * x^-6 * y * x^-2 ] T18.50 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^3 * x^-1 * z^3 ] T18.51 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^6 * z^-1 * y ] T18.52 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-5 * z^2 ] T18.53 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y * x^-3 * y^3 ] T18.54 : Triangle type {19,38,38} Group order 38 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-19, y * z^-1 ] T18.55 : Triangle type {20,20,20} Group order 40 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * y^-2 ] T18.56 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x^-2 * y^-1, y^-15 * x * y^-3, x * z^-1 ] T18.57 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-4 * x^2 * y^-7 ] T18.58 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^4 * x^-2 * y^3 ] T18.59 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^3 * y^-3 ] T18.60 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-5 * y^2 ] T18.61 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x^2 * y * z^-3 ] T18.62 : Triangle type {37,37,37} Group order 37 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y * x^-3 * y^3 ] Genus 19 T19.1 : Triangle type {2,3,12} Group order 432 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y * x * z * y * x * z * y * x * z * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T19.2 : Triangle type {2,3,24} Group order 288 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^8 * y * x * y * z^-5 ] T19.3 : Triangle type {2,4,5} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T19.4 : Triangle type {2,4,7} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T19.5 : Triangle type {2,4,8} Group order 288 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^3 * y * x * y^-1 * z^-3 * x ] T19.6 : Triangle type {2,4,8} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, (y^-1 * z)^6 ] T19.7 : Triangle type {2,4,8} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T19.8 : Triangle type {2,4,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T19.9 : Triangle type {2,4,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T19.10 : Triangle type {2,4,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T19.11 : Triangle type {2,4,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y * z^-6 ] T19.12 : Triangle type {2,4,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-14 * x * z * y^-1 * z^-4 ] T19.13 : Triangle type {2,4,76} Group order 152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y^-1 * z^-6 ] T19.14 : Triangle type {2,5,5} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (y * z^-1)^4 ] T19.15 : Triangle type {2,6,9} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * y * z^-4 ] T19.16 : Triangle type {2,6,9} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, (y^-2 * z)^3 ] T19.17 : Triangle type {2,6,9} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 ] T19.18 : Triangle type {2,6,9} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, (y^-2 * z)^3 ] T19.19 : Triangle type {2,6,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T19.20 : Triangle type {2,6,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1)^4 ] T19.21 : Triangle type {2,6,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, x * z^2 * y^-1 * z * y * x * z * y^-1 * z^-2 ] T19.22 : Triangle type {2,6,21} Group order 126 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^5 * y * z^-1 * x * y^-1 * z^-13 ] T19.23 : Triangle type {2,6,57} Group order 114 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-1 * x * z^4 * y^-1 * z^-13 ] T19.24 : Triangle type {2,7,7} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T19.25 : Triangle type {2,8,8} Group order 144 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^8, z^-2 * y^3 * z^-1 * y * z^-1 ] T19.26 : Triangle type {2,8,8} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T19.27 : Triangle type {2,8,8} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T19.28 : Triangle type {2,10,10} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, (y * z^-2 * y)^2, y * x * z * y^2 * x * y^-1 * z^-1 ] T19.29 : Triangle type {2,12,12} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-3 * z^-3 ] T19.30 : Triangle type {2,12,12} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T19.31 : Triangle type {2,12,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-2 * z^2 * y^-5 * z^2 * y^-1 ] T19.32 : Triangle type {2,12,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^12 ] T19.33 : Triangle type {2,15,30} Group order 90 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^3 * y^-1 * z * y^-9 ] T19.34 : Triangle type {2,39,78} Group order 78 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^39 ] T19.35 : Triangle type {2,40,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-1 * y^10 * z^-1 * y^8 ] T19.36 : Triangle type {2,40,40} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^40 ] T19.37 : Triangle type {2,76,76} Group order 76 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^37 * z^-1 ] T19.38 : Triangle type {3,3,6} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T19.39 : Triangle type {3,3,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T19.40 : Triangle type {3,3,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x^-1 * y * x^-1 * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 ] T19.41 : Triangle type {3,3,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 ] T19.42 : Triangle type {3,3,39} Group order 117 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-2 * x^-1 * z^3 ] T19.43 : Triangle type {3,4,6} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, x^-1 * y^-1 * z^-2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T19.44 : Triangle type {3,4,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y * z^-1 * x^-1 * z^2 ] T19.45 : Triangle type {3,4,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T19.46 : Triangle type {3,4,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T19.47 : Triangle type {3,4,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T19.48 : Triangle type {3,5,6} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, y * z^-1 * y * x^-1 * z * y ] T19.49 : Triangle type {3,6,26} Group order 78 Chiral action Defining relators: [ x^3, x * y * z, y^-1 * z^-1 * x^-1 * z^2 ] T19.50 : Triangle type {3,8,24} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T19.51 : Triangle type {3,9,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, (z * y^-2)^3 ] T19.52 : Triangle type {3,9,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * y^3 * z^-2 ] T19.53 : Triangle type {3,9,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * z^-1 * y * x * y^-1 * z^-1 ] T19.54 : Triangle type {3,9,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * x ] T19.55 : Triangle type {3,9,9} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^3 * z^-2, y * z^-1 * y * x * y^-1 * z^-1 ] T19.56 : Triangle type {3,12,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, (x^-1 * z * y)^2 ] T19.57 : Triangle type {3,12,12} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T19.58 : Triangle type {3,20,60} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-12 * z * y^-5 * z^2 ] T19.59 : Triangle type {3,21,21} Group order 63 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-13 * z * y^-5 * z^2 ] T19.60 : Triangle type {3,57,57} Group order 57 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-11 * z * y^-6 * z ] T19.61 : Triangle type {4,4,4} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y^-1 ] T19.62 : Triangle type {4,4,4} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z * y^-1 * x * z * x^-1 ] T19.63 : Triangle type {4,4,4} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T19.64 : Triangle type {4,4,4} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T19.65 : Triangle type {4,4,5} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2 ] T19.66 : Triangle type {4,4,6} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (y^-1 * x)^3 ] T19.67 : Triangle type {4,4,6} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (y^-1 * x)^3 ] T19.68 : Triangle type {4,4,20} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * y^-1 * z ] T19.69 : Triangle type {4,4,20} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^-1 * z^2, y * x^-1 * y^-1 * x * z^-2 ] T19.70 : Triangle type {4,4,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y * z^-1 * x^-1 * y^-1 * z^-3 ] T19.71 : Triangle type {4,4,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-2 ] T19.72 : Triangle type {4,4,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-10 * x * y^-1 * x * y^-1 * z^-8 ] T19.73 : Triangle type {4,4,38} Group order 76 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^10 * y^-1 * x * z^8 ] T19.74 : Triangle type {4,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z * y * z^-1 * x^-1 * z^3 ] T19.75 : Triangle type {4,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-3 * x^-1 * y * z^-2 ] T19.76 : Triangle type {4,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y * z^-1 * y * z^-2 ] T19.77 : Triangle type {4,8,8} Group order 72 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^2 * x^2 * y^-1 * z^-1 ] T19.78 : Triangle type {4,8,8} Group order 72 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * z * y^-1, z * y * x^2 * z^2 ] T19.79 : Triangle type {4,8,8} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3 ] T19.80 : Triangle type {4,8,8} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T19.81 : Triangle type {4,8,16} Group order 64 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-1 * z^2 ] T19.82 : Triangle type {4,8,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T19.83 : Triangle type {4,8,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * x^-1 * z^4 ] T19.84 : Triangle type {4,12,15} Group order 60 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x * z^-1 ] T19.85 : Triangle type {4,12,15} Group order 60 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x * z^2 ] T19.86 : Triangle type {4,14,28} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^2 * z^-4 * y * z^-1 * y^2 ] T19.87 : Triangle type {4,26,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z^4 * y^-4 * z ] T19.88 : Triangle type {6,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z * y * x^-2 * z * y * x ] T19.89 : Triangle type {6,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * z * x^-1 ] T19.90 : Triangle type {6,6,6} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, x^6, y^6 ] T19.91 : Triangle type {6,9,18} Group order 54 Chiral action Defining relators: [ x * y * z, y^-2 * x * z, x^6, x^-1 * y^-1 * x^2 * y^-1 * z ] T19.92 : Triangle type {6,9,18} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^3 * y^-2 * z^3 ] T19.93 : Triangle type {6,9,18} Group order 54 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z ] T19.94 : Triangle type {6,9,18} Group order 54 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^6 ] T19.95 : Triangle type {6,16,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-3 ] T19.96 : Triangle type {6,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^4 * z^-3 ] T19.97 : Triangle type {6,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^6 ] T19.98 : Triangle type {8,12,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^8 ] T19.99 : Triangle type {8,12,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-2 * y^2 * z^-2 ] T19.100 : Triangle type {9,15,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^9 ] T19.101 : Triangle type {9,15,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x^3 * y^-3 ] T19.102 : Triangle type {12,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T19.103 : Triangle type {12,12,12} Group order 48 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^3 * x^-1 * y * z^-1 * y ] T19.104 : Triangle type {14,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-3 * x^2 * y^-3 ] T19.105 : Triangle type {14,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^5 * z^-3 ] T19.106 : Triangle type {14,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^5 * x^-1 * y^4 ] T19.107 : Triangle type {14,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-2 * y * x^-2 * z * x^-9 ] T19.108 : Triangle type {14,21,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * y * z^-3 ] T19.109 : Triangle type {15,15,15} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^2 * x^-3 * y^4 ] T19.110 : Triangle type {20,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^3 ] T19.111 : Triangle type {20,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-10 * x^2 * z^-2 ] T19.112 : Triangle type {20,40,40} Group order 40 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-20, y * z^-1 ] T19.113 : Triangle type {20,40,40} Group order 40 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-1 * y * x^-6 * y * x^-2 ] T19.114 : Triangle type {39,39,39} Group order 39 Reflexible action Defining relators: [ x^-2 * y^-1, y^-15 * x * y^-4, x * z^-1 ] T19.115 : Triangle type {39,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^7 * y^-1 ] T19.116 : Triangle type {39,39,39} Group order 39 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^2 * x^-2 * y^3 ] Genus 20 T20.1 : Triangle type {2,4,42} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y * z^-6 ] T20.2 : Triangle type {2,4,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y^-1 * z^-6 ] T20.3 : Triangle type {2,6,6} Group order 228 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y * x * z * y * x * y * x * z * y^-1 * z^-2 * x ] T20.4 : Triangle type {2,6,22} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-8 * x * y * z^-13 ] T20.5 : Triangle type {2,6,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y * x * y^-1 * z^-12 * x ] T20.6 : Triangle type {2,8,9} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-4 * x * y * z^-4 ] T20.7 : Triangle type {2,8,28} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-4 * x * z^3 * y * x * y^-1 * z^-5 ] T20.8 : Triangle type {2,10,12} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-6 * x * y * z^-5 ] T20.9 : Triangle type {2,12,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * y^-1 * z^-4 ] T20.10 : Triangle type {2,18,45} Group order 90 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-4 * z^4 ] T20.11 : Triangle type {2,22,44} Group order 88 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-5 * y^9 * z^-2 * y^5 * z^-1 ] T20.12 : Triangle type {2,41,82} Group order 82 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^41 ] T20.13 : Triangle type {2,42,42} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^42 ] T20.14 : Triangle type {2,80,80} Group order 80 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^39 * z^-1 ] T20.15 : Triangle type {3,4,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2 ] T20.16 : Triangle type {3,6,6} Group order 114 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y ] T20.17 : Triangle type {3,6,6} Group order 114 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x * z * y * x * z * y^-1 * z ] T20.18 : Triangle type {3,22,22} Group order 66 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^12 * y^-9 ] T20.19 : Triangle type {3,60,60} Group order 60 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-12 * z * y^-7 ] T20.20 : Triangle type {4,4,21} Group order 84 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-14 * x * y * z^-6 ] T20.21 : Triangle type {4,4,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-10 * x * y^-1 * z^-9 ] T20.22 : Triangle type {4,9,9} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z * y^-1 * z^2 * y^-2 * z^2 * y^-1 ] T20.23 : Triangle type {4,12,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^2 ] T20.24 : Triangle type {4,15,20} Group order 60 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1 ] T20.25 : Triangle type {4,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y * z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-3 * y ] T20.26 : Triangle type {5,11,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-4 * z ] T20.27 : Triangle type {5,12,12} Group order 60 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-1 ] T20.28 : Triangle type {5,12,12} Group order 60 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T20.29 : Triangle type {5,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^2 * z^-3 ] T20.30 : Triangle type {5,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^3 * z^-2 ] T20.31 : Triangle type {6,6,11} Group order 66 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^6 * y^-1 * x * y * x^-1 * z^3 ] T20.32 : Triangle type {6,6,30} Group order 60 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y * x^-1 * z^5 ] T20.33 : Triangle type {6,10,10} Group order 60 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, (z^-2 * y * z^-1 * y)^2 ] T20.34 : Triangle type {6,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^7 * z^-1 ] T20.35 : Triangle type {8,8,14} Group order 56 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y^-1 * z^-3 * x * y^-1 * x * z^2 ] T20.36 : Triangle type {9,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-3 * x^3 * z^-2 ] T20.37 : Triangle type {9,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-2 * z^3 ] T20.38 : Triangle type {11,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-1 * x^4 * z^-3 ] T20.39 : Triangle type {11,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^7 * z^-1 ] T20.40 : Triangle type {11,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^8 ] T20.41 : Triangle type {11,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-1 * x * y^-1 * x^7 ] T20.42 : Triangle type {11,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 ] T20.43 : Triangle type {12,12,24} Group order 48 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y * x^-1 * z^2 ] T20.44 : Triangle type {12,16,16} Group order 48 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z ] T20.45 : Triangle type {21,42,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^6 * x^-1 * y^4 ] T20.46 : Triangle type {21,42,42} Group order 42 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-3 * x^2 * z^-3 ] T20.47 : Triangle type {21,42,42} Group order 42 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-21, y * z^-1 ] T20.48 : Triangle type {22,22,22} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^6 * x^-2 * y^4 ] T20.49 : Triangle type {22,22,22} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-3 * x^2 * y^-3 ] T20.50 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x^-2 * y^-1, y^-16 * x * y^-4, x * z^-1 ] T20.51 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-8 * x * y^-5 ] T20.52 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-5 * x^3 * y^-3 ] T20.53 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-4 * y^4 ] T20.54 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^3 * x^-1 * y^3 ] T20.55 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-4 * z^3 ] T20.56 : Triangle type {41,41,41} Group order 41 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x * z^-2 * x^6 ] Genus 21 T21.1 : Triangle type {2,3,16} Group order 384 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-10 * x * y * z^-5 ] T21.2 : Triangle type {2,3,16} Group order 384 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-2 * x * z * y^-1 * z^-3, z^-1 * x * z * y * z^-5 * x * y^-1 * z^-5 ] T21.3 : Triangle type {2,4,6} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.4 : Triangle type {2,4,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, (z^-1 * y)^5 ] T21.5 : Triangle type {2,4,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T21.6 : Triangle type {2,4,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T21.7 : Triangle type {2,4,12} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-12 ] T21.8 : Triangle type {2,4,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-4 ] T21.9 : Triangle type {2,4,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.10 : Triangle type {2,4,20} Group order 200 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^2 * y * z^-1 * x * z * y^-1 * z^-3 * x * z ] T21.11 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, x * z * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T21.12 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-11 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T21.13 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z^-3 ] T21.14 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.15 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * y * z^-5 ] T21.16 : Triangle type {2,4,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^5 * y * x * y^-1 * z^-5 * x ] T21.17 : Triangle type {2,4,44} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y * z^-6 ] T21.18 : Triangle type {2,4,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y^-1 * z^-6 ] T21.19 : Triangle type {2,6,6} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-2 * y)^2 ] T21.20 : Triangle type {2,6,8} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8 ] T21.21 : Triangle type {2,6,8} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.22 : Triangle type {2,6,8} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-3 * z^-2 * y^2 ] T21.23 : Triangle type {2,6,8} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^8 ] T21.24 : Triangle type {2,6,8} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z * y * x * y^-1 * z^-2 * y * z^-1 ] T21.25 : Triangle type {2,8,8} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T21.26 : Triangle type {2,8,8} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.27 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-10 * x * y * z^-5 ] T21.28 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^11 * y^-1 * z^-3 ] T21.29 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T21.30 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T21.31 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^3 * y * x * y^-1 * z^-3 * x ] T21.32 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z * y^-1 * z^-4 ] T21.33 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, y^2 * z^-1 * y^2 * z^-3 ] T21.34 : Triangle type {2,8,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^8 ] T21.35 : Triangle type {2,8,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^8 * y^-1 * z^-4 ] T21.36 : Triangle type {2,8,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^7 * y * z^-5 ] T21.37 : Triangle type {2,12,12} Group order 120 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * y^7 * z^-1 * y^2 ] T21.38 : Triangle type {2,14,14} Group order 112 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-2 * y, y^-3 * z * y^-8 * z^2 ] T21.39 : Triangle type {2,16,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * y^2 * z^-3 ] T21.40 : Triangle type {2,16,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-6 * z^2 * y^-5 * z^2 * y^-1 ] T21.41 : Triangle type {2,20,20} Group order 100 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^6 * z^-1 * y * z^-2 ] T21.42 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^3 * z^-2 ] T21.43 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-3 * z^-1 * y^2 ] T21.44 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-9 * z^3 ] T21.45 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-13 * y^8 * z^-1 ] T21.46 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^9 * z^-2 * y^5 * z^-1 * y ] T21.47 : Triangle type {2,24,24} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-9 * z * y^-1 * z ] T21.48 : Triangle type {2,43,86} Group order 86 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^43 ] T21.49 : Triangle type {2,44,44} Group order 88 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^44 ] T21.50 : Triangle type {2,84,84} Group order 84 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^41 * z^-1 ] T21.51 : Triangle type {3,3,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^8 ] T21.52 : Triangle type {3,3,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^8, z^3 * y * x^-1 * z^2 * y^-1 * x ] T21.53 : Triangle type {3,3,43} Group order 129 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * x * z^3 ] T21.54 : Triangle type {3,4,4} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x * z * y)^2 ] T21.55 : Triangle type {3,6,6} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^6 ] T21.56 : Triangle type {3,8,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-1 * x * z * y, y^8 ] T21.57 : Triangle type {3,8,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^8 ] T21.58 : Triangle type {3,8,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T21.59 : Triangle type {3,8,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * z^3 ] T21.60 : Triangle type {3,8,8} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^8 ] T21.61 : Triangle type {3,22,66} Group order 66 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-14 * z * y^-5 * z^2 ] T21.62 : Triangle type {3,63,63} Group order 63 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-13 * z * y^-7 ] T21.63 : Triangle type {4,4,4} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * z^-1 * y * x * y^-1 * z * y^-1 ] T21.64 : Triangle type {4,4,4} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T21.65 : Triangle type {4,4,6} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y ] T21.66 : Triangle type {4,4,10} Group order 100 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-2 ] T21.67 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-5 * x * z^2 * y * z^-3 * x * y^-1 ] T21.68 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * z^3 ] T21.69 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z * y * z^-1 ] T21.70 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (y^-1 * x)^3 ] T21.71 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x * z ] T21.72 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^2 * y * x^-1 * z^3 ] T21.73 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T21.74 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-4 * x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.75 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T21.76 : Triangle type {4,4,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-5 * x * z^2 * y^-1 * z^-4 ] T21.77 : Triangle type {4,4,22} Group order 88 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 ] T21.78 : Triangle type {4,4,42} Group order 84 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-14 * x * y^-1 * z^-6 ] T21.79 : Triangle type {4,6,6} Group order 96 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * z * y^-1, y * x * y^-1 * x * z * y, y^6 ] T21.80 : Triangle type {4,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, (y^-1 * x)^3 ] T21.81 : Triangle type {4,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T21.82 : Triangle type {4,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, z^-1 * y^2 * x^-1 * y^3 ] T21.83 : Triangle type {4,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T21.84 : Triangle type {4,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T21.85 : Triangle type {4,8,8} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z * y * x^-1 * z * y^-1 * z ] T21.86 : Triangle type {4,8,8} Group order 80 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T21.87 : Triangle type {4,15,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^3 * z^-1 * y^7 * z^-2 * y ] T21.88 : Triangle type {4,16,16} Group order 64 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * z^2 ] T21.89 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2 ] T21.90 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-2 * y * z^-1 * y^4 * z^-1 * y * z^-4 * y ] T21.91 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * z^-1 ] T21.92 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1 ] T21.93 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1 ] T21.94 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (y * z^-1 * y^2)^2 ] T21.95 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T21.96 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y^2 ] T21.97 : Triangle type {4,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3 ] T21.98 : Triangle type {4,20,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2 ] T21.99 : Triangle type {4,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^6 * z^-4 * y * z^-1 * y^2 ] T21.100 : Triangle type {4,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^5 * z^-4 * y * z^-1 * y * z^-1 ] T21.101 : Triangle type {6,12,12} Group order 60 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^6 ] T21.102 : Triangle type {7,8,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^8 ] T21.103 : Triangle type {7,9,9} Group order 63 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^-1 * z * y^-4 * z * y^-1 * z ] T21.104 : Triangle type {7,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-6 * z ] T21.105 : Triangle type {7,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-4 * x^-1 * z^3 ] T21.106 : Triangle type {7,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-3 * x^-1 * z^3 ] T21.107 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x ] T21.108 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2 ] T21.109 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1 ] T21.110 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, z^-2 * y * z^-1 * y^2 * z^-1 * y ] T21.111 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^8, x^8 ] T21.112 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1, x^8 ] T21.113 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^8 ] T21.114 : Triangle type {8,8,8} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8, x^8 ] T21.115 : Triangle type {8,8,28} Group order 56 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y^-1 * x * z^3 ] T21.116 : Triangle type {8,8,28} Group order 56 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-1 * x * z^3 ] T21.117 : Triangle type {8,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^8 ] T21.118 : Triangle type {8,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^8 ] T21.119 : Triangle type {8,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^3 * x^-1 * z^3 ] T21.120 : Triangle type {12,16,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^12 ] T21.121 : Triangle type {12,16,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-3 * y^2 * z^-3 ] T21.122 : Triangle type {12,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * z * x^-3 ] T21.123 : Triangle type {12,24,24} Group order 48 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-5 * z * y ] T21.124 : Triangle type {15,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-5 * y * x^-7 * z * x^-2 ] T21.125 : Triangle type {15,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-4 * z^3 ] T21.126 : Triangle type {15,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^4 * x^-3 * y^5 ] T21.127 : Triangle type {16,16,24} Group order 48 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-1 * y ] T21.128 : Triangle type {16,16,24} Group order 48 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * x^-2 * z^2 ] T21.129 : Triangle type {16,16,24} Group order 48 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * y * x * z^-3 ] T21.130 : Triangle type {22,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-1 * x^4 * z^-3 ] T21.131 : Triangle type {22,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^10 * x^-1 * y^4 ] T21.132 : Triangle type {22,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * x^2 * z^-3 ] T21.133 : Triangle type {22,44,44} Group order 44 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-5 * y, z^3 * x^-1 * z^3 ] T21.134 : Triangle type {22,44,44} Group order 44 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-22, y * z^-1 ] T21.135 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x^-2 * y^-1, y^-17 * x * y^-4, x * z^-1 ] T21.136 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^9 * x^-2 * y^4 ] T21.137 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^10 ] T21.138 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-7 * y ] T21.139 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^5 * y^-3 ] T21.140 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-6, z^3 * x^-1 * z^3 ] T21.141 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * x * z^-3 ] T21.142 : Triangle type {43,43,43} Group order 43 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-2, y^-1 * z * y^-3 * z^2 ] Genus 22 T22.1 : Triangle type {2,3,8} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 ] T22.2 : Triangle type {2,3,8} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T22.3 : Triangle type {2,3,12} Group order 504 Chiral action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-2 ] T22.4 : Triangle type {2,4,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2 * y * z^-1)^2, z^-1 * x * z * y * x * y^-1 * z^-3 * y * z^-1 ] T22.5 : Triangle type {2,4,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T22.6 : Triangle type {2,4,46} Group order 184 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y * z^-6 ] T22.7 : Triangle type {2,4,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y^-1 * z^-6 ] T22.8 : Triangle type {2,5,8} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T22.9 : Triangle type {2,6,6} Group order 252 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T22.10 : Triangle type {2,6,6} Group order 252 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T22.11 : Triangle type {2,6,12} Group order 168 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y^-2 * z^-1 * y * z^-2 ] T22.12 : Triangle type {2,6,12} Group order 168 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^-3 * z^-1 * x * z * y^-1 ] T22.13 : Triangle type {2,6,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-10 * x * y * z^-13 ] T22.14 : Triangle type {2,6,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4 ] T22.15 : Triangle type {2,6,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * z^4 * y * z^-1 * x * z * y^-1 * z^-14 ] T22.16 : Triangle type {2,6,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T22.17 : Triangle type {2,6,66} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y * x * z * y^-1 * z^-13 * x ] T22.18 : Triangle type {2,8,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^-1 * x * y^-3 * z^-4 ] T22.19 : Triangle type {2,9,18} Group order 126 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-9 ] T22.20 : Triangle type {2,10,55} Group order 110 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-4 * x * z^2 * y^-1 * z^-4 ] T22.21 : Triangle type {2,18,18} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^7 * y^-8 * z * y^-2 ] T22.22 : Triangle type {2,45,90} Group order 90 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^45 ] T22.23 : Triangle type {2,46,46} Group order 92 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^46 ] T22.24 : Triangle type {2,88,88} Group order 88 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^43 * z^-1 ] T22.25 : Triangle type {3,3,4} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x ] T22.26 : Triangle type {3,3,4} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, (z^-1 * x^-1 * y^-1)^3 ] T22.27 : Triangle type {3,3,6} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^-1 * x * z * y * x^-1 * y * x * z * y^-1 ] T22.28 : Triangle type {3,6,6} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1 ] T22.29 : Triangle type {3,6,6} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T22.30 : Triangle type {3,6,6} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T22.31 : Triangle type {3,6,6} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^-2 * y^2 * z^-1 * y ] T22.32 : Triangle type {3,6,6} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y^2 * z^-2 * y * z^-1 ] T22.33 : Triangle type {3,12,12} Group order 84 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z ] T22.34 : Triangle type {3,12,12} Group order 84 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * y^-1 * z^2 ] T22.35 : Triangle type {3,23,69} Group order 69 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-15 * z * y^-5 * z^2 ] T22.36 : Triangle type {3,24,24} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T22.37 : Triangle type {3,24,24} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^14 * y^-9 ] T22.38 : Triangle type {3,24,24} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-16 * z * y^-5 * z^2 ] T22.39 : Triangle type {3,66,66} Group order 66 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-14 * z * y^-6 * z ] T22.40 : Triangle type {4,4,4} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-1 * y * x^-1 * z * x^-1 * z, z^-1 * x^-1 * y * x^-1 * y * z^-1 * y ] T22.41 : Triangle type {4,4,4} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (y^-1 * x)^3, (z^-1 * x)^3 ] T22.42 : Triangle type {4,4,23} Group order 92 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y * z^-7 ] T22.43 : Triangle type {4,4,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-6 ] T22.44 : Triangle type {4,5,5} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, (z^-1 * y)^3 ] T22.45 : Triangle type {4,6,12} Group order 84 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T22.46 : Triangle type {4,8,10} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z * y * z^-2 * x * z ] T22.47 : Triangle type {4,9,18} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 ] T22.48 : Triangle type {4,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^3 * x^-1 * y^-2 * z ] T22.49 : Triangle type {4,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z * y * z^-1 * x^-1 * z^3 ] T22.50 : Triangle type {4,30,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y * z^-4 * y^7 * z^-2 * y ] T22.51 : Triangle type {5,12,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^5 * z^-4 ] T22.52 : Triangle type {5,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-2 * z^3 ] T22.53 : Triangle type {5,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-1 * z^4 ] T22.54 : Triangle type {6,6,6} Group order 84 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * y^-1 * z ] T22.55 : Triangle type {6,6,6} Group order 84 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T22.56 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T22.57 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^12 ] T22.58 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T22.59 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^6 ] T22.60 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y * x * y^-1 * z^-5 * x^-1 * z ] T22.61 : Triangle type {6,6,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * y^-1 * x ] T22.62 : Triangle type {6,6,33} Group order 66 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z * y^-1 * z^-5 * x * z^4 ] T22.63 : Triangle type {6,8,8} Group order 72 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y^-2 * x^2 * y^-1 * z ] T22.64 : Triangle type {6,10,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^10 ] T22.65 : Triangle type {6,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^3 * y^-4 * z ] T22.66 : Triangle type {6,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^4 * y^-1 * z^4 ] T22.67 : Triangle type {9,9,9} Group order 63 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * x^-1, y^-1 * x^3 * y^-2 ] T22.68 : Triangle type {9,18,18} Group order 54 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, z^-1 * y^3 * z^-2 ] T22.69 : Triangle type {9,18,18} Group order 54 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, z^-1 * y * x^2 * z^-2 ] T22.70 : Triangle type {9,18,18} Group order 54 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * z ] T22.71 : Triangle type {9,18,18} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 ] T22.72 : Triangle type {10,25,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^5 * y^-3 * z * y^-1 ] T22.73 : Triangle type {10,25,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-2 * x^3 * z^-3 ] T22.74 : Triangle type {10,25,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x * y^-2 * x^5 * z^-1 ] T22.75 : Triangle type {10,25,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^10 ] T22.76 : Triangle type {12,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-7 * y^2 ] T22.77 : Triangle type {16,24,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 * z^-1 * x^6 * y^-1 * x ] T22.78 : Triangle type {16,24,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x * y^-3 * x^5 ] T22.79 : Triangle type {16,24,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y * z^-2 * y^6 ] T22.80 : Triangle type {16,24,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-2 * x * z^-3 * x * y * z^-3 ] T22.81 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-5 * x^3 * y^-5 ] T22.82 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-8 * x^2 * y^-6 ] T22.83 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-5 * y, z^-3 * x^2 * z^-3 ] T22.84 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-4 * y ] T22.85 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^3 * x^-1 * z^3 ] T22.86 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^6 * z^-2 ] T22.87 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-3 * x^4 * z^-1 ] T22.88 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^7 * z^-1 ] T22.89 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-7 * z^2 * x^-3 ] T22.90 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * z^-2 * y^6 ] T22.91 : Triangle type {23,46,46} Group order 46 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-23, y * z^-1 ] T22.92 : Triangle type {45,45,45} Group order 45 Reflexible action Defining relators: [ x^-2 * y^-1, y^-18 * x * y^-4, x * z^-1 ] T22.93 : Triangle type {45,45,45} Group order 45 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-4 * y * z^-3 ] Genus 23 T23.1 : Triangle type {2,4,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y * z^-6 ] T23.2 : Triangle type {2,4,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * z * y^-1 * z^-4 ] T23.3 : Triangle type {2,4,92} Group order 184 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y^-1 * z^-6 ] T23.4 : Triangle type {2,6,69} Group order 138 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^9 * y^-1 * z^-13 * x ] T23.5 : Triangle type {2,8,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-1 * x * z^9 * y * x * y^-1 * z^-4 ] T23.6 : Triangle type {2,8,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^9 * y^-1 * z^-5 ] T23.7 : Triangle type {2,12,20} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, x * z * y * x * z * y * x * y^-1 * z^-5 ] T23.8 : Triangle type {2,47,94} Group order 94 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^47 ] T23.9 : Triangle type {2,48,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^9 * z^-2 * y^6 * z^-1 ] T23.10 : Triangle type {2,48,48} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^48 ] T23.11 : Triangle type {2,92,92} Group order 92 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^45 * z^-1 ] T23.12 : Triangle type {3,5,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-5 ] T23.13 : Triangle type {3,69,69} Group order 69 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-15 * z * y^-7 ] T23.14 : Triangle type {4,4,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-18 * x^-1 * y^-1 * z^-5 ] T23.15 : Triangle type {4,4,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-3 * x * z^3 * y * z^-5 ] T23.16 : Triangle type {4,4,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-5 * x * z^2 * y * z^-4 ] T23.17 : Triangle type {4,4,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-3 * x * z^3 * y * z^-1 * x * z * y^-1 * z^-2 ] T23.18 : Triangle type {4,4,46} Group order 92 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-7 ] T23.19 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, (y * z^-1 * y)^2 ] T23.20 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, z^-1 * y^2 * x^-1 * y^3 ] T23.21 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-2 ] T23.22 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z * y^2 * x * z^2 ] T23.23 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z * y^2 * x^-1 * z^2 ] T23.24 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * z * x^-1 ] T23.25 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^8 ] T23.26 : Triangle type {4,6,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^6 ] T23.27 : Triangle type {4,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-2 * y * z^-1 * y^4 * z^-1 * y * z^-3 * y * z^-1 ] T23.28 : Triangle type {4,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-3 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T23.29 : Triangle type {6,20,20} Group order 60 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y^4 ] T23.30 : Triangle type {8,8,16} Group order 64 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y * z^-2 * x * z^5 ] T23.31 : Triangle type {8,8,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, y^-1 * x^6 * y^-1, z^2 * y * x^-1 * y * x^-1 * z^4 ] T23.32 : Triangle type {8,14,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-4 * x^-1 * z^3 ] T23.33 : Triangle type {10,12,12} Group order 60 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * y * x^2 * z^-1 * y * z^-1 ] T23.34 : Triangle type {24,48,48} Group order 48 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-24, y * z^-1 ] T23.35 : Triangle type {24,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * y * x^-3 ] T23.36 : Triangle type {24,48,48} Group order 48 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, z^-1 * y^4 * z^-3 ] T23.37 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x^-2 * y^-1, y^-19 * x * y^-4, x * z^-1 ] T23.38 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-9 * x * y^-6 ] T23.39 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-5 * x * y^-6 ] T23.40 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^3 * y^-5 ] T23.41 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-4 * x * y^-3 ] T23.42 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^3 * x^-1 * z^3 ] T23.43 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-2 * x * z^-3 * x * y * z^-3 ] T23.44 : Triangle type {47,47,47} Group order 47 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^5, y^-4 * z^3 ] Genus 24 T24.1 : Triangle type {2,4,27} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-14 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T24.2 : Triangle type {2,4,50} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-43 * x * y * z^-6 ] T24.3 : Triangle type {2,4,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y^-1 * z^-6 ] T24.4 : Triangle type {2,6,26} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-7 * x * z^5 * y * z^-5 * x * y^-1 * z^-7 ] T24.5 : Triangle type {2,8,18} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^5 * y * x * z * y^-1 * z^-1 * x ] T24.6 : Triangle type {2,8,18} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-18 ] T24.7 : Triangle type {2,10,14} Group order 140 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-14 ] T24.8 : Triangle type {2,10,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-5 * x * z * y * z^-5 ] T24.9 : Triangle type {2,12,30} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y^-1 * x * z * y^-1 * z^-2 * x ] T24.10 : Triangle type {2,14,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-3 * z^3 * y^-5 * z^3 ] T24.11 : Triangle type {2,15,20} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y * x * z * y^2 * z^-1 * y * z^-1, y * z^-2 * x * y^-1 * z^-3 ] T24.12 : Triangle type {2,26,52} Group order 104 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-4 * y^11 * z^-1 * y^9 * z^-1 ] T24.13 : Triangle type {2,27,27} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-23 * z * y^-1 ] T24.14 : Triangle type {2,34,51} Group order 102 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-5 * z^3 * y^-9 ] T24.15 : Triangle type {2,49,98} Group order 98 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^49 ] T24.16 : Triangle type {2,50,50} Group order 100 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^50 ] T24.17 : Triangle type {2,96,96} Group order 96 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^47 * z^-1 ] T24.18 : Triangle type {3,3,26} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z * y^-1 * z^-2 ] T24.19 : Triangle type {3,3,49} Group order 147 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^2 * y^-1 * z^-1 ] T24.20 : Triangle type {3,4,7} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, (y * z^-2)^2 ] T24.21 : Triangle type {3,4,7} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^3 * y^-1 * x^-1 * z^3 ] T24.22 : Triangle type {3,12,28} Group order 84 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y * z^-1 ] T24.23 : Triangle type {3,14,21} Group order 84 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-4 * z^3 ] T24.24 : Triangle type {3,25,75} Group order 75 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-17 * z * y^-5 * z^2 ] T24.25 : Triangle type {3,26,26} Group order 78 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^16 * y^-9 ] T24.26 : Triangle type {3,72,72} Group order 72 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-16 * z * y^-7 ] T24.27 : Triangle type {4,4,25} Group order 100 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-1 * y * z^-2 * x * z^-3 ] T24.28 : Triangle type {4,4,25} Group order 100 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-19 * x^-1 * y^-1 * z^-5 ] T24.29 : Triangle type {4,4,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-18 * x^-1 * y * z^-5 ] T24.30 : Triangle type {4,5,6} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^-5 ] T24.31 : Triangle type {4,5,6} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^-5, (x * z * y)^2 ] T24.32 : Triangle type {4,5,6} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^-5, (y * z^-2)^2 ] T24.33 : Triangle type {4,8,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z * y * z^-2 * x^-1 * z ] T24.34 : Triangle type {4,17,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^5 * z^-1 * y^7 * z^-2 * y ] T24.35 : Triangle type {4,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^8 * z^-1 * y * z^-1 * y^4 * z^-1 * y ] T24.36 : Triangle type {4,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z * y^-1 * z^2 * y^-4 * z ] T24.37 : Triangle type {4,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y * z^-3 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T24.38 : Triangle type {5,13,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^9 ] T24.39 : Triangle type {5,14,14} Group order 70 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^7 * z^-1 * y * z^-2 * y * z^-1 * y ] T24.40 : Triangle type {5,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^6 * z^-3 ] T24.41 : Triangle type {5,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^9 ] T24.42 : Triangle type {6,6,13} Group order 78 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, y^-1 * z * x^-1 * z^2, x^6 ] T24.43 : Triangle type {6,6,13} Group order 78 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, y^-1 * z^-1 * x^-1 * z^2, x^6 ] T24.44 : Triangle type {6,6,13} Group order 78 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^13 ] T24.45 : Triangle type {6,20,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^7 * z^-3 ] T24.46 : Triangle type {6,30,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-2 ] T24.47 : Triangle type {7,9,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-1 * z^3 ] T24.48 : Triangle type {7,10,10} Group order 70 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^3 * z^-1 * y * z^-2 * y * z^-1 * y ] T24.49 : Triangle type {7,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^6 * z^-2 ] T24.50 : Triangle type {7,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-2 * y^3 * z^-3 ] T24.51 : Triangle type {7,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^4 * z^-3 ] T24.52 : Triangle type {8,8,9} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 ] T24.53 : Triangle type {8,28,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^2 * y^-2 * x^-1 * z^3 ] T24.54 : Triangle type {8,28,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-5 * z^2 ] T24.55 : Triangle type {9,9,21} Group order 63 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^-1 * y * x^-1 * z^2 ] T24.56 : Triangle type {9,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-9 ] T24.57 : Triangle type {9,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T24.58 : Triangle type {9,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^4 * x^-3 * z^2 ] T24.59 : Triangle type {10,10,30} Group order 60 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z * y * z^-1 * x^-1 * z^3 ] T24.60 : Triangle type {10,10,30} Group order 60 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T24.61 : Triangle type {10,15,15} Group order 60 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, (z^-1 * x)^3 ] T24.62 : Triangle type {10,15,15} Group order 60 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, x^-1 * z * x^-1 * y^-1 * z, y * z^-1 * y * x^-1 * z * y ] T24.63 : Triangle type {12,12,15} Group order 60 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x * z^-1 * y * z^-1 ] T24.64 : Triangle type {12,12,15} Group order 60 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y * x * z^2 ] T24.65 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, z^-1 * x^4 * z^-3 ] T24.66 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x * y^-8 ] T24.67 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-2 * x^7 * z^-1 * x * z^-1 ] T24.68 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-6 * x^3 * y^-2 ] T24.69 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-4 * y * z^-3 ] T24.70 : Triangle type {13,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^4 * y^-2 * x^4 * y^-2 * x^3 ] T24.71 : Triangle type {14,14,28} Group order 56 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-3 * x^2 * y^-3 ] T24.72 : Triangle type {14,14,28} Group order 56 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, z^-2 * x^2 * z^-2 ] T24.73 : Triangle type {14,14,28} Group order 56 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3 ] T24.74 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-1 * z * y^-7 ] T24.75 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z^3 * y^-3 * z^2 ] T24.76 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-10 ] T24.77 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^5 * z^-3 ] T24.78 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^17 ] T24.79 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^3 * x^-5 ] T24.80 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y * z^-1 * y^3 * x^-3 * y^4 ] T24.81 : Triangle type {17,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y^3 * x^-5 ] T24.82 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-3 * z * y^-3 * x^2 * y^-5 ] T24.83 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^3 * x^-1 * z^3 ] T24.84 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-2 * x^6 ] T24.85 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-14 * x * z^-2 ] T24.86 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-1 * x^8 * y^-1 * x ] T24.87 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-25, y * z^-1 ] T24.88 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-2, y^-3 * x^2 * y^-3 ] T24.89 : Triangle type {25,50,50} Group order 50 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-5 * x * z^-3 ] T24.90 : Triangle type {26,26,26} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, (y^3 * z^-1 * y^3)^2 ] T24.91 : Triangle type {26,26,26} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^4 * y^-4 ] T24.92 : Triangle type {26,26,26} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-3 * x^2 * z^-3 ] T24.93 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x^-2 * y^-1, y^-20 * x * y^-4, x * z^-1 ] T24.94 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^3 * z^-2 * x^6 ] T24.95 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y * z^-3 * y^4 * z^-1 ] T24.96 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^2 * x^-4 * z^3 * x^-1 * z * x^-1 * z * x^-1 ] T24.97 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-9 * x^2 * y^-6 ] T24.98 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^2 * y^-3 * x^2 * y^-3 * x ] T24.99 : Triangle type {49,49,49} Group order 49 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^5 * z^-3 ] Genus 25 T25.1 : Triangle type {2,3,10} Group order 720 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-2 * x * z * y * z^-3 * x * z * y * z^-2 * x * z^4 ] T25.2 : Triangle type {2,3,12} Group order 576 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T25.3 : Triangle type {2,3,12} Group order 576 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-3 * x * z, z^-1 * x * z * y * x * z * y * x * z * y * x * z^3 * y^-1 * z^-3 ] T25.4 : Triangle type {2,3,24} Group order 384 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^3 * y * z^-3 * x * y * z^-1 * x * z^3, z * y * x * z^2 * y * z^-2 * x * z^-3 * x * z ] T25.5 : Triangle type {2,3,30} Group order 360 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^4 * y^-1 * z^-5, z^-1 * x * z * y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T25.6 : Triangle type {2,4,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-1 * y * z^-1 * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T25.7 : Triangle type {2,4,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^10 ] T25.8 : Triangle type {2,4,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^12 ] T25.9 : Triangle type {2,4,16} Group order 256 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T25.10 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^7 * y^-1 * z^-5 ] T25.11 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-1 * z^-4 ] T25.12 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T25.13 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T25.14 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * y * x * z * y^-2 * z^-5 ] T25.15 : Triangle type {2,4,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T25.16 : Triangle type {2,4,28} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * y * z^-5 ] T25.17 : Triangle type {2,4,52} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-45 * x * y * z^-6 ] T25.18 : Triangle type {2,4,100} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-43 * x * y^-1 * z^-6 ] T25.19 : Triangle type {2,6,6} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T25.20 : Triangle type {2,6,6} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-3 * z^-2 * y^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T25.21 : Triangle type {2,6,9} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, z^-1 * y^2 * x * y^-2 * z^-1 * y * x * y^-1 * z^-1 ] T25.22 : Triangle type {2,6,9} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-4 * x * y * z^-4 ] T25.23 : Triangle type {2,6,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, z * y^-1 * z * y^-2 * z^-1 * x * z^2 ] T25.24 : Triangle type {2,6,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, y * z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T25.25 : Triangle type {2,6,21} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-1 * z^-4 ] T25.26 : Triangle type {2,6,27} Group order 162 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z * y^-1 * z^-4 ] T25.27 : Triangle type {2,6,27} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^27 ] T25.28 : Triangle type {2,6,75} Group order 150 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^10 * y^-1 * z^-14 * x ] T25.29 : Triangle type {2,10,10} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^10 ] T25.30 : Triangle type {2,10,10} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-1 * x * z, y * x * z * y^2 * z^-3 ] T25.31 : Triangle type {2,12,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^5 * z^-3, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T25.32 : Triangle type {2,12,12} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-12 ] T25.33 : Triangle type {2,12,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y^12 ] T25.34 : Triangle type {2,15,30} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-15 ] T25.35 : Triangle type {2,16,16} Group order 128 Chiral action Defining relators: [ x^2, x * y * z, y * x * y^-2 * z^3 ] T25.36 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T25.37 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, (y^-5 * z^3)^2 ] T25.38 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y^3 * x * y^-1 * z^-3 * x ] T25.39 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-2 * x * z * y^-1 * z^-4 ] T25.40 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, z^-1 * y^4 * z^-3 ] T25.41 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T25.42 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z^5 * y^-7 * z * y^-2 ] T25.43 : Triangle type {2,16,16} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z^-1 * y^4 * z^-3 ] T25.44 : Triangle type {2,22,55} Group order 110 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-6 * z^4 ] T25.45 : Triangle type {2,28,28} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^11 * z^-1 * y^10 ] T25.46 : Triangle type {2,51,102} Group order 102 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^37 * y^-12 * z ] T25.47 : Triangle type {2,52,52} Group order 104 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^38 * y^-13 ] T25.48 : Triangle type {2,100,100} Group order 100 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^49 * z^-1 ] T25.49 : Triangle type {3,3,5} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z^2 * y * z^-1)^2 ] T25.50 : Triangle type {3,3,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, (x^-1 * y^-1 * z^-1)^4 ] T25.51 : Triangle type {3,3,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z ] T25.52 : Triangle type {3,3,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T25.53 : Triangle type {3,3,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x^-1 * z * y)^2 ] T25.54 : Triangle type {3,3,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-2 * x * z^2, (z^-1 * x^-1 * y^-1)^3 ] T25.55 : Triangle type {3,4,6} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, x * z * y^-1 * x * z * y ] T25.56 : Triangle type {3,4,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T25.57 : Triangle type {3,4,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x * z ] T25.58 : Triangle type {3,4,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * y * x * y^-1 * x * z * y * z^-1 ] T25.59 : Triangle type {3,4,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z ] T25.60 : Triangle type {3,4,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (z^-1 * y)^3 ] T25.61 : Triangle type {3,4,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T25.62 : Triangle type {3,4,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T25.63 : Triangle type {3,4,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T25.64 : Triangle type {3,4,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T25.65 : Triangle type {3,6,6} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (x * z * y)^2 ] T25.66 : Triangle type {3,6,6} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T25.67 : Triangle type {3,6,6} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T25.68 : Triangle type {3,6,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, (x^-1 * z * y)^2 ] T25.69 : Triangle type {3,8,24} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-8 ] T25.70 : Triangle type {3,8,24} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y^-1 * x * z^2 ] T25.71 : Triangle type {3,9,9} Group order 108 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y ] T25.72 : Triangle type {3,9,9} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-1 * z * y^-3 * z^2 * y^-2 ] T25.73 : Triangle type {3,10,30} Group order 90 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^5 * y^-2 * z * y^-1 ] T25.74 : Triangle type {3,12,12} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * z * y * z^-1 ] T25.75 : Triangle type {3,21,21} Group order 84 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-4 * z * y^-1 * z ] T25.76 : Triangle type {3,26,78} Group order 78 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-18 * z * y^-5 * z^2 ] T25.77 : Triangle type {3,27,27} Group order 81 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z * y^-2 * z * y^-3 * z * y^-1 ] T25.78 : Triangle type {3,27,27} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-19 * z * y^-5 * z^2 ] T25.79 : Triangle type {3,75,75} Group order 75 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-17 * z * y^-6 * z ] T25.80 : Triangle type {4,4,5} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^2 * y^-1 * x^-1 * z^2 ] T25.81 : Triangle type {4,4,5} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, (x * z^-2)^2 ] T25.82 : Triangle type {4,4,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^6 ] T25.83 : Triangle type {4,4,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6 ] T25.84 : Triangle type {4,4,8} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y ] T25.85 : Triangle type {4,4,8} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y^-1 * x * z^-1 * y ] T25.86 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^8 ] T25.87 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1 ] T25.88 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T25.89 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z * y)^2 ] T25.90 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z^3 * y^-1 ] T25.91 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * z^3 ] T25.92 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1 ] T25.93 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T25.94 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T25.95 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T25.96 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1 ] T25.97 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y, (x * z^-1 * y)^2 ] T25.98 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^4 * y^-1 * x^-1 * z^3 ] T25.99 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x^-1 * y^-1 * x * z * y * z^-2 ] T25.100 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, (x * z^-1)^4 ] T25.101 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, (x * z^-1)^4 ] T25.102 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-3)^2 ] T25.103 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, (x * z^-3)^2 ] T25.104 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T25.105 : Triangle type {4,4,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T25.106 : Triangle type {4,4,14} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^5 * y * x^-1 * z * y * z^-6 * x^-1 ] T25.107 : Triangle type {4,4,26} Group order 104 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * x^-1 * y^-1 * z^-2 ] T25.108 : Triangle type {4,4,26} Group order 104 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y * z^-10 ] T25.109 : Triangle type {4,4,50} Group order 100 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-19 * x^-1 * y * z^-5 ] T25.110 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^2 * y * x * z * y^-1 ] T25.111 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T25.112 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * z * y ] T25.113 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^2 * y * x^-1 * z * y^-1 ] T25.114 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * z^2 * y^-1 ] T25.115 : Triangle type {4,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6 ] T25.116 : Triangle type {4,8,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-1 * z^-5 * x * z^4 ] T25.117 : Triangle type {4,8,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T25.118 : Triangle type {4,10,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^2 * y^-1 * z * y^-4 * z ] T25.119 : Triangle type {4,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 ] T25.120 : Triangle type {4,34,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^6 * z^-1 * y^8 * z^-1 * y ] T25.121 : Triangle type {6,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T25.122 : Triangle type {6,6,6} Group order 96 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^-1 * y ] T25.123 : Triangle type {6,8,24} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^6 ] T25.124 : Triangle type {6,9,18} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T25.125 : Triangle type {6,9,18} Group order 72 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T25.126 : Triangle type {6,11,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^5 * z^-4 ] T25.127 : Triangle type {6,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z * y^-1 * z^-1 * x^-1 * z^3 ] T25.128 : Triangle type {6,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-4 ] T25.129 : Triangle type {6,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^5 * z^-1 * y * z^-2 * y * z^-1 * y ] T25.130 : Triangle type {6,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^6, y * x^-3 * z * x^-2 ] T25.131 : Triangle type {6,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z * y * z^-1 ] T25.132 : Triangle type {6,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^5 * z^-4 ] T25.133 : Triangle type {8,16,16} Group order 64 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^2 * x^-1 * y * z^-1 ] T25.134 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, (y * z^-1)^4 ] T25.135 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, (y * z^-1)^4 ] T25.136 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2 ] T25.137 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^8 ] T25.138 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-2 * x^2 * y^-2 ] T25.139 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^8 ] T25.140 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T25.141 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T25.142 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2 ] T25.143 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T25.144 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-1 * y^4 * z^-3 ] T25.145 : Triangle type {8,16,16} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^8 ] T25.146 : Triangle type {10,12,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y^3 * x^-4 * y^3 ] T25.147 : Triangle type {11,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-5 * y^5 ] T25.148 : Triangle type {11,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z^3 * x^-3 * z^2 ] T25.149 : Triangle type {11,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-2 * x^3 * z^-3 ] T25.150 : Triangle type {11,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^11 ] T25.151 : Triangle type {11,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-1 * z * x^-1 * z^4 * x^-5 ] T25.152 : Triangle type {12,12,30} Group order 60 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * x^-2 * z^3 ] T25.153 : Triangle type {12,15,20} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y * x^-4 * y^4 ] T25.154 : Triangle type {14,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^6 * z^-2 ] T25.155 : Triangle type {14,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^2 * x^-3 * y^3 * z^-1 * y^2 ] T25.156 : Triangle type {14,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-6 * z * x^-6 * y * x^-1 ] T25.157 : Triangle type {15,15,15} Group order 60 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^3 * x^-3 * y^3 ] T25.158 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^2 * y^-1 * z^4 * y^-1 * z^4 ] T25.159 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^3 * x^-5 ] T25.160 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-1 * y^9 * x^-1 * y ] T25.161 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-8 * y * x^-7 * z * x^-2 ] T25.162 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-3 * x^2 * y^-3 ] T25.163 : Triangle type {18,27,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z^3 * y^-2 * z^3 ] T25.164 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-1 * x^4 * z^-3 ] T25.165 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^10 * x^-2 * y^6 ] T25.166 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^6 * z^-2 ] T25.167 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^2 * x^-6 ] T25.168 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-6 * x * y^-4 ] T25.169 : Triangle type {26,52,52} Group order 52 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-26, y * z^-1 ] T25.170 : Triangle type {51,51,51} Group order 51 Reflexible action Defining relators: [ x^-2 * y^-1, y^-21 * x * y^-4, x * z^-1 ] T25.171 : Triangle type {51,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-5 * z^2 ] T25.172 : Triangle type {51,51,51} Group order 51 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z^4 * x^-5 ] Genus 26 T26.1 : Triangle type {2,3,10} Group order 750 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, y * x * z * y * x * z^2 * y * x * z * y^-1 * z * y^-1 * z^-2 * x * z ] T26.2 : Triangle type {2,3,11} Group order 660 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-5 * x * y * z^-5, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z, y * z^-2 * x * z^3 * y * x * y^-2 * z^-1 * x * z^3 ] T26.3 : Triangle type {2,4,54} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-47 * x * y * z^-6 ] T26.4 : Triangle type {2,4,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-45 * x * y^-1 * z^-6 ] T26.5 : Triangle type {2,5,10} Group order 250 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T26.6 : Triangle type {2,6,6} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-2 * z^-1 * y ] T26.7 : Triangle type {2,6,28} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^14 * y * x * z^5 * y^-1 * z^-5 * x * z^2 ] T26.8 : Triangle type {2,6,78} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^11 * y^-1 * x * y^-1 * z^-13 * x ] T26.9 : Triangle type {2,8,8} Group order 200 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y^-4 * z^-1 * y * x * y^-1 ] T26.10 : Triangle type {2,8,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^3 * y * x * z^8 * y^-1 * z^-5 * x ] T26.11 : Triangle type {2,10,15} Group order 150 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^6 * y * z^-3 * x * z^3 * y^-1 * z^-1 * x ] T26.12 : Triangle type {2,10,65} Group order 130 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-1 * x * z^6 * y^-1 * x * z * y^-1 * z^-3 ] T26.13 : Triangle type {2,20,30} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * y^4 * z^-4 ] T26.14 : Triangle type {2,28,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-3 * z^3 * y^-6 * z * y^-1 ] T26.15 : Triangle type {2,53,106} Group order 106 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^39 * y^-12 * z ] T26.16 : Triangle type {2,54,54} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^40 * y^-13 ] T26.17 : Triangle type {2,104,104} Group order 104 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^38 * y^-12 * z ] T26.18 : Triangle type {3,3,4} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 * x * z^-1, x * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * x * y^-1 * z^-1 ] T26.19 : Triangle type {3,3,4} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 * x * z^-1, z^2 * x^-1 * z * y * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x ] T26.20 : Triangle type {3,3,5} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x ] T26.21 : Triangle type {3,3,28} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, y * x * z * y * x * z^3 ] T26.22 : Triangle type {3,4,4} Group order 300 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T26.23 : Triangle type {3,4,4} Group order 300 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x * y^-1 * z^-1 * y * x * z * y^-1 * z^-1 ] T26.24 : Triangle type {3,6,6} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T26.25 : Triangle type {3,6,6} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y * z^-1 ] T26.26 : Triangle type {3,28,28} Group order 84 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^18 * y^-9 ] T26.27 : Triangle type {3,78,78} Group order 78 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-18 * z * y^-7 ] T26.28 : Triangle type {4,4,4} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z * x^-1, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T26.29 : Triangle type {4,4,4} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T26.30 : Triangle type {4,4,27} Group order 108 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y^-1 * z^-3 * x * y^-1 * x * z^5 ] T26.31 : Triangle type {4,4,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-10 ] T26.32 : Triangle type {4,5,20} Group order 100 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, x * y^-2 * x * z^-2, y^-5 ] T26.33 : Triangle type {4,5,20} Group order 100 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-5 ] T26.34 : Triangle type {4,6,16} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^2 * y * z^-1 * x^-1 * z^4 ] T26.35 : Triangle type {4,10,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-1 * z^2 * y^-1 * z * y^-4 * z ] T26.36 : Triangle type {4,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^9 * z^-1 * y * z^-1 * y^6 ] T26.37 : Triangle type {5,5,5} Group order 125 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-5, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1 ] T26.38 : Triangle type {5,14,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-9 * y * z^-1 * y^2 ] T26.39 : Triangle type {5,15,15} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-3 * z * y^-1 * z^9 * y^-1 ] T26.40 : Triangle type {5,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^5 * y^-4 ] T26.41 : Triangle type {5,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^5 * y^-1 * z^3 ] T26.42 : Triangle type {6,6,14} Group order 84 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^6, y * z^-1 * x^2 * z * y ] T26.43 : Triangle type {6,6,14} Group order 84 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, x^6, (x * y^-1 * x)^2, y^2 * x^2 * z^2 ] T26.44 : Triangle type {6,6,14} Group order 84 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-6 * x^-1 * y * x^-1 * y * x^-1 * y * z^-5 ] T26.45 : Triangle type {6,6,39} Group order 78 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-5 * x * y^-1 * z^-7 ] T26.46 : Triangle type {6,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^7 * z^-2 ] T26.47 : Triangle type {8,8,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y * z^-3 * x^-1 * y * x^-1 * z^4 ] T26.48 : Triangle type {9,9,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * y * x^-1 * z * x^-1 ] T26.49 : Triangle type {10,30,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-10 ] T26.50 : Triangle type {10,30,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-3 * x^2 * y^-3 ] T26.51 : Triangle type {12,15,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y * x^-1 * y^3 * x^-6 * y ] T26.52 : Triangle type {12,20,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y * x^-1 * y^3 * x^-6 * y ] T26.53 : Triangle type {14,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^3 * x^-1 * z * x^-9 ] T26.54 : Triangle type {14,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-1 * z * x^-1 * z^4 * x^-2 * z^3 ] T26.55 : Triangle type {14,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^3 * x^-4 * z ] T26.56 : Triangle type {15,20,20} Group order 60 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^4 * y^-1 * z^-1 ] T26.57 : Triangle type {15,20,20} Group order 60 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^4 * y^-1 * z^-1 ] T26.58 : Triangle type {27,54,54} Group order 54 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-27, y * z^-1 ] T26.59 : Triangle type {27,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y^2 * x^-6 ] T26.60 : Triangle type {27,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-4 * y^5 * x^-1 ] T26.61 : Triangle type {27,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^7 * z^-1 ] T26.62 : Triangle type {27,54,54} Group order 54 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-5 * x^3 * z^-7 ] T26.63 : Triangle type {28,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-3 * x^2 * y^-3 ] T26.64 : Triangle type {28,28,28} Group order 56 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-1 * x, z^-1 * y^3 * z^-1 * y ] T26.65 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x^-2 * y^-1, y^-22 * x * y^-4, x * z^-1 ] T26.66 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^11 * x^-1 * y^6 ] T26.67 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^11 * x^-2 ] T26.68 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-4 * y^4 * x^-2 ] T26.69 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-8 ] T26.70 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^3 * y^-3 ] T26.71 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-4 * x * z^-3 ] T26.72 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^6 * x^-1 * z^4 ] T26.73 : Triangle type {53,53,53} Group order 53 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z^3 * y^-3 * z^2 ] Genus 27 T27.1 : Triangle type {2,3,12} Group order 624 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^2 * y * z^-1 * x * z^2 * y^-1 * z^-3 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x ] T27.2 : Triangle type {2,4,8} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z ] T27.3 : Triangle type {2,4,8} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y * z^-2 ] T27.4 : Triangle type {2,4,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x ] T27.5 : Triangle type {2,4,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-16 * x * z^7 * y^-1 * x * y^-1 * z^-5 ] T27.6 : Triangle type {2,4,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-49 * x * y * z^-6 ] T27.7 : Triangle type {2,4,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z * y^-1 * z^-4 ] T27.8 : Triangle type {2,4,108} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-47 * x * y^-1 * z^-6 ] T27.9 : Triangle type {2,5,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z^2 * y^-1 * z^-3, y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 ] T27.10 : Triangle type {2,8,8} Group order 208 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-1 * z ] T27.11 : Triangle type {2,8,8} Group order 208 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * z ] T27.12 : Triangle type {2,8,20} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^7 * y * z^-5 * x * z^7 ] T27.13 : Triangle type {2,8,20} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^20 ] T27.14 : Triangle type {2,8,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^11 * y * z^-6 ] T27.15 : Triangle type {2,8,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^12 * y * x * z^5 ] T27.16 : Triangle type {2,9,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-9 ] T27.17 : Triangle type {2,12,12} Group order 156 Chiral action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * z * y^2 * x * y^-1 * z ] T27.18 : Triangle type {2,12,12} Group order 156 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y * x * z * y^-2 * z * y^-1 * z^2 ] T27.19 : Triangle type {2,14,63} Group order 126 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-4 * x * y^-1 * z^-4 ] T27.20 : Triangle type {2,20,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-8 * z^3 * y^-6 * z^3 ] T27.21 : Triangle type {2,30,30} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-26 * z * y^-1 ] T27.22 : Triangle type {2,38,57} Group order 114 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-7 * z^3 * y^-9 ] T27.23 : Triangle type {2,55,110} Group order 110 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^41 * y^-12 * z ] T27.24 : Triangle type {2,56,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^11 * z^-1 * y^8 * z^-2 ] T27.25 : Triangle type {2,56,56} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^42 * y^-13 ] T27.26 : Triangle type {2,108,108} Group order 108 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^40 * y^-12 * z ] T27.27 : Triangle type {3,3,6} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T27.28 : Triangle type {3,4,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, z^-1 * y * z^-1 * x^-1 * z * y^2 ] T27.29 : Triangle type {3,4,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T27.30 : Triangle type {3,4,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, y * z^-1 * y * x^-1 * z^3 ] T27.31 : Triangle type {3,28,84} Group order 84 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-5 * z^2 ] T27.32 : Triangle type {3,81,81} Group order 81 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-19 * z * y^-7 ] T27.33 : Triangle type {4,4,4} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^2 * y * z^-1 ] T27.34 : Triangle type {4,4,4} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-2 ] T27.35 : Triangle type {4,4,6} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y^-1 * z^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T27.36 : Triangle type {4,4,15} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-7 * x * z * y^-1 * z^-6 ] T27.37 : Triangle type {4,4,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^28 ] T27.38 : Triangle type {4,4,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-6 * x ] T27.39 : Triangle type {4,4,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-6 * x^-1 ] T27.40 : Triangle type {4,4,54} Group order 108 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y^-1 * z^-3 * x * y^-1 * x^-1 * z^5 ] T27.41 : Triangle type {4,6,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T27.42 : Triangle type {4,6,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y * x^-1 * z^4 ] T27.43 : Triangle type {4,8,8} Group order 104 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * x * y^-1 * z^-1 * x ] T27.44 : Triangle type {4,8,8} Group order 104 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T27.45 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T27.46 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2 ] T27.47 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * z ] T27.48 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (y^-1 * x)^3, y^-3 * x^-1 * z^2 ] T27.49 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T27.50 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y * x^-1 * y * x^-1 * z^3 ] T27.51 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y * x * y^-1 * z^-3 * x^-1 * y^-1 * x^-1 * z^5 ] T27.52 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z * y * z^-3 ] T27.53 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z * y * x * z^3 ] T27.54 : Triangle type {4,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^8 ] T27.55 : Triangle type {4,12,21} Group order 84 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x * z^3 ] T27.56 : Triangle type {4,19,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^4 * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-2 ] T27.57 : Triangle type {4,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 ] T27.58 : Triangle type {4,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-2 ] T27.59 : Triangle type {4,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-3 * z * y^-7 * z * y^-1 * z * y^-5 * z ] T27.60 : Triangle type {4,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^4 ] T27.61 : Triangle type {4,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 ] T27.62 : Triangle type {5,5,6} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, x^-5, z^6 ] T27.63 : Triangle type {6,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, (y * z^-1 * y)^2 ] T27.64 : Triangle type {6,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^6 * z^-3 ] T27.65 : Triangle type {7,10,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-2 * z^2 ] T27.66 : Triangle type {7,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-4 ] T27.67 : Triangle type {7,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^5 * x^-1 * z^4 ] T27.68 : Triangle type {7,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^8 ] T27.69 : Triangle type {8,8,10} Group order 80 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^8 ] T27.70 : Triangle type {8,8,10} Group order 80 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, y^-2 * x^2 * z^2 ] T27.71 : Triangle type {8,8,10} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y * z^-1 * x^-1 * z^3 * y * x^-1 * z^4 ] T27.72 : Triangle type {8,8,10} Group order 80 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^10 ] T27.73 : Triangle type {8,8,36} Group order 72 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y * x^-1 * z^4 ] T27.74 : Triangle type {8,8,36} Group order 72 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-3 * x * z^5 ] T27.75 : Triangle type {8,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^5 * z^-1 * y * z^-1 ] T27.76 : Triangle type {8,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8, z^-3 * y^2 * z^-3 ] T27.77 : Triangle type {9,9,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, y^-1 * x^3 * y^-2 ] T27.78 : Triangle type {9,9,18} Group order 72 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, x * z^-1 * y * x * z^-2 ] T27.79 : Triangle type {9,21,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-9 ] T27.80 : Triangle type {9,21,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-9 ] T27.81 : Triangle type {10,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-3 * y^4 ] T27.82 : Triangle type {10,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 ] T27.83 : Triangle type {12,30,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z * x^-5 * z^4 ] T27.84 : Triangle type {15,20,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^9 * y^-3 * x * y^-1 * x^2 ] T27.85 : Triangle type {15,20,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * x^-3 * y^4 ] T27.86 : Triangle type {15,20,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^4 * y^-2 * x^-3 * z^2 ] T27.87 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x * y^-2 * x * y^-9 * x * y^-1 ] T27.88 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * z * y^-7 ] T27.89 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^5 * x^-1 * z^4 ] T27.90 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z^3 * y^-3 * z^2 ] T27.91 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-1 * z^2 * y^-6 ] T27.92 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-11 * z * x^-6 * y * x^-1 ] T27.93 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^3 * x^-4 * y^6 ] T27.94 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z^3 * x^-5 ] T27.95 : Triangle type {19,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-3 * y^3 * x^-5 ] T27.96 : Triangle type {20,20,30} Group order 60 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^6 * y^-2 ] T27.97 : Triangle type {20,20,30} Group order 60 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, y^-1 * z * y^-1 * z^3 * x^-2 * z^4 ] T27.98 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-5 * y^4 * x^-1 ] T27.99 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^2 * y^-1 * z^4 * y^-1 * z^4 ] T27.100 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^3 * y^-3 * x * y^-1 ] T27.101 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * z * y^-7 ] T27.102 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-28, y * z^-1 ] T27.103 : Triangle type {28,56,56} Group order 56 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-6 * z * x^-6 * z * x^-1 ] T27.104 : Triangle type {55,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^14 * x^-2 * z^3 ] T27.105 : Triangle type {55,55,55} Group order 55 Reflexible action Defining relators: [ x^-2 * y^-1, y^-23 * x * y^-4, x * z^-1 ] T27.106 : Triangle type {55,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-2 * y * x^-1 * y * x^-7 * z * x^-2 ] T27.107 : Triangle type {55,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-1 * z^2 * x^-6 ] T27.108 : Triangle type {55,55,55} Group order 55 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-4 * x * y^-3 ] Genus 28 T28.1 : Triangle type {2,3,8} Group order 1296 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-2 * x * z * y * x * z * y * x * z^2 * y^-1 * z^-2 ] T28.2 : Triangle type {2,3,12} Group order 648 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, z^12 ] T28.3 : Triangle type {2,3,12} Group order 648 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z^2 * y * x * z^3 * y * x * y^-1 * x * z * y^-1 * z^-1 * x * z, z * y * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x ] T28.4 : Triangle type {2,3,18} Group order 486 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * x * z^4 * y * z^-3 * x * z * y^-1 * z^-1 ] T28.5 : Triangle type {2,3,18} Group order 486 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^5 * y * z^-5 * x * z, z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3 * x, z^2 * y * z^-1 * x * z^2 * y * z^-2 * y * x * y^-1 * z^-2 * x ] T28.6 : Triangle type {2,3,18} Group order 486 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^8 * y^-1 * z^-2 * x * z^6 * y^-1 * z^-2 ] T28.7 : Triangle type {2,3,24} Group order 432 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z^3 * y * z^-1 * y * z^-3 * x * z, z^4 * y * z^-1 * x * z * y * z^-1 * x * z^5 ] T28.8 : Triangle type {2,4,6} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^6, y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T28.9 : Triangle type {2,4,8} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z * y^-1 * z^2 * y^-2 * z^-2 * x * z^2 ] T28.10 : Triangle type {2,4,58} Group order 232 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-51 * x * y * z^-6 ] T28.11 : Triangle type {2,4,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-49 * x * y^-1 * z^-6 ] T28.12 : Triangle type {2,6,6} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T28.13 : Triangle type {2,6,6} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T28.14 : Triangle type {2,6,6} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, z * y * z^-1 * x * y^-1 * z^-2 * x ] T28.15 : Triangle type {2,6,6} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-1 * z * y^2 * z^-1 * y^3 * z^-1 * y * x * y^-2 * z^-1 * y ] T28.16 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T28.17 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, x * z^4 * y * z^-7 ] T28.18 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-3)^2 ] T28.19 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, (y * z^-3)^2 ] T28.20 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T28.21 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-1 * x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-1 ] T28.22 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * z^2 * y^-1 * z^-5 ] T28.23 : Triangle type {2,6,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 ] T28.24 : Triangle type {2,6,30} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^3 * y * z^-1 * x * z^5 ] T28.25 : Triangle type {2,6,30} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-6 * x * z * y * x * z^13 * y * x * y^-1 * z^-7 ] T28.26 : Triangle type {2,6,30} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-10 * x * z^5 * y * z^-1 * x * y^-1 * z^-12 ] T28.27 : Triangle type {2,6,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^20 * y * x * y * z^-6 * x ] T28.28 : Triangle type {2,8,8} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, z^-1 * x * y^-3 * z^2 * y^-1 * z^-1 ] T28.29 : Triangle type {2,9,18} Group order 162 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^2 * x * y^-1 * z^-1, y^-9, x * y^-4 * z^-3 * y ] T28.30 : Triangle type {2,9,18} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-9 ] T28.31 : Triangle type {2,9,18} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T28.32 : Triangle type {2,9,18} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^3 * y^2 * x * z^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T28.33 : Triangle type {2,10,16} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-4 * x * z^5 * y^-1 * z^-6 ] T28.34 : Triangle type {2,10,70} Group order 140 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^7 * y^-1 * x * z^3 * y^-1 * z^-2 ] T28.35 : Triangle type {2,12,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^5 * z^-3, z^-1 * x * z * y * z^-4 * x * z * y^-1 * z^-3 ] T28.36 : Triangle type {2,12,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T28.37 : Triangle type {2,12,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^-5 * z^-1 * x * z^2 ] T28.38 : Triangle type {2,18,63} Group order 126 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-2 * z^4 ] T28.39 : Triangle type {2,21,42} Group order 126 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^3 * y^-1 * z^5 * y^-8 * z^2 * y^-1 ] T28.40 : Triangle type {2,30,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-7 * y^11 * z^-1 * y^8 * z^-2 ] T28.41 : Triangle type {2,57,114} Group order 114 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^43 * y^-12 * z ] T28.42 : Triangle type {2,58,58} Group order 116 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^44 * y^-13 ] T28.43 : Triangle type {2,112,112} Group order 112 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^42 * y^-12 * z ] T28.44 : Triangle type {3,3,4} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 ] T28.45 : Triangle type {3,3,6} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z * y^-1 * z^-1 * x^-1 * z * y * x ] T28.46 : Triangle type {3,3,6} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T28.47 : Triangle type {3,3,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y^3, x * z^2 * y * x * z * y * z^-1 ] T28.48 : Triangle type {3,3,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T28.49 : Triangle type {3,3,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, (z^-1 * x^-1 * y^-1)^3 ] T28.50 : Triangle type {3,3,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-9 ] T28.51 : Triangle type {3,3,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^-1 * x * z * y * x^-1 * y^-1 * z^-3 ] T28.52 : Triangle type {3,3,21} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-3 * x^-1 * z^4 ] T28.53 : Triangle type {3,3,57} Group order 171 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T28.54 : Triangle type {3,4,4} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1, y * z^-1 * x^-1 * y * x^-1 * y^2 * x * z ] T28.55 : Triangle type {3,4,6} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T28.56 : Triangle type {3,4,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-2 * y * x^-1 * z * y^2 ] T28.57 : Triangle type {3,4,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z ] T28.58 : Triangle type {3,4,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T28.59 : Triangle type {3,4,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T28.60 : Triangle type {3,5,6} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^-5, (z^-1 * y)^3 ] T28.61 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y * z^-2 * x^-1 * y^-2 * z ] T28.62 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T28.63 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2 ] T28.64 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T28.65 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T28.66 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (y * z^-1 * y)^2 ] T28.67 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^6 ] T28.68 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-2 * y * x * y^3 * z^-2 * y ] T28.69 : Triangle type {3,6,6} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (z^-1 * x^-1 * y^-1)^3 ] T28.70 : Triangle type {3,6,8} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T28.71 : Triangle type {3,6,14} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, x * y^-2 * x * z * y ] T28.72 : Triangle type {3,6,38} Group order 114 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x^-1 * z^2 * y ] T28.73 : Triangle type {3,9,18} Group order 108 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y ] T28.74 : Triangle type {3,9,18} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-4 * z * y^-1 * z ] T28.75 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, x^-1 * y^-2 * x * y^-1 * z ] T28.76 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y * x^-1 * y * x^-1 * y^-1 * x * z ] T28.77 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T28.78 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (z * y^-3)^3 ] T28.79 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^3 * x^-1 * z^3 ] T28.80 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z^3 * y^-4 * z^3 ] T28.81 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * z^-2 * y * z^-2 * y * z^-2 * y^2 ] T28.82 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^-1 * z * y * x^-1 * y^-3 ] T28.83 : Triangle type {3,12,12} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, z^2 * y^-1 * z * y^-6 * z * y^-1 ] T28.84 : Triangle type {3,29,87} Group order 87 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, z * y^-19 * z * y^-7 * z ] T28.85 : Triangle type {3,30,30} Group order 90 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^19 * y^-8 * z * y^-1 ] T28.86 : Triangle type {3,30,30} Group order 90 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 ] T28.87 : Triangle type {3,30,30} Group order 90 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-21 * z * y^-6 * z^2 ] T28.88 : Triangle type {3,84,84} Group order 84 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-6 * z ] T28.89 : Triangle type {4,4,4} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T28.90 : Triangle type {4,4,29} Group order 116 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y * z^-1 * x * z^3 ] T28.91 : Triangle type {4,4,29} Group order 116 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^29 ] T28.92 : Triangle type {4,4,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y * x^-1 * z^10 ] T28.93 : Triangle type {4,5,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T28.94 : Triangle type {4,6,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^6, (z^-1 * x)^3 ] T28.95 : Triangle type {4,6,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * x)^3 ] T28.96 : Triangle type {4,6,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T28.97 : Triangle type {4,6,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T28.98 : Triangle type {4,12,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^3 ] T28.99 : Triangle type {4,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T28.100 : Triangle type {4,38,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y ] T28.101 : Triangle type {5,16,16} Group order 80 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y * z^-7 * y * z^-1 * y^3 * z^-1 * y^2 ] T28.102 : Triangle type {5,16,16} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z * y^-1 * z * y^-3 * z * y^-1 * z * y^-5 * z * y^-1 ] T28.103 : Triangle type {5,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-10 * y * z^-3 ] T28.104 : Triangle type {5,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-9 * y * z^-3 ] T28.105 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^6 ] T28.106 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6 ] T28.107 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^6 ] T28.108 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^6 ] T28.109 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T28.110 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^6, y^6, y^-1 * z^-1 * x^-2 * z * x^-1 * z ] T28.111 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * z^-1 * x)^2, y^6 ] T28.112 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^6 ] T28.113 : Triangle type {6,6,6} Group order 108 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * x^-1 * z * y^-1, x^6, y^6 ] T28.114 : Triangle type {6,6,15} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * x * z^2 ] T28.115 : Triangle type {6,6,15} Group order 90 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * z^-5 * x^-1 * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z ] T28.116 : Triangle type {6,6,15} Group order 90 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-7 * x^-1 * y * x * y^-1 * z^-6 ] T28.117 : Triangle type {6,6,42} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * z^-2 * x * z^4 * y * x^-1 * y^-1 * z^-3 * x ] T28.118 : Triangle type {6,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y^2 * z^-2 ] T28.119 : Triangle type {6,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^3 * z^-1 * y ] T28.120 : Triangle type {6,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T28.121 : Triangle type {6,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * x^2 * z * y^-1 ] T28.122 : Triangle type {6,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^5 * z^-1 * y * z^-1 * y^3 * z^-1 ] T28.123 : Triangle type {8,9,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^8 ] T28.124 : Triangle type {8,10,10} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^3 * z^-1 * y * z^-2 * y * z^-1 * y ] T28.125 : Triangle type {8,12,24} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3 ] T28.126 : Triangle type {8,12,24} Group order 72 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^8 ] T28.127 : Triangle type {8,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8, z^-4 * y * z^-3 ] T28.128 : Triangle type {8,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^8 ] T28.129 : Triangle type {9,9,9} Group order 81 Chiral action Defining relators: [ x * y * z, z^-1 * y * x * z^-1, y * z^-1 * x^2 * z^-1 * x^-1, x^2 * y^-1 * x^4 * y^-2 ] T28.130 : Triangle type {9,9,9} Group order 81 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-2, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2 ] T28.131 : Triangle type {9,9,9} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^9 ] T28.132 : Triangle type {9,9,9} Group order 81 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y ] T28.133 : Triangle type {9,9,9} Group order 81 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z * x^-1 * y^-1 * x * z * x^-1 ] T28.134 : Triangle type {9,9,9} Group order 81 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, (y^-1 * x)^3 ] T28.135 : Triangle type {9,9,9} Group order 81 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * x ] T28.136 : Triangle type {9,12,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T28.137 : Triangle type {9,12,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, y^-1 * z * x^-1 * y^-1 * z ] T28.138 : Triangle type {9,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-9 ] T28.139 : Triangle type {9,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-4 * x * z^-3 ] T28.140 : Triangle type {10,10,35} Group order 70 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^3 * y * x * z^3 ] T28.141 : Triangle type {10,10,35} Group order 70 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^3 * y * x * z^3 ] T28.142 : Triangle type {12,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^-1 * z * x^-3 * y^-1 * z * y^-1 * z ] T28.143 : Triangle type {12,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-4 * y * x * z^-1 ] T28.144 : Triangle type {12,12,12} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^3 * x^-1 * y * z^-1 * y ] T28.145 : Triangle type {15,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^7 * z^-1 ] T28.146 : Triangle type {15,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^15 ] T28.147 : Triangle type {20,30,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^5 * x^-2 * y^4 ] T28.148 : Triangle type {20,30,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 * z^-1 * x^9 * y^-1 * x^2 ] T28.149 : Triangle type {20,30,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-6 * y^3 ] T28.150 : Triangle type {21,21,21} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-5 * x^3 * y^-4 ] T28.151 : Triangle type {21,21,21} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * x^-3 * z^4 ] T28.152 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^10 * y^-1 * x * y^-1 * x^2 ] T28.153 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-1 * z^2 * x^-8 ] T28.154 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^6 * y^-2 ] T28.155 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^4 * x^-1 * y^4 ] T28.156 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-4 * x^2 * y^-1 * z^3 * y^-2 ] T28.157 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * y * z^-6 ] T28.158 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-5 * y^4 ] T28.159 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-1 * z * x^-1 * z^2 * x^-5 * z^3 ] T28.160 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-2 * z * y^-2 * z * y^-6 * z * y^-3 ] T28.161 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-4 * y * z^-3 ] T28.162 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * x^-4 * y^4 ] T28.163 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-7 * z ] T28.164 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^15 * x^-2 * z^3 ] T28.165 : Triangle type {29,58,58} Group order 58 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-29, y * z^-1 ] T28.166 : Triangle type {30,30,30} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-7 * x^2 * y^-7 ] T28.167 : Triangle type {57,57,57} Group order 57 Reflexible action Defining relators: [ x^-2 * y^-1, y^-24 * x * y^-4, x * z^-1 ] T28.168 : Triangle type {57,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^2 * y^-3 * x^7 ] T28.169 : Triangle type {57,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x * y^-4 * x^3 * z^-1 * x ] T28.170 : Triangle type {57,57,57} Group order 57 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^7 * z^-1 ] Genus 29 T29.1 : Triangle type {2,4,6} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-2 * y * x * z^2 * y^-1 * z * y^-1 * z^-1 * x ] T29.2 : Triangle type {2,4,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z * y * x * z^6 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T29.3 : Triangle type {2,4,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * z^5 * y * z^-2 * x * y^-1 * z^-5 ] T29.4 : Triangle type {2,4,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, x * z^7 * y * z^-1 * x * y^-1 * z^-6 ] T29.5 : Triangle type {2,4,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 ] T29.6 : Triangle type {2,4,116} Group order 232 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-51 * x * y^-1 * z^-6 ] T29.7 : Triangle type {2,5,8} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-1)^4, (y * z^-3)^2 ] T29.8 : Triangle type {2,5,8} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-3)^2, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T29.9 : Triangle type {2,6,6} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x ] T29.10 : Triangle type {2,6,6} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T29.11 : Triangle type {2,6,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T29.12 : Triangle type {2,6,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, (y * z^-3 * y)^2 ] T29.13 : Triangle type {2,6,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * z^-3 ] T29.14 : Triangle type {2,6,15} Group order 210 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y^-3 * z^-1 * x * y^-1 * z^-1 ] T29.15 : Triangle type {2,6,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T29.16 : Triangle type {2,6,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-4 ] T29.17 : Triangle type {2,6,87} Group order 174 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-5 * x * z * y * x * z^13 * y * x * z^7 * y^-1 ] T29.18 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^12 ] T29.19 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T29.20 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^6 * y * z^-5 ] T29.21 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^-3 * z^-2 * x * z, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T29.22 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x, z^-1 * x * y^-3 * z^-4 ] T29.23 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-1 * x * y^-3 * z^-4, x * z^2 * y^-2 * z^2 * y^-1 * z^-1 ] T29.24 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-12 ] T29.25 : Triangle type {2,8,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-12 ] T29.26 : Triangle type {2,8,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^7 * y * z^-5 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z ] T29.27 : Triangle type {2,8,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^13 * y^-1 * z^-6 ] T29.28 : Triangle type {2,12,12} Group order 168 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-2 * z^2 * y^-5 * z * y^-1 * z ] T29.29 : Triangle type {2,18,18} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-2 * y^10 * z^-2 * y^2 ] T29.30 : Triangle type {2,32,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-8 * y^11 * z^-1 * y^9 * z^-1 * y ] T29.31 : Triangle type {2,32,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-5 * z^3 * y^-6 * z * y^-1 ] T29.32 : Triangle type {2,32,32} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z^5 * y^-9 * z ] T29.33 : Triangle type {2,59,118} Group order 118 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^45 * y^-12 * z ] T29.34 : Triangle type {2,60,60} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^46 * y^-13 ] T29.35 : Triangle type {2,116,116} Group order 116 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^44 * y^-12 * z ] T29.36 : Triangle type {3,4,4} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * y^-1 * z^-1 * y * x * z * y * z^-1 ] T29.37 : Triangle type {3,4,8} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^-3 * x^-1 * y^-1 * z * y^-1 ] T29.38 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T29.39 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T29.40 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T29.41 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T29.42 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T29.43 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T29.44 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, x^-1 * z^2 * y^-1 * x * z^3 ] T29.45 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T29.46 : Triangle type {3,4,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-3 * x^-1 * y^-1 * z * y ] T29.47 : Triangle type {3,6,6} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * z * y^-1, y^-2 * z * y^-1 * x * y^-1 * z^2 ] T29.48 : Triangle type {3,6,6} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T29.49 : Triangle type {3,6,6} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-1 * x * y^3 * z^-2 * y ] T29.50 : Triangle type {3,10,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1 * y^2)^2 ] T29.51 : Triangle type {3,10,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x^-1 * z * y)^2, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T29.52 : Triangle type {3,10,10} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^3 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^2 ] T29.53 : Triangle type {3,15,15} Group order 105 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-2 * x * z * y^-1 ] T29.54 : Triangle type {3,24,24} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T29.55 : Triangle type {3,24,24} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T29.56 : Triangle type {3,87,87} Group order 87 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-8 ] T29.57 : Triangle type {4,4,9} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^4 * y^-1 * x^-1 * z^4 ] T29.58 : Triangle type {4,4,9} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-2 * x * z^3 * y * z^-3 ] T29.59 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T29.60 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-3 * x^-1 * y^-1 * x * z^4 ] T29.61 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T29.62 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * z^4 ] T29.63 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-6 * x^-1 * y^-1 * z^-5 * x * z * y^-1 * z^-2 ] T29.64 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^3 * y^-1 * z^-1 * x * z^3 ] T29.65 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T29.66 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * z^4 ] T29.67 : Triangle type {4,4,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * z^4 ] T29.68 : Triangle type {4,4,30} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1 ] T29.69 : Triangle type {4,4,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^30 ] T29.70 : Triangle type {4,4,58} Group order 116 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^18 * y * x^-1 * z^10 ] T29.71 : Triangle type {4,5,5} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x * z * y ] T29.72 : Triangle type {4,5,5} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T29.73 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3 ] T29.74 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T29.75 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^8 ] T29.76 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T29.77 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * y^-1 * z^-4 ] T29.78 : Triangle type {4,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * z^-3 * x^-1 * y^-1 * x^-1 * z^5 ] T29.79 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-2 * z * y^-1 * z * y^-5 * z^2 ] T29.80 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^3 * z^-2, x^-1 * z * y * x * z * y ] T29.81 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3 ] T29.82 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, x^-1 * z * y * x * z * y, (y * z^-2)^2 ] T29.83 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-1 * z^2 * y^-3 * z * y^-1 * z * y^-2 * z ] T29.84 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (z^-1 * y)^3, y^3 * x^-1 * y * z^-2 ] T29.85 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-4 * z^3 * y^-1 ] T29.86 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-1 * z * y^-4 ] T29.87 : Triangle type {4,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T29.88 : Triangle type {4,21,28} Group order 84 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * y^-1 * z * y^-1 ] T29.89 : Triangle type {4,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-3 * z * y^-7 * z * y^-1 * z * y^-4 * z * y^-1 ] T29.90 : Triangle type {4,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T29.91 : Triangle type {5,6,6} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, x^-1 * y^-1 * x^2 * z * x^-1 ] T29.92 : Triangle type {5,6,6} Group order 120 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^6 ] T29.93 : Triangle type {6,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y ] T29.94 : Triangle type {6,6,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, (x * z * y)^2 ] T29.95 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y * z^-1, x^6, y^2 * x^2 * z^-1 * y ] T29.96 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^6, z * y * x^2 * y^-2, z^-2 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-2 ] T29.97 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, z * y^-1 * x^2 * z^2 ] T29.98 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, (y * z^-1 * y)^2 ] T29.99 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, y * z^-1 * x^2 * y^-1 * z ] T29.100 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^3 * x^-1 * z^3 ] T29.101 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-2, z^-2 * x^-1 * z * y, x^6 ] T29.102 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z * y * x^-1 * y^-2, x^6 ] T29.103 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T29.104 : Triangle type {6,8,8} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T29.105 : Triangle type {6,12,12} Group order 84 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, x^6, y^2 * x^2 * z^2 ] T29.106 : Triangle type {6,12,12} Group order 84 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z^-2 * y^2 * z^-1 * y ] T29.107 : Triangle type {6,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-2 * z^2 ] T29.108 : Triangle type {8,8,20} Group order 80 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * x^-1 * y^-1 * z, (x * z^-1 * x)^2 ] T29.109 : Triangle type {8,8,20} Group order 80 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^-1 * z^-1 * x^-1 * z^2 ] T29.110 : Triangle type {8,8,20} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T29.111 : Triangle type {8,8,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y * z^-1 * x^-1 * z^3 * y * x^-1 * z^4 ] T29.112 : Triangle type {9,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2 ] T29.113 : Triangle type {9,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-9 ] T29.114 : Triangle type {10,14,35} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-10 ] T29.115 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-16 ] T29.116 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-7 * z * y ] T29.117 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^2 * x^-5 * z^2 ] T29.118 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, y * x^-7 * z ] T29.119 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z * x^-1 * z^3 * x^-3 * z^4 ] T29.120 : Triangle type {16,32,32} Group order 64 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-1 * x * z^-1 * x * z^-2 ] T29.121 : Triangle type {30,60,60} Group order 60 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^2 * x^-3 * y^4 ] T29.122 : Triangle type {30,60,60} Group order 60 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-30, y * z^-1 ] T29.123 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x^-2 * y^-1, y^-25 * x * y^-4, x * z^-1 ] T29.124 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-8 ] T29.125 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^3 * y^-9 * x * y^-1 * x * y^-1 ] T29.126 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^2 * x^-4 * y^4 ] T29.127 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y^2 * x^-6 * y^2 ] T29.128 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y * x^-4 * y^4 ] T29.129 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^5 * y^-3 ] T29.130 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^3 * y^-6 * z^2 ] T29.131 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-3 * y^2 * x^-8 ] T29.132 : Triangle type {59,59,59} Group order 59 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^7 * z^-2 ] Genus 30 T30.1 : Triangle type {2,4,33} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-19 * x * z^7 * y^-1 * x * y^-1 * z^-5 ] T30.2 : Triangle type {2,4,62} Group order 248 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 ] T30.3 : Triangle type {2,4,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-53 * x * y^-1 * z^-6 ] T30.4 : Triangle type {2,6,32} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-8 * x * z^9 * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T30.5 : Triangle type {2,8,22} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-3 * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T30.6 : Triangle type {2,12,14} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-2 * x * z^5 * y^-1 * z^-6 ] T30.7 : Triangle type {2,14,70} Group order 140 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * x * y^-1 * z^-4, (y^-2 * z^4 * y^-1)^2 ] T30.8 : Triangle type {2,22,66} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-9 * z^2 * y^-7 * z^2 * y^-2 ] T30.9 : Triangle type {2,26,65} Group order 130 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y * z^-4 * x, y * z^-4 * y^6 * z^-1 * y ] T30.10 : Triangle type {2,33,33} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-29 * z * y^-1 ] T30.11 : Triangle type {2,61,122} Group order 122 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^47 * y^-12 * z ] T30.12 : Triangle type {2,62,62} Group order 124 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^48 * y^-13 ] T30.13 : Triangle type {2,120,120} Group order 120 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^46 * y^-12 * z ] T30.14 : Triangle type {3,3,61} Group order 183 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-3 * x * z^4 ] T30.15 : Triangle type {3,31,93} Group order 93 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-22 * z * y^-6 * z^2 ] T30.16 : Triangle type {3,32,32} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^21 * y^-8 * z * y^-1 ] T30.17 : Triangle type {3,90,90} Group order 90 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-21 * z * y^-8 ] T30.18 : Triangle type {4,4,31} Group order 124 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^31 ] T30.19 : Triangle type {4,4,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^19 * y * x^-1 * z^10 ] T30.20 : Triangle type {4,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^5 * y^-1 * x^-1 * z^4 ] T30.21 : Triangle type {4,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^2 * y^-1 * x * z^2 ] T30.22 : Triangle type {4,12,16} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^2 * y * z^-1 * x^-1 * z^4 ] T30.23 : Triangle type {4,21,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-3 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 * z ] T30.24 : Triangle type {4,22,22} Group order 88 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-10 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-4 ] T30.25 : Triangle type {4,28,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * x * z^2 * y^-1 ] T30.26 : Triangle type {4,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-2 ] T30.27 : Triangle type {5,16,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-9 * y * z^-1 * y^3 ] T30.28 : Triangle type {5,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z^9 * y^-1 ] T30.29 : Triangle type {5,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-1 * z * y^-1 * z^10 ] T30.30 : Triangle type {6,6,16} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-9 * x^-1 * y * x^-1 * y * x^-1 * y * z^-4 ] T30.31 : Triangle type {6,13,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-4 ] T30.32 : Triangle type {6,14,14} Group order 84 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^2 * z^-1 * y * z^-1 * x^-1 * z^-1 * y * z^-1 * y^5 * z^-1 ] T30.33 : Triangle type {6,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * x * y^-4 ] T30.34 : Triangle type {7,11,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-2 * z^2 ] T30.35 : Triangle type {7,12,12} Group order 84 Chiral action Defining relators: [ x * y * z, y * x^2 * z, z * x^-2 * y * x^-1, z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-3 ] T30.36 : Triangle type {7,12,12} Group order 84 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^-3 * y^-1 * z^-1, y^3 * z^-1 * y^5 * z^-2 * y ] T30.37 : Triangle type {7,12,12} Group order 84 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-5 * z * y^-1 * z^2 * y^-1 * z * y^-1 ] T30.38 : Triangle type {7,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-3 * z ] T30.39 : Triangle type {7,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-1 * z^3 ] T30.40 : Triangle type {7,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-4 ] T30.41 : Triangle type {8,8,11} Group order 88 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^4 * y^-1 * x * y^-1 * x^-1 * y * x^-1 * z^4 ] T30.42 : Triangle type {8,10,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, (y^-1 * z * y^-1 * z * y^-1)^2 ] T30.43 : Triangle type {8,18,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^4 * y^-4 ] T30.44 : Triangle type {11,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-11 ] T30.45 : Triangle type {11,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-3 * x^2 * y^-3 ] T30.46 : Triangle type {11,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-11 ] T30.47 : Triangle type {11,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y^3 * x^-3 * y^3 ] T30.48 : Triangle type {11,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-11 ] T30.49 : Triangle type {12,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-5 * z * y ] T30.50 : Triangle type {12,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * x^-2 * y^2 ] T30.51 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^-1 * z^2 * x^-4 * z^3 ] T30.52 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z * x^-1 * z^3 * x^-6 * z ] T30.53 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z^3 * x^-5 * z^2 ] T30.54 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-3 * y * x^-8 * z * x^-1 ] T30.55 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-4 * x^5 * y^-1 * x ] T30.56 : Triangle type {13,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z * x^-4 * z^4 ] T30.57 : Triangle type {14,14,35} Group order 70 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^2 * y^-1 * x * z^2 ] T30.58 : Triangle type {14,14,35} Group order 70 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T30.59 : Triangle type {14,14,35} Group order 70 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^-3 * y * x * z^-3 ] T30.60 : Triangle type {16,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-2 * z * x^-1 * z^3 * x^-3 * z^4 ] T30.61 : Triangle type {16,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * z^-2 * y^2 * x^-4 * y^2 ] T30.62 : Triangle type {16,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-16 ] T30.63 : Triangle type {16,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-3 * y^2 * z^-3 ] T30.64 : Triangle type {21,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y * x^-7 * y^2 ] T30.65 : Triangle type {21,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^9 * y^-1 * x^7 * z^-1 * x^4 ] T30.66 : Triangle type {21,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^9 * x^-1 * y^6 ] T30.67 : Triangle type {21,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-2, y^-1 * z^4 * y^-2 * z^2 ] T30.68 : Triangle type {21,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * x^5 * z^-3 * x * z^-3 ] T30.69 : Triangle type {22,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y * x^-1 * y * x^-1 * y * z^-1 * y ] T30.70 : Triangle type {22,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2 ] T30.71 : Triangle type {22,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, y^-2 * x^2 * y^-2 ] T30.72 : Triangle type {22,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^5 * z^-1 * x * z^-1 ] T30.73 : Triangle type {22,22,33} Group order 66 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^4 * x^-1 * y^-1 * z^4 * x^-1 * z * x^-1 ] T30.74 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-7 * x^3 * y^-7 ] T30.75 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^3 * y^-6 * x ] T30.76 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-5 * y^4 ] T30.77 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-3 * x^3 * y^-7 ] T30.78 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^3 * x^-6 * z ] T30.79 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-8 * y^2 ] T30.80 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-2 * x^7 * z^-3 * x * z^-1 * x ] T30.81 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^6 * x^-1 * z^4 ] T30.82 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * x^-2 * y^4 * z^-1 * y^2 ] T30.83 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^2 * y^-4 * z^4 ] T30.84 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^2 * x^-7 ] T30.85 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-7 * y^2 ] T30.86 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^6 * z^-2 ] T30.87 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, x^-1 * y * z^-2 * y^5 * z^-1 * y ] T30.88 : Triangle type {31,62,62} Group order 62 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-31, y * z^-1 ] T30.89 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x^-2 * y^-1, y^-26 * x * y^-4, x * z^-1 ] T30.90 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-5 * x * y^-3 ] T30.91 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^3 * y^-4 * x^3 * y^-3 * x * y^-3 ] T30.92 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-1 * y^3 * x^-3 * y^4 ] T30.93 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y^3 * x^-4 * y^3 ] T30.94 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-2 * y^4 ] T30.95 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x^3 * y^-3 ] T30.96 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-8 * z^3 ] T30.97 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y * x^-4 * y^4 ] T30.98 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, x^-1 * y^3 * x^-3 * y^4 ] T30.99 : Triangle type {61,61,61} Group order 61 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-2 * y^6 ] Genus 31 T31.1 : Triangle type {2,3,21} Group order 504 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^-1 * x * z * y * z^-1 * x * z * y * z^-2 * x * z^2 * y^-1 * z^-2 ] T31.2 : Triangle type {2,3,30} Group order 450 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^4 * y * z^-3 * x * y * z^-1 * x * z^5 * y^-1 * z^-3 ] T31.3 : Triangle type {2,4,6} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T31.4 : Triangle type {2,4,14} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * z^-1 * x * z^4 ] T31.5 : Triangle type {2,4,14} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z * y * x * z^2 * y^2 * z^-2 * x * y^-1 * z^-1, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T31.6 : Triangle type {2,4,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T31.7 : Triangle type {2,4,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^7 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z^2 ] T31.8 : Triangle type {2,4,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, (y^-1 * z)^6 ] T31.9 : Triangle type {2,4,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y * z^-2 * y * x * y^-1 * z^3 * y^-1 * z ] T31.10 : Triangle type {2,4,28} Group order 280 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^6 * y * z^-1 * x * y^-1 * z^-5 * x ] T31.11 : Triangle type {2,4,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 ] T31.12 : Triangle type {2,4,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-17 * x * z^6 * y * z^-8 ] T31.13 : Triangle type {2,4,124} Group order 248 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-55 * x * y^-1 * z^-6 ] T31.14 : Triangle type {2,5,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-1 * x * y^-1 * z^-2 * x, (z * y^-1 * z)^3 ] T31.15 : Triangle type {2,6,6} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T31.16 : Triangle type {2,6,33} Group order 198 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^19 * y * x * y^-1 * z^-8 * x * z^4 ] T31.17 : Triangle type {2,6,93} Group order 186 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^15 * y * z^-1 * x * z^4 * y * z^-1 * x * y * z^-6 * x * z ] T31.18 : Triangle type {2,15,30} Group order 150 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y^-1 * z^3 * y^-3 * z * y^-7 ] T31.19 : Triangle type {2,16,16} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-1 * z^5 * y^-7 * z * y^-2 ] T31.20 : Triangle type {2,16,16} Group order 160 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T31.21 : Triangle type {2,18,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, z * y^-4 * z^2 * y^-1 * z ] T31.22 : Triangle type {2,24,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^4 * z^-3 * y ] T31.23 : Triangle type {2,24,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y * x * z * y^3 * z^-2 * x * z ] T31.24 : Triangle type {2,24,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T31.25 : Triangle type {2,24,24} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^7 * y^-1 * z^5 * y^-7 * z * y^-1 * z ] T31.26 : Triangle type {2,28,28} Group order 140 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-4 * z * y^-6 * z * y^-1 * z ] T31.27 : Triangle type {2,63,126} Group order 126 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^49 * y^-12 * z ] T31.28 : Triangle type {2,64,64} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-8 * y^11 * z^-1 * y^10 * z^-1 ] T31.29 : Triangle type {2,64,64} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^50 * y^-13 ] T31.30 : Triangle type {2,124,124} Group order 124 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^48 * y^-12 * z ] T31.31 : Triangle type {3,3,15} Group order 225 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z^4 * y^-1 * z^-2 ] T31.32 : Triangle type {3,4,4} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x * y^-1 * z^-1 * y)^2, (x * z * y^-1 * z^-1)^2 ] T31.33 : Triangle type {3,6,7} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, y^-1 * z^-1 * y * x^-1 * z * y * x^-1 ] T31.34 : Triangle type {3,6,7} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z * y, z^3 * y^-1 * x^-1 * z^3 ] T31.35 : Triangle type {3,6,7} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z^2, z^3 * y^-1 * x^-1 * z^3 ] T31.36 : Triangle type {3,6,7} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z * y^2 * x * y^-1 * z ] T31.37 : Triangle type {3,6,10} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z * y^2 * x^-1 * z^3 ] T31.38 : Triangle type {3,6,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-3 * x^-1 * z^2 * y^-1 ] T31.39 : Triangle type {3,6,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3 ] T31.40 : Triangle type {3,6,42} Group order 126 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x^-1 * y * z^-2 ] T31.41 : Triangle type {3,15,35} Group order 105 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * x * z * y^-1 ] T31.42 : Triangle type {3,32,96} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-6 * z^2 ] T31.43 : Triangle type {3,33,33} Group order 99 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-6 * z^2 ] T31.44 : Triangle type {3,93,93} Group order 93 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-22 * z * y^-7 * z ] T31.45 : Triangle type {4,4,7} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z^2, z^2 * y * x * z^-1 * x^-1 ] T31.46 : Triangle type {4,4,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y * x^-1 * z * y * x^-1 * z * y^-1 * z * y^-1 ] T31.47 : Triangle type {4,4,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y * x^-1 * z * y * x * z * y^-1 * z * y^-1 ] T31.48 : Triangle type {4,4,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^8 ] T31.49 : Triangle type {4,4,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y * x * z ] T31.50 : Triangle type {4,4,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^2 * y * x^-1 * z^3 ] T31.51 : Triangle type {4,4,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T31.52 : Triangle type {4,4,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1 ] T31.53 : Triangle type {4,4,14} Group order 140 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-1 * z^-1 * x^-1 * y * x^-1 * z^4 ] T31.54 : Triangle type {4,4,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-1 * x * z^4 ] T31.55 : Triangle type {4,4,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-6 * x^-1 * y^-1 * z^-5 * x * z * y * z^-2 ] T31.56 : Triangle type {4,4,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y * z^-10 ] T31.57 : Triangle type {4,4,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-1 * x^-1 * z^4 ] T31.58 : Triangle type {4,4,62} Group order 124 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^21 * y * x^-1 * z^9 ] T31.59 : Triangle type {4,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T31.60 : Triangle type {4,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, (x * z^-2)^2, z^6 ] T31.61 : Triangle type {4,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^6, x^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 ] T31.62 : Triangle type {4,6,12} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T31.63 : Triangle type {4,9,12} Group order 108 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x * y^-1 * z^-1 ] T31.64 : Triangle type {4,9,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^-9 ] T31.65 : Triangle type {4,10,20} Group order 100 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * x * z * y^-1 ] T31.66 : Triangle type {4,10,20} Group order 100 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x * z^-1 * y ] T31.67 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, (y^-3 * z * y^-2)^2 ] T31.68 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-3 * z^2 * y^-1 * z * y^-2 * z * y^-2 ] T31.69 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2 ] T31.70 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T31.71 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2 ] T31.72 : Triangle type {4,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2 ] T31.73 : Triangle type {4,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^2 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T31.74 : Triangle type {4,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^2 * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 * z ] T31.75 : Triangle type {5,5,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * x, (z^-1 * x)^3 ] T31.76 : Triangle type {6,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T31.77 : Triangle type {6,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * x^2 * z^-2 ] T31.78 : Triangle type {6,10,15} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2 ] T31.79 : Triangle type {6,12,28} Group order 84 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, y^-1 * z * x^-1 * z^2 ] T31.80 : Triangle type {6,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-1 * z^3 ] T31.81 : Triangle type {8,10,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-1 * z^3 ] T31.82 : Triangle type {8,10,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, (y^-1 * z^4)^2 ] T31.83 : Triangle type {8,16,16} Group order 80 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y^-2 * x^2 * y^-2 ] T31.84 : Triangle type {8,16,16} Group order 80 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x * y^-2 * x * y^-1 * z^-1 ] T31.85 : Triangle type {8,16,16} Group order 80 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^8 ] T31.86 : Triangle type {8,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^5 * x^-1 * z^4 ] T31.87 : Triangle type {8,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^4 * y^-2 * z^2 ] T31.88 : Triangle type {9,24,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-3 * y^2 * z^-3 ] T31.89 : Triangle type {9,24,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-9 ] T31.90 : Triangle type {10,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-10 ] T31.91 : Triangle type {10,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-4 * x * z^-3 ] T31.92 : Triangle type {10,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-10 ] T31.93 : Triangle type {12,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * y * x^-8 * z * x^-1 ] T31.94 : Triangle type {12,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, y * x^-5 * y^3 * z^-1 * y ] T31.95 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * y^-3 * x^3 * y^-3 * x^4 ] T31.96 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^2 * z^-1 * x^7 * z^-1 * x^2 ] T31.97 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3 ] T31.98 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^2 * x^-3 * z^4 ] T31.99 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-4 * y * x^-1 * y ] T31.100 : Triangle type {12,24,24} Group order 72 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y * z^-1 * y ] T31.101 : Triangle type {15,15,15} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-5 * z, y^-1 * z^5 * y^-4 ] T31.102 : Triangle type {18,18,18} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, y^-1 * x^3 * y^-2 ] T31.103 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, x^-1 * y * x^-1 * y^4 * x^-2 * y^4 ] T31.104 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^3, x^-7 * z^3 ] T31.105 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-4 * x^2 * y^-4 * x * y^-1 * x * y^-1 * x ] T31.106 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-3 * x^8 ] T31.107 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^7 * z^-2 ] T31.108 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-7 * x * z^-4 * x * z^-1 ] T31.109 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-6, y^5 * z^-4 ] T31.110 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^17 * y^-1 * x * y^-1 * x * y^-1 * x ] T31.111 : Triangle type {22,33,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-1 * y * z^-3 * x^2 * z^-4 ] T31.112 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-32, y * z^-1 ] T31.113 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-14 * y^2 * x^-1 ] T31.114 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-7 * z^2 ] T31.115 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^3 * z^-2 * y^6 * z^-1 * y^2 ] T31.116 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z^2 * x^-5 * z^2 ] T31.117 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^6 * x^-1 * z^4 ] T31.118 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^17 * x^-2 * z^3 ] T31.119 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-2 * z^5 * x^2 * y^-3 ] T31.120 : Triangle type {32,64,64} Group order 64 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y * x^-8 * y ] T31.121 : Triangle type {63,63,63} Group order 63 Reflexible action Defining relators: [ x^-2 * y^-1, y^26 * x^-1 * y^5, x * z^-1 ] T31.122 : Triangle type {63,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-2 * z * x^-1 * z^3 * x^-4 * z^3 ] T31.123 : Triangle type {63,63,63} Group order 63 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^6 * x^-1 * z^4 ] Genus 32 T32.1 : Triangle type {2,4,66} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 ] T32.2 : Triangle type {2,4,128} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-57 * x * y^-1 * z^-6 ] T32.3 : Triangle type {2,5,10} Group order 310 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, x * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-1 ] T32.4 : Triangle type {2,5,10} Group order 310 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z^2 * y * x * y^-1 * z^-2 * x ] T32.5 : Triangle type {2,6,6} Group order 372 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y * x * z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T32.6 : Triangle type {2,6,34} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-19 * x * z^5 * y^-1 * z^-9 ] T32.7 : Triangle type {2,6,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^18 * y * x * z^7 * y^-1 * z^-3 * x * z^2 ] T32.8 : Triangle type {2,8,44} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-3 * x * z^3 * y * x * y^-1 * z^-14 ] T32.9 : Triangle type {2,10,18} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-2 * x * z^9 * y^-1 * z^-6 ] T32.10 : Triangle type {2,10,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^7 * y * z^-2 * x * z^6 ] T32.11 : Triangle type {2,16,20} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z^3 * y * x * z * y^3 * x * y^-1 * z^-3 ] T32.12 : Triangle type {2,18,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-5 * z^4 * y^-4 * z^4 * y^-1 ] T32.13 : Triangle type {2,34,68} Group order 136 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-10 * y^21 * z^-2 ] T32.14 : Triangle type {2,65,130} Group order 130 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^51 * y^-12 * z ] T32.15 : Triangle type {2,66,66} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^52 * y^-13 ] T32.16 : Triangle type {2,128,128} Group order 128 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^50 * y^-12 * z ] T32.17 : Triangle type {3,6,6} Group order 186 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x * z * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y ] T32.18 : Triangle type {3,6,6} Group order 186 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y^2 * z^-2 * y * x * y^2 * z^-1 * y * z^-1 ] T32.19 : Triangle type {3,10,20} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^10 ] T32.20 : Triangle type {3,34,34} Group order 102 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^21 * y^-3 * z * y^-7 * z ] T32.21 : Triangle type {3,96,96} Group order 96 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-8 ] T32.22 : Triangle type {4,4,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y * z^-11 ] T32.23 : Triangle type {4,4,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y^-1 * z^-10 ] T32.24 : Triangle type {4,8,14} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x * z^4 * y * z^-1 * x^-1 * z^4 ] T32.25 : Triangle type {4,12,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y * x^-1 * z^4 ] T32.26 : Triangle type {4,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-9 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-2 * z * y^-1 ] T32.27 : Triangle type {5,5,5} Group order 155 Chiral action Defining relators: [ x * y * z, x^-5, x * y^-2 * x * z * y, y^-5 ] T32.28 : Triangle type {5,5,5} Group order 155 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * x^-1 ] T32.29 : Triangle type {5,17,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^5 * y^-1 * z^9 * y^-1 * z ] T32.30 : Triangle type {5,18,18} Group order 90 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-6 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-4 ] T32.31 : Triangle type {5,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-9 * y * z^-1 * y * z^-2 ] T32.32 : Triangle type {5,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y * z^-9 * y * z^-1 * y * z^-2 ] T32.33 : Triangle type {6,6,17} Group order 102 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-6 * x^-1 * z^5 * y^-1 * z^-5 ] T32.34 : Triangle type {6,6,48} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-1 * x * z^3 * y * x * z^3 * y^-1 * z^-7 ] T32.35 : Triangle type {6,14,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y * z^-1 * y * z^-1 ] T32.36 : Triangle type {6,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-2 * z^2 ] T32.37 : Triangle type {8,8,22} Group order 88 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^4 * y^-1 * x * y^-1 * x * z^5 ] T32.38 : Triangle type {8,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T32.39 : Triangle type {9,10,10} Group order 90 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^9, (y * z^-1 * y * z^-1 * y)^2 ] T32.40 : Triangle type {9,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-4 * y * z^-3 ] T32.41 : Triangle type {9,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-9 ] T32.42 : Triangle type {10,10,40} Group order 80 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z * y * z^-2 * x^-1 * z^4 ] T32.43 : Triangle type {10,10,40} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4 ] T32.44 : Triangle type {10,16,16} Group order 80 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, z^-1 * y^2 * z^-2 * y^3 ] T32.45 : Triangle type {10,16,16} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T32.46 : Triangle type {12,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-5 * z * y ] T32.47 : Triangle type {14,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, x^-1 * z^3 * x^-4 * z^2 ] T32.48 : Triangle type {14,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-14 ] T32.49 : Triangle type {14,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-5 * z * x^-7 * y * x^-1 ] T32.50 : Triangle type {14,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z, y^-2 * z^3 * y^-1 * x * y^-4 ] T32.51 : Triangle type {14,35,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-5 * x^7 ] T32.52 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-5 * y^4 ] T32.53 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-1 * x * z^-11 ] T32.54 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * y^4 * x^-6 ] T32.55 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-1 * y * x^-1 * y^4 * x^-3 * y^3 ] T32.56 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^4 * x^-1 * y^4 ] T32.57 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-1 * x * z^-1 * x^10 * z^-1 * x * z^-1 ] T32.58 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, x^-1 * y^4 * x^-2 * y^4 ] T32.59 : Triangle type {17,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-8 * y * x^-7 * z * x^-1 ] T32.60 : Triangle type {18,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-2 * z * x^-5 * z * x^-1 ] T32.61 : Triangle type {18,18,36} Group order 72 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, y * x * z^-3 * y * z^-1 * y * z^-3 ] T32.62 : Triangle type {33,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-8 * x * y^-8 ] T32.63 : Triangle type {33,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^7 * z^-1 ] T32.64 : Triangle type {33,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-1 * y * x^-1 * y^4 * x^-2 * y^4 ] T32.65 : Triangle type {33,66,66} Group order 66 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-4 * y^2 * z^-4 ] T32.66 : Triangle type {33,66,66} Group order 66 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-33, y * z^-1 ] T32.67 : Triangle type {34,34,34} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-4 * x * z^-6 * x^2 * y * z^-5 ] T32.68 : Triangle type {34,34,34} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, x^2 * z^-10 ] T32.69 : Triangle type {34,34,34} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^3, x^-6 * z^4 ] T32.70 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x^-2 * y^-1, y^27 * x^-1 * y^5, x * z^-1 ] T32.71 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z^2 * x^-4 * z^3 ] T32.72 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-1 * z^3 * x^-7 ] T32.73 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^15 * x^-1 * y^6 ] T32.74 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y^-1 * z^4 * y^-1 * z^3 ] T32.75 : Triangle type {65,65,65} Group order 65 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-1, y^4 * z^-4 * y * z^-5 * y * z^-1 * y * z^-1 ] Genus 33 T33.1 : Triangle type {2,3,8} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^3 * y * x * z * y * x * z * y * x * z^2 * y^2 * z^-2 * x * y^-1 * z^-2 ] T33.2 : Triangle type {2,3,12} Group order 768 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, y * z^-1 * x * z^3 * y * x * z * y^-2 * z^-2 * x * z^2 ] T33.3 : Triangle type {2,3,12} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T33.4 : Triangle type {2,3,12} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12, z^-2 * x * z^3 * y * z^-2 * x * z^2 * y^-1 * z^-1 ] T33.5 : Triangle type {2,3,12} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T33.6 : Triangle type {2,4,6} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T33.7 : Triangle type {2,4,6} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^2 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^2 * y^-1 * z^-1 * x ] T33.8 : Triangle type {2,4,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T33.9 : Triangle type {2,4,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, z^-2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T33.10 : Triangle type {2,4,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T33.11 : Triangle type {2,4,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T33.12 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T33.13 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T33.14 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.15 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.16 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * x * z * y^2 * z^-1 * x * z^2 * y^-1, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z ] T33.17 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T33.18 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T33.19 : Triangle type {2,4,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T33.20 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x ] T33.21 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x, z^2 * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^2 ] T33.22 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y^-1 * z^2)^4 ] T33.23 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^2 * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T33.24 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T33.25 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-4 * x * z^5 * y^-1 * z^-2 ] T33.26 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^5 * y * x * z^4 * y^-1 * z^-1 * x ] T33.27 : Triangle type {2,4,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, z^-12 ] T33.28 : Triangle type {2,4,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^10 * y^-1 * x * y^-1 * z^-5 ] T33.29 : Triangle type {2,4,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-20 * x * z^8 * y * x * z * y^-1 * z^-5 ] T33.30 : Triangle type {2,4,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z * y * x * z^6 * y^-1 * z^-1 * x * y^-1 * z^-4 ] T33.31 : Triangle type {2,4,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z^7 * y^-1 * z^-6 ] T33.32 : Triangle type {2,4,68} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 * x * y * z^-7 ] T33.33 : Triangle type {2,4,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-59 * x * y^-1 * z^-6 ] T33.34 : Triangle type {2,5,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y^2 * z^-1 * y^2 * z^-2 * x * z, z * y * z^-2 * y^2 * z^-1 * y * x * z ] T33.35 : Triangle type {2,6,6} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z * y^-2 * z * y^3 * z^-1 * x * y^-1 * z^-1 * x ] T33.36 : Triangle type {2,6,6} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-2 * z * y^-1 * z^-2 ] T33.37 : Triangle type {2,6,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y^-2 * z^2 * y^-1 * z^-1, (y * z^-1 * y)^4 ] T33.38 : Triangle type {2,6,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, (y * z^-1 * y)^4 ] T33.39 : Triangle type {2,6,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T33.40 : Triangle type {2,6,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T33.41 : Triangle type {2,6,6} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, (z^-1 * y^2 * z^-1)^3 ] T33.42 : Triangle type {2,6,7} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, z^-3 * x * y * z^-3 ] T33.43 : Triangle type {2,6,7} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-3 * x * y * z^-3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.44 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, z^8 ] T33.45 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^8 ] T33.46 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^8 ] T33.47 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, z^8, y^-1 * z * y^-3 * z^-1 * y * x * z ] T33.48 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^8 ] T33.49 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y ] T33.50 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T33.51 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^8, z^-2 * x * y^-2 * z^-3 * y ] T33.52 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^2 * z^-1 * x * z^2 ] T33.53 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z^2 * y^-2 * z^-1 * x ] T33.54 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.55 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-3)^2 ] T33.56 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1 ] T33.57 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2 ] T33.58 : Triangle type {2,8,8} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-1)^4 ] T33.59 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T33.60 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^2 * y^-3 * z^-2 * x * z ] T33.61 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^6 * y * x * z^2 * y^-1 * z^-2 ] T33.62 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^4 * y * z^-1 * x * y^-1 * z^-5 ] T33.63 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-5 * x * z^4 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-7 ] T33.64 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z * y * z^-2 * x * z^3 * y * z^-2 * x * z^2 * y * z^-2 * x * y * z^-6 * x * z^2 ] T33.65 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-2 * x * y^-1 * x * z * y^-1 * z^-4 ] T33.66 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-2 * x * y^-1 * z^-6 ] T33.67 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-5 * x ] T33.68 : Triangle type {2,8,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^6 * y * z^-5 * x ] T33.69 : Triangle type {2,8,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^6 * y^-1 * z^-15 ] T33.70 : Triangle type {2,8,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^5 * y * z^-15 ] T33.71 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y * z^-1 * y, z * y^-4 * z * y^-1 * z^-1 * x ] T33.72 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z * y^-4 * z * y^-1 * z^-1 * x ] T33.73 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T33.74 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-1 * y, y^12 ] T33.75 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^12 ] T33.76 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^12 ] T33.77 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-12 ] T33.78 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z^2 * y^-2 * z^-3 * y ] T33.79 : Triangle type {2,12,12} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 ] T33.80 : Triangle type {2,12,28} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-1 * x * z * y * x * z^5 * y * x * y^-1 * z^-4 ] T33.81 : Triangle type {2,14,77} Group order 154 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y^-1 * z^-5 ] T33.82 : Triangle type {2,20,20} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^6 * z^-1 * y^7 * z^-2 * y ] T33.83 : Triangle type {2,36,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, z^-1 * y * z^-2 * y^10 * z^-4 ] T33.84 : Triangle type {2,36,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-32 * z * y^-1 ] T33.85 : Triangle type {2,36,36} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-12 * y^24 ] T33.86 : Triangle type {2,46,69} Group order 138 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z * y^-9 * z^2 * y^-7 * z^4 ] T33.87 : Triangle type {2,67,134} Group order 134 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^53 * y^-12 * z ] T33.88 : Triangle type {2,68,68} Group order 136 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^54 * y^-13 ] T33.89 : Triangle type {2,132,132} Group order 132 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^52 * y^-12 * z ] T33.90 : Triangle type {3,3,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x * z * x^-1 * z * x^-1 * y^-1 * z^-1 * x * z * y * x^-1 * y^-1 * z^-1, (x * z * y)^4 ] T33.91 : Triangle type {3,3,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, y * z^-1 * x^-1 * y * x^-1 * z * y * x * z ] T33.92 : Triangle type {3,3,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y^-1 * x * y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z * y * x ] T33.93 : Triangle type {3,3,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z * y^-1 * z^-1)^2 ] T33.94 : Triangle type {3,3,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T33.95 : Triangle type {3,3,67} Group order 201 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * z^-1 * x^-2 * z^4 ] T33.96 : Triangle type {3,4,4} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T33.97 : Triangle type {3,4,4} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, (x * z * y^-1 * z^-1 * y)^2 ] T33.98 : Triangle type {3,4,4} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, (z^-1 * x^-1 * y^-1)^3 ] T33.99 : Triangle type {3,4,4} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T33.100 : Triangle type {3,4,4} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y * z^-1 * x^-1 * y * x^-1 * y * z^-1 * x^-1 * z ] T33.101 : Triangle type {3,4,4} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, (x * z * y^-1 * z^-1 * y)^2 ] T33.102 : Triangle type {3,4,12} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * y^-1 * z^-1 * x^-1 * z * y^-1 * z ] T33.103 : Triangle type {3,4,12} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x * y^-1 * x * z^3 ] T33.104 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T33.105 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y^-1 * x * z * y ] T33.106 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x * z ] T33.107 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, z^-2 * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T33.108 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (x * z * y)^2 ] T33.109 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T33.110 : Triangle type {3,4,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, (z^-1 * y)^3 ] T33.111 : Triangle type {3,6,6} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.112 : Triangle type {3,6,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T33.113 : Triangle type {3,6,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, (y * z^-1)^4 ] T33.114 : Triangle type {3,6,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.115 : Triangle type {3,6,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T33.116 : Triangle type {3,6,6} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.117 : Triangle type {3,7,7} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-7, (y * z^-1)^4 ] T33.118 : Triangle type {3,7,7} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^-7 ] T33.119 : Triangle type {3,10,30} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^10 ] T33.120 : Triangle type {3,34,102} Group order 102 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-1 * z * y^-7 * z ] T33.121 : Triangle type {3,99,99} Group order 99 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-7 * z ] T33.122 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * y * x * y^-1 * x^2 * y^-1 * z * x^-1 * y^-1 * z ] T33.123 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-1 * y * x^2 * y^-1 * z * y^-1 * z^-1 ] T33.124 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4 ] T33.125 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * y * x * y^-1 * x^2 * y^-1 * z * x^-1 * y^-1 * z^-1 ] T33.126 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-1 * y * x^-1 * y^2 * z^-1 * y ] T33.127 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, (x * y^-1)^4 ] T33.128 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, (x * z * y)^2, (x * y^-1)^4 ] T33.129 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T33.130 : Triangle type {4,4,4} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z^-1 * y * x * z * x^-1 ] T33.131 : Triangle type {4,4,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * x^-2 * y^-1 * z^-2 ] T33.132 : Triangle type {4,4,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, (y^-1 * x)^3, z^6 ] T33.133 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.134 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T33.135 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1 ] T33.136 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.137 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^6, (y * z^-1)^4, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T33.138 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1 ] T33.139 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x ] T33.140 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^6 ] T33.141 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.142 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T33.143 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, x^-1 * z^2 * y * x * z^2 * y ] T33.144 : Triangle type {4,4,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T33.145 : Triangle type {4,4,10} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1 ] T33.146 : Triangle type {4,4,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^10 ] T33.147 : Triangle type {4,4,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^18 ] T33.148 : Triangle type {4,4,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^3 * y^-1 * z^-1 * x * z^4 ] T33.149 : Triangle type {4,4,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^3 * y * z^-1 * x * y * z^-1 * x^-1 * z^2 ] T33.150 : Triangle type {4,4,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-13 * x * y * z^-4 ] T33.151 : Triangle type {4,4,34} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4 * x^-1 * z^2 * y^-1 * z ] T33.152 : Triangle type {4,4,34} Group order 136 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 * x * y * z^-11 ] T33.153 : Triangle type {4,4,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y^-1 * z^-11 ] T33.154 : Triangle type {4,6,20} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^5 * y^-1 * x * z^4 ] T33.155 : Triangle type {4,8,8} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T33.156 : Triangle type {4,8,8} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * z^-2 ] T33.157 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T33.158 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.159 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * z^2 ] T33.160 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^8 ] T33.161 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T33.162 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2 ] T33.163 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1 ] T33.164 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^8 ] T33.165 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T33.166 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 ] T33.167 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T33.168 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T33.169 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2 ] T33.170 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8 ] T33.171 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^8 ] T33.172 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1 ] T33.173 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^8 ] T33.174 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^8 ] T33.175 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, (y * z^-1 * y)^2 ] T33.176 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z^-1 * y^2 * x^-1 * z * y * z^-1, y * z^-1 * y * x^-1 * z^2 * y ] T33.177 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x * z^-1 * x, x * z^-1 * y * x^-1 * y^-1 * z^-1, (y * z^-1 * y)^2 ] T33.178 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z * y^2 * x * z^-1 * x, y^8 ] T33.179 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^3 * x^-1 * z^3 ] T33.180 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, x^-1 * y * x^-2 * z^3 ] T33.181 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^8 ] T33.182 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^8 ] T33.183 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T33.184 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4 ] T33.185 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T33.186 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^8 ] T33.187 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T33.188 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^8 ] T33.189 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-2 * y * x^-1 * z * y^2 ] T33.190 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^8 ] T33.191 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T33.192 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^8 ] T33.193 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8 ] T33.194 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1)^4 ] T33.195 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-1 * y^2)^2 ] T33.196 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1 * y^2)^2 ] T33.197 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8 ] T33.198 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z^8 ] T33.199 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T33.200 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z, y^8 ] T33.201 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2 ] T33.202 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T33.203 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T33.204 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.205 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, (x^-1 * z * y)^2 ] T33.206 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x ] T33.207 : Triangle type {4,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * y^2 * x * z^-1 * x ] T33.208 : Triangle type {4,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^5 * z^-1 * y * z^-1 ] T33.209 : Triangle type {4,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T33.210 : Triangle type {4,23,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-1 * y * z^-1 * y^10 * z^-1 * y ] T33.211 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-2 * z * y^-1 * z * y^-4 * z * y^-2 ] T33.212 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-1 * z^2 * y^-3 * z * y^-1 * z * x * y^-3 ] T33.213 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.214 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y * z^-2 ] T33.215 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (y^-3 * z * y^-2)^2 ] T33.216 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z * y^-2 ] T33.217 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z^2 ] T33.218 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z * y^-5 * z * y^-1 * z * y^-5 * z ] T33.219 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-5 * z^3 ] T33.220 : Triangle type {4,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-3 * x * y^-2 * z * y^-1 * z ] T33.221 : Triangle type {4,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T33.222 : Triangle type {4,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^2 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T33.223 : Triangle type {5,5,5} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, y^-5, z * y * x^-2 * y * z^-1 * x ] T33.224 : Triangle type {5,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^-5 ] T33.225 : Triangle type {5,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y * x * y^-1 * x * y^-1 * z^-1 ] T33.226 : Triangle type {5,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-5, x * z^-1 * x^2 * y^-2, (y^-1 * x)^3 ] T33.227 : Triangle type {6,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, (x * z * y^-1)^2 ] T33.228 : Triangle type {6,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y ] T33.229 : Triangle type {6,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T33.230 : Triangle type {6,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T33.231 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^-2 * x^2 * y^-1 * z ] T33.232 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z^-1 * y^3 * z^-2 ] T33.233 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T33.234 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^3 * x^-1 * y^-1 * z * y ] T33.235 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^6 ] T33.236 : Triangle type {6,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T33.237 : Triangle type {6,28,28} Group order 84 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y * z^-1 * x^-1 * z^-1 * y * z^-1 * y^4 * z^-1 * y ] T33.238 : Triangle type {7,12,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T33.239 : Triangle type {7,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-1 * z^3 ] T33.240 : Triangle type {7,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-3 * z ] T33.241 : Triangle type {7,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^9 ] T33.242 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y^2 * x * z^-1 * x, x^8 ] T33.243 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, (y^-1 * x)^3, y^3 * x * z^2 ] T33.244 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, (y^-1 * x)^3, (x * z^-1 * y)^2 ] T33.245 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z * y, x^-1 * y^-1 * x^2 * z^-2, y^-1 * z^-1 * x^2 * z * y^-1, (x * z^-1 * y)^2 ] T33.246 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T33.247 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T33.248 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z * y * x^-1 * y^-1 * x * z^3 ] T33.249 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-6 * x * y^-1 * x * y * x^-1 * y * z^-3 ] T33.250 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^3, x^8 ] T33.251 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-3 * x^-1 * y^-1 * z^-2 ] T33.252 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T33.253 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T33.254 : Triangle type {8,8,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T33.255 : Triangle type {8,8,44} Group order 88 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-3 * x^-1 * y^-1 * x * z^4 ] T33.256 : Triangle type {8,8,44} Group order 88 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x * z^4 * y * x * z^4 ] T33.257 : Triangle type {8,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^4 * y^-5 ] T33.258 : Triangle type {8,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * x * y^-4 ] T33.259 : Triangle type {10,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-1 * x^4 * z^-3 ] T33.260 : Triangle type {10,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^10 ] T33.261 : Triangle type {12,12,14} Group order 84 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, y^-1 * x^3 * y^-2, z^-1 * y * x^2 * z * y ] T33.262 : Triangle type {12,12,14} Group order 84 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y^2 * x^2 * z^-2, (y^-1 * x)^3 ] T33.263 : Triangle type {12,12,14} Group order 84 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, y^-1 * x * y^-1 * x * y^-1 * x * z^4 ] T33.264 : Triangle type {12,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-5 * x^5 * y^-1 ] T33.265 : Triangle type {12,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x * y^-5 * x^5 * y^-1 * x ] T33.266 : Triangle type {18,24,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-1 * x^4 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T33.267 : Triangle type {18,24,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, (x^-2 * z^4)^2 ] T33.268 : Triangle type {18,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^18 ] T33.269 : Triangle type {18,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^4 * x^-2 * z^4 ] T33.270 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^2 * z^-1 * y^9 ] T33.271 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-1 * y^3 * x^-6 ] T33.272 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 * x^5 * y^-4 * x * y^-1 * x * y^-1 * x ] T33.273 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, (z^-3 * x * z^-1)^3 ] T33.274 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-1 * y^4 ] T33.275 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-3 * x^8 ] T33.276 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-13 * z * x^-7 * z^2 * x^-1 ] T33.277 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^5 * z^-4 ] T33.278 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-4 * y * z^-4 ] T33.279 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-5 * y * x^3 * z^-3 ] T33.280 : Triangle type {23,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-4 * y^3 * x^-6 ] T33.281 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-34, y * z^-1 ] T33.282 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-5 * x^2 * z^-3 ] T33.283 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y^4 * x^-6 ] T33.284 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-10 * z * y^-3 ] T33.285 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^6 * z^-2 ] T33.286 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^2 * z^-1 * y^6 * z^-3 ] T33.287 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^4 * y^-8 ] T33.288 : Triangle type {34,68,68} Group order 68 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, x^-1 * y^4 * x^-4 * y^2 ] T33.289 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x^-2 * y^-1, y^28 * x^-1 * y^5, x * z^-1 ] T33.290 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-13 * x^2 * y^-8 ] T33.291 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^4 * y^-4 * x^2 * y^-4 * x * y^-1 * x * y^-1 * x ] T33.292 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^3 * x^-1 * y^4 * x^-2 * y^4 ] T33.293 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y^4 * x^-3 * y^3 ] T33.294 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y^3 * x^-2 * y^4 ] T33.295 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-5 * y^4 ] T33.296 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-4 * y * x^2 * z^-3 ] T33.297 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^4 * y^-2 * x^-3 * z^3 ] T33.298 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * x * y^-3, x^-2 * y^2 * x^-7 ] T33.299 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-7 * y^4 * z^-4 ] T33.300 : Triangle type {67,67,67} Group order 67 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^3 * x^-2 * y^4 ] Genus 34 T34.1 : Triangle type {2,4,5} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^-2 ] T34.2 : Triangle type {2,4,5} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * z^-1 ] T34.3 : Triangle type {2,4,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T34.4 : Triangle type {2,4,70} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 * x * y * z^-7 ] T34.5 : Triangle type {2,4,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 * x * y^-1 * z^-7 ] T34.6 : Triangle type {2,5,5} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-2 * z^-1 ] T34.7 : Triangle type {2,5,5} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, z^-1 * y * z^-1 * x * z * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T34.8 : Triangle type {2,6,36} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^5 * y * z^-1 * x * y^-1 * z^-4 * x ] T34.9 : Triangle type {2,6,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^21 * y * x * z * y^-1 * z^-5 * x * z^7 ] T34.10 : Triangle type {2,6,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^14 * y * z^-2 * x * z^8 * y * x * y^-1 * z^-8 * x * z ] T34.11 : Triangle type {2,6,102} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-15 * x * z^8 * y * x * y * z^-6 * x * z^2 * y^-1 ] T34.12 : Triangle type {2,8,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T34.13 : Triangle type {2,9,12} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^2 * z^-4 ] T34.14 : Triangle type {2,9,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T34.15 : Triangle type {2,10,10} Group order 220 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^10 ] T34.16 : Triangle type {2,10,10} Group order 220 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, y^10 ] T34.17 : Triangle type {2,10,85} Group order 170 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^6 * y * z^-3 * x * y * z^-6 ] T34.18 : Triangle type {2,12,42} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-3 * x * y * z^-5 ] T34.19 : Triangle type {2,15,15} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z * y * z^-1 * y^2 * z^-1 * x * y^-1 ] T34.20 : Triangle type {2,36,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^2 * y^-3 * z^4 * y^-4 * z^3 * y^-1 * z ] T34.21 : Triangle type {2,69,138} Group order 138 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^55 * y^-12 * z ] T34.22 : Triangle type {2,70,70} Group order 140 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^56 * y^-13 ] T34.23 : Triangle type {2,136,136} Group order 136 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^54 * y^-12 * z ] T34.24 : Triangle type {3,6,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, x^-1 * z^2 * y^-1 * x * z^3 ] T34.25 : Triangle type {3,6,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T34.26 : Triangle type {3,8,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T34.27 : Triangle type {3,15,20} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^2 * z^-1 ] T34.28 : Triangle type {3,35,105} Group order 105 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-1 * z * y^-7 * z ] T34.29 : Triangle type {3,36,36} Group order 108 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 * z^-1 * y * z^-2 * y^2 ] T34.30 : Triangle type {3,36,36} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-25 * z * y^-1 * z * y^-7 * z ] T34.31 : Triangle type {3,36,36} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-2 * z * y^-6 * z^2 ] T34.32 : Triangle type {3,36,36} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^23 * y^-3 * z * y^-7 * z ] T34.33 : Triangle type {3,102,102} Group order 102 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-1 * z * y^-8 ] T34.34 : Triangle type {4,4,35} Group order 140 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z * y * z^-2 * x * z^3 ] T34.35 : Triangle type {4,4,35} Group order 140 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^22 * y * x^-1 * y * x^-1 * z^11 ] T34.36 : Triangle type {4,4,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 * x * y^-1 * z^-11 ] T34.37 : Triangle type {4,6,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T34.38 : Triangle type {4,6,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y * x * y^-1 * x * z^-2 ] T34.39 : Triangle type {4,6,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * z * y, x * z * y^-1 * x * y^-1 * z^-1 ] T34.40 : Triangle type {4,6,8} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y * x * z * y ] T34.41 : Triangle type {4,6,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T34.42 : Triangle type {4,8,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x * z^4 * y * z^-1 * x * z^4 ] T34.43 : Triangle type {4,9,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-4 * z^3 ] T34.44 : Triangle type {4,10,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, (z^-1 * y)^3 ] T34.45 : Triangle type {4,12,18} Group order 108 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^3 * z^-1 * x ] T34.46 : Triangle type {4,12,18} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^4 * y^-1 * x * z^4 ] T34.47 : Triangle type {4,46,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^4 * z^-3 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y ] T34.48 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * z, z^-2 * x^2 * z * y ] T34.49 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * y^2, y^2 * x^2 * y^-1 * z^-1 ] T34.50 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^2 * x^2 * z^2 ] T34.51 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, z^-1 * x * z^-1 * x * z * y ] T34.52 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1 ] T34.53 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * y^-1, x^-1 * y^-1 * x^2 * z * x^-1 ] T34.54 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * z ] T34.55 : Triangle type {5,10,10} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, z * y * x^2 * z^2, y * x^-1 * y^-1 * x * z^-1 * y ] T34.56 : Triangle type {5,18,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z^2 ] T34.57 : Triangle type {5,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^3 * y^-1 * z * y^-1 * z^9 * y^-1 * z ] T34.58 : Triangle type {5,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z * y^-1 * z^9 * y^-1 * z ] T34.59 : Triangle type {6,6,18} Group order 108 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z^3 ] T34.60 : Triangle type {6,6,18} Group order 108 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z * y * x * y^-1 * x * z^3 ] T34.61 : Triangle type {6,6,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^7 * y * z^-5 * x * z^5 ] T34.62 : Triangle type {6,6,18} Group order 108 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y^-1 * z^-1 * x^-1 * y * x * z^3 * y * x * z^2 * y * z^-1 * x^-1 * z ] T34.63 : Triangle type {6,6,51} Group order 102 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y^-1 * z^-1 * x^-1 * y * z^-4 * x^-1 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T34.64 : Triangle type {6,9,9} Group order 108 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, x^-1 * y^-1 * x^2 * y^-1 * z ] T34.65 : Triangle type {6,9,9} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * z^4 * y^-1 * z ] T34.66 : Triangle type {6,12,16} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T34.67 : Triangle type {6,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x * z^-2 ] T34.68 : Triangle type {6,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-3 * x * z * y^-1 ] T34.69 : Triangle type {6,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-4 * z^4 * y^-3 ] T34.70 : Triangle type {6,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^9 * x * y^-4 * z ] T34.71 : Triangle type {6,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y^4 ] T34.72 : Triangle type {9,27,27} Group order 81 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^-2 * z^2 * y^-1 * z * y^-3 ] T34.73 : Triangle type {9,27,27} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * x * y^-4 ] T34.74 : Triangle type {10,16,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-10 ] T34.75 : Triangle type {10,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T34.76 : Triangle type {10,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-2 * y^2 * z^-2 ] T34.77 : Triangle type {10,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * z^3 ] T34.78 : Triangle type {12,12,21} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-1 * x * z^3 ] T34.79 : Triangle type {15,25,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-5 * y^4 * x^-2 ] T34.80 : Triangle type {15,25,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, y^-1 * z^9 ] T34.81 : Triangle type {15,25,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z, y^-2 * z^4 * x * y^-4 ] T34.82 : Triangle type {15,25,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^4 * z^-2 * x^7 * y^-1 * x * y^-1 * x ] T34.83 : Triangle type {16,16,20} Group order 80 Chiral action Defining relators: [ x * y * z, y * x^-2 * y * z^-1, y^-1 * z * x^-1 * z^2 ] T34.84 : Triangle type {16,16,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T34.85 : Triangle type {18,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^10 * x^-1 * y ] T34.86 : Triangle type {18,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^4 * x^-6 ] T34.87 : Triangle type {24,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-4 * x^4 * z^-8 ] T34.88 : Triangle type {24,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * y * x^-7 * y^2 * x^-1 ] T34.89 : Triangle type {24,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^12 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T34.90 : Triangle type {24,36,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * y^-3 * z, x^-1 * z^3 * x^-6 ] T34.91 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-4 * z * y^-7 * x * y^-3 * z * y^-2 ] T34.92 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-3 * z^4 * x^-6 ] T34.93 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, (x^-6 * y * x^-2)^2 ] T34.94 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^19 * x^-2 * z^3 ] T34.95 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, y^-1 * z^5 * y^-4 ] T34.96 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^4 * x^-1 * z^4 ] T34.97 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^2 * y^-1 * z^9 ] T34.98 : Triangle type {35,70,70} Group order 70 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-35, y * z^-1 ] T34.99 : Triangle type {36,36,36} Group order 72 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * x^-6 ] T34.100 : Triangle type {69,69,69} Group order 69 Reflexible action Defining relators: [ x^-2 * y^-1, y^29 * x^-1 * y^5, x * z^-1 ] T34.101 : Triangle type {69,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-4 * x * y^-3 ] T34.102 : Triangle type {69,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-3 * y^4 * z^-4 ] T34.103 : Triangle type {69,69,69} Group order 69 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^4 * x^-3 * y^3 ] Genus 35 T35.1 : Triangle type {2,4,8} Group order 544 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T35.2 : Triangle type {2,4,8} Group order 544 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * x * z ] T35.3 : Triangle type {2,4,12} Group order 408 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z ] T35.4 : Triangle type {2,4,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 * x * y * z^-7 ] T35.5 : Triangle type {2,4,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z^4 * y * z^-2 * x * z * y^-1 * z^-5 ] T35.6 : Triangle type {2,4,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 * x * y^-1 * z^-7 ] T35.7 : Triangle type {2,6,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, x * z^2 * y * x * z * y^-1 * z^-5 ] T35.8 : Triangle type {2,6,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, y * z^-3 * x * y^-1 * z^-4 ] T35.9 : Triangle type {2,6,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^11 * y * z^-2 * x * z^3 * y * z^-7 * x * y^-1 * z^-8 * x * z ] T35.10 : Triangle type {2,8,8} Group order 272 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * y * z^-1 * x * z ] T35.11 : Triangle type {2,8,8} Group order 272 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, z^2 * y * x * y^-1 * z^-2 * x ] T35.12 : Triangle type {2,8,8} Group order 272 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x ] T35.13 : Triangle type {2,8,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-5 * x * z^4 * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T35.14 : Triangle type {2,8,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^7 * y * z^-2 * x * z^2 * y * z^-2 * x * y^-1 * z^-8 * x ] T35.15 : Triangle type {2,12,12} Group order 204 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y^-1 * z * y^-2 * z^-1 * x * z * y^-1 ] T35.16 : Triangle type {2,12,16} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^7 * y * x * z * y * x * y * x * y^-1 * z^-3 * x * z ] T35.17 : Triangle type {2,12,16} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^-2 * x * z * y^-1 * z^-4, y^12 ] T35.18 : Triangle type {2,12,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y * z^-3 * x * z * y^-1 * z^-3 * x, y^12 ] T35.19 : Triangle type {2,16,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * x * z^5 ] T35.20 : Triangle type {2,16,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y * z^-1 * x * z * y^-1 * z^-3, (y^-5 * z^3)^2 ] T35.21 : Triangle type {2,20,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-9 * z^3 * y^-5 * z^3 ] T35.22 : Triangle type {2,20,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^8 * y^-11 ] T35.23 : Triangle type {2,21,21} Group order 168 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y * z^-1, y^2 * z^-1 * y^6 * z^-2 * y^8 * z^-2 ] T35.24 : Triangle type {2,22,77} Group order 154 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-4 * z^5 ] T35.25 : Triangle type {2,71,142} Group order 142 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^57 * y^-12 * z ] T35.26 : Triangle type {2,72,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-11 * y^23 * z^-1 ] T35.27 : Triangle type {2,72,72} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^58 * y^-13 ] T35.28 : Triangle type {2,140,140} Group order 140 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^56 * y^-12 * z ] T35.29 : Triangle type {3,15,30} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z * y^-2 * x * y^-1 * z ] T35.30 : Triangle type {3,20,20} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^6 * z^-1 * y^2 * z^-1 ] T35.31 : Triangle type {3,105,105} Group order 105 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-1 * z * y^-6 * z^2 ] T35.32 : Triangle type {4,4,4} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^3 * z * x^-1 * z * x^-1 * y^-1 ] T35.33 : Triangle type {4,4,4} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T35.34 : Triangle type {4,4,6} Group order 204 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z ] T35.35 : Triangle type {4,4,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-8 * x * z^3 * y * z^-1 * x^-1 * y * z^-4 ] T35.36 : Triangle type {4,4,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-8 * x * z^3 * y * z^-1 * x^-1 * z * y^-1 * z^-3 ] T35.37 : Triangle type {4,4,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^23 * y * x^-1 * y * x^-1 * z^11 ] T35.38 : Triangle type {4,4,70} Group order 140 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^22 * y * x^-1 * z^12 ] T35.39 : Triangle type {4,6,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y^-1 * z^-2 * x * z^4 ] T35.40 : Triangle type {4,8,8} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-1 * z * y * x^-1 * z * y^-1 * z * y^-1 ] T35.41 : Triangle type {4,8,8} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x * y^-2 * x * z * y ] T35.42 : Triangle type {4,8,8} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-2 * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T35.43 : Triangle type {4,8,8} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * y^-1 * z, (x * y^-2)^2 ] T35.44 : Triangle type {4,8,8} Group order 136 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y * z^-1 * y^2 * z^-2 ] T35.45 : Triangle type {4,8,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y^-1 * z^-3 * x^-1 * y^-1 * x^-1 * z^4 ] T35.46 : Triangle type {4,8,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y^-1 * z^-3 * x^-1 * y^-1 * x * z^4 ] T35.47 : Triangle type {4,10,12} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^-2 * z^-1, z^-1 * x * z * y^-1 * x * y^-1 * z^-2 ] T35.48 : Triangle type {4,10,12} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^10 ] T35.49 : Triangle type {4,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z * y^-5 * z * y^-1 * z * y^-4 * z * y^-1 ] T35.50 : Triangle type {4,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-3 ] T35.51 : Triangle type {6,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, x * z * y * x^-1 * y^-1 * z^-2 ] T35.52 : Triangle type {6,6,10} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, x^-1 * z * y^-1 * x * z^2, z^2 * y * x^-1 * z * y^-1 ] T35.53 : Triangle type {6,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^2 * y * z^-1 ] T35.54 : Triangle type {6,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, x^6 ] T35.55 : Triangle type {6,16,16} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^6 * z^-1 * y * z^-1 * y * x * z^-1 * y * z^-1 * y * z^-1 * y ] T35.56 : Triangle type {6,16,16} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 * z^-2 ] T35.57 : Triangle type {6,18,45} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T35.58 : Triangle type {6,18,45} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^2 ] T35.59 : Triangle type {6,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y * z^-3 ] T35.60 : Triangle type {8,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y * x * z^3 * y * z^-1 * x * z^4 ] T35.61 : Triangle type {8,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-6 * x^-1 * y * x^-1 * y * z^-4 ] T35.62 : Triangle type {8,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, y * z^-2 * x^-1 * z^3 ] T35.63 : Triangle type {8,8,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^2 * y * x^-1 * z^3 ] T35.64 : Triangle type {8,11,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * y^-1 * z^3 ] T35.65 : Triangle type {8,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (y * z^-1 * y)^2 ] T35.66 : Triangle type {8,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T35.67 : Triangle type {8,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^5 * y^-2 * z * y^-1 * z^2 ] T35.68 : Triangle type {8,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^4 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T35.69 : Triangle type {8,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^9 ] T35.70 : Triangle type {8,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-4 ] T35.71 : Triangle type {8,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-2 * z^2 ] T35.72 : Triangle type {10,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x * z^-1 * x^3 * z^-3 ] T35.73 : Triangle type {10,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-2 * z^2, x^-10 ] T35.74 : Triangle type {10,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-10 ] T35.75 : Triangle type {10,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-10 ] T35.76 : Triangle type {11,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-11 ] T35.77 : Triangle type {11,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-11 ] T35.78 : Triangle type {11,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-1 * y * x^-5 * y^3 * z^-1 * y^2 ] T35.79 : Triangle type {11,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-1 * z^3 * x^-2 * z^4 ] T35.80 : Triangle type {11,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^3 * x^-2 * z^4 ] T35.81 : Triangle type {12,12,42} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * x * z^3 ] T35.82 : Triangle type {15,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^3 * y^-3 * x^6 * y^-1 * x * y^-1 * x ] T35.83 : Triangle type {15,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^-3 * x^8 * y^-2 ] T35.84 : Triangle type {16,16,40} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * x * z^2 ] T35.85 : Triangle type {16,16,40} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-3 * y * x^2 * z^-3 ] T35.86 : Triangle type {16,16,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T35.87 : Triangle type {20,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^6 * y^-2 ] T35.88 : Triangle type {20,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, x * y^-1 * z^2 * y^-3 * x * y^-4 ] T35.89 : Triangle type {20,20,20} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * x^4 * y^-4 ] T35.90 : Triangle type {36,72,72} Group order 72 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-36, y * z^-1 ] T35.91 : Triangle type {36,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * y^-3 * x^6 * y^-1 * x^2 ] T35.92 : Triangle type {36,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z^5 * y^-4 ] T35.93 : Triangle type {36,72,72} Group order 72 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^13 * z^-2 * x^4 ] T35.94 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x^-2 * y^-1, y^30 * x^-1 * y^5, x * z^-1 ] T35.95 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-17 * x * y^-6 ] T35.96 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-2 * x * y^-5 * x * y^-4 * x * y^-1 * x ] T35.97 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^10 * x^-2 ] T35.98 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-5 * x^5 * y^-1 * x ] T35.99 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-4 * x^5 * y^-1 ] T35.100 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-4 * x * z^-3 ] T35.101 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-5 * z^4 ] T35.102 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-2 * z^2 * x^-7 ] T35.103 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-2 * z^5 * y^-1 * z^3 ] T35.104 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-7 * y^3 ] T35.105 : Triangle type {71,71,71} Group order 71 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x^7 * z^-1 * x^4 ] Genus 36 T36.1 : Triangle type {2,3,16} Group order 672 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * z^-2 * x * z * y * x * y^-1 * z^3 * y^-1 * z^-2 ] T36.2 : Triangle type {2,3,16} Group order 672 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z^3 ] T36.3 : Triangle type {2,3,20} Group order 600 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z^11 * y * z^-1 * x * z^6 * y^-1 ] T36.4 : Triangle type {2,4,14} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-6 * y * x * y^-1 * z^-1 * y * z^-6 ] T36.5 : Triangle type {2,4,39} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-23 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T36.6 : Triangle type {2,4,74} Group order 296 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 * x * y * z^-7 ] T36.7 : Triangle type {2,4,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 * x * y^-1 * z^-7 ] T36.8 : Triangle type {2,5,15} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z^2 * y^-1 * z^-3, (z^-1 * y)^5 ] T36.9 : Triangle type {2,6,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^8, y * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T36.10 : Triangle type {2,6,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T36.11 : Triangle type {2,6,10} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^10 ] T36.12 : Triangle type {2,6,10} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^10 ] T36.13 : Triangle type {2,6,38} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^26 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^5 ] T36.14 : Triangle type {2,8,26} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z * y * x * y * x * y^-1 * z^-3 * x * z^8 ] T36.15 : Triangle type {2,10,20} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, y * z^-2 * x * z^8 * y * x * z^3 * y^-1 * z^-1 * x * z^3 ] T36.16 : Triangle type {2,10,20} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^7 * y * x * z * y * x * z * y * x * y * x * y^-1 * z^-3 * x * y^-1 * z^-1 * x * z ] T36.17 : Triangle type {2,10,20} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^10 ] T36.18 : Triangle type {2,10,90} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * z^-3 * x * z^6 ] T36.19 : Triangle type {2,14,14} Group order 196 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * z * y * x * y^-6 * z^-1 * x * y^-1 * z^-1 * y, z^-3 * x * z^2 * y * x * z * y * x * y * x * y^-1 * z^-4 ] T36.20 : Triangle type {2,14,14} Group order 196 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-2 * z * y^-2 * z * y^-3 * z * y^-3 * z, y^-14 ] T36.21 : Triangle type {2,14,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-2 * x * z * y^-1 * z^-3 * x, y^-3 * z^3 * y^-5 * z^3 ] T36.22 : Triangle type {2,20,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-4 * y^2 * z^-4 ] T36.23 : Triangle type {2,21,28} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y^-3 * z^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T36.24 : Triangle type {2,26,78} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-1 * y^9 * z^-3 * y^9 * z^-2 * y ] T36.25 : Triangle type {2,38,76} Group order 152 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-13 * y^11 * z^-1 * y^12 ] T36.26 : Triangle type {2,39,39} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-35 * z * y^-1 ] T36.27 : Triangle type {2,50,75} Group order 150 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-13 * z^2 * y^-8 * z * y^-1 ] T36.28 : Triangle type {2,73,146} Group order 146 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^59 * y^-12 * z ] T36.29 : Triangle type {2,74,74} Group order 148 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^60 * y^-13 ] T36.30 : Triangle type {2,144,144} Group order 144 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^58 * y^-12 * z ] T36.31 : Triangle type {3,3,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, z * y * x^-1 * y * x^-1 * y^-1 * z^-2 * x ] T36.32 : Triangle type {3,3,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^3 * y * x^-1 * z^2 * y^-1 * x ] T36.33 : Triangle type {3,3,10} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^10 ] T36.34 : Triangle type {3,3,38} Group order 228 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-4 * x^-1 * z^4 ] T36.35 : Triangle type {3,3,73} Group order 219 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^4 * y * x * z^4 ] T36.36 : Triangle type {3,7,21} Group order 147 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^3 * x^-1 * y^-1 * z^2, y^-7 ] T36.37 : Triangle type {3,10,10} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^10 ] T36.38 : Triangle type {3,10,10} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3, z * y * z^-1 * x^-1 * y^-3 ] T36.39 : Triangle type {3,10,10} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^3 * x^-1 * y^-1 * x * z * y^3 ] T36.40 : Triangle type {3,20,30} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2 ] T36.41 : Triangle type {3,37,111} Group order 111 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-26 * z * y^-1 * z * y^-7 * z ] T36.42 : Triangle type {3,38,38} Group order 114 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^25 * y^-3 * z * y^-7 * z ] T36.43 : Triangle type {3,108,108} Group order 108 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-25 * z * y^-1 * z * y^-6 * z^2 ] T36.44 : Triangle type {4,4,7} Group order 196 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * x^-1 * z^3 ] T36.45 : Triangle type {4,4,37} Group order 148 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * y * x * z^-3 ] T36.46 : Triangle type {4,4,37} Group order 148 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^24 * y * x^-1 * y * x^-1 * z^11 ] T36.47 : Triangle type {4,4,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^23 * y * x^-1 * z^12 ] T36.48 : Triangle type {4,6,6} Group order 168 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x^-1 * z * y * x * z^2 * y ] T36.49 : Triangle type {4,10,15} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x * z^-1 * x^-1 * z * x^-1 * z ] T36.50 : Triangle type {4,25,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-7 * z * y^-2 ] T36.51 : Triangle type {4,26,26} Group order 104 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 * z^-2 * y^4 * z^-1 * y^14 * z^-1 ] T36.52 : Triangle type {4,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T36.53 : Triangle type {5,6,6} Group order 150 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T36.54 : Triangle type {5,6,6} Group order 150 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T36.55 : Triangle type {5,19,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z^10 * y^-1 * z * y^-1 * z^2 ] T36.56 : Triangle type {5,20,20} Group order 100 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y * z^-1, y^2 * x^2 * z^2 ] T36.57 : Triangle type {5,20,20} Group order 100 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-6 * z * y^-2 ] T36.58 : Triangle type {5,20,20} Group order 100 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, y^2 * x^2 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T36.59 : Triangle type {5,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-2 * z * y^-7 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 ] T36.60 : Triangle type {5,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2 ] T36.61 : Triangle type {5,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-5 ] T36.62 : Triangle type {5,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-10 ] T36.63 : Triangle type {5,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z^2 ] T36.64 : Triangle type {5,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 ] T36.65 : Triangle type {6,6,19} Group order 114 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, x * z^-2 * y * z^-2 ] T36.66 : Triangle type {6,6,19} Group order 114 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^2 ] T36.67 : Triangle type {6,6,19} Group order 114 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^7 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^5 ] T36.68 : Triangle type {6,12,48} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T36.69 : Triangle type {7,13,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-4 * x^2 * y^-5 ] T36.70 : Triangle type {7,14,14} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 ] T36.71 : Triangle type {7,14,14} Group order 98 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, x^-7 ] T36.72 : Triangle type {7,14,14} Group order 98 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * z^-1 * x)^2, y^-1 * x * y^-1 * x * y^-2, x^-7 ] T36.73 : Triangle type {7,14,14} Group order 98 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-6 * z * y^-1 * z * y^-2 * z * y^-1 * z ] T36.74 : Triangle type {7,14,14} Group order 98 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-7, x^-1 * y^-1 * x^3 * z * x^-2 ] T36.75 : Triangle type {7,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^9 ] T36.76 : Triangle type {7,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z^9 ] T36.77 : Triangle type {7,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^5 * y^-4 ] T36.78 : Triangle type {8,8,13} Group order 104 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z * y * z^-1 * x * z^2, x^8 ] T36.79 : Triangle type {8,8,13} Group order 104 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^8 * y^-1 * x^-1 * z^4 ] T36.80 : Triangle type {9,10,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9, y^-1 * z * y^-4 * x * y^-4 ] T36.81 : Triangle type {9,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^5 * x^-1 * z^4 ] T36.82 : Triangle type {9,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * y^-4 ] T36.83 : Triangle type {9,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * y^-1 * z^3 ] T36.84 : Triangle type {10,10,10} Group order 100 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, (x * y^-2)^2, y^2 * x * z * y^3 * x * y^-3 * z ] T36.85 : Triangle type {10,10,10} Group order 100 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^4 * z^-2, y^-10 ] T36.86 : Triangle type {10,10,10} Group order 100 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y, x^10, y^-10 ] T36.87 : Triangle type {10,10,10} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-4 * x * y^-4 ] T36.88 : Triangle type {10,10,45} Group order 90 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^4 * y * x^-1 * z^4 ] T36.89 : Triangle type {10,10,45} Group order 90 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-1 * x * z^3 * y^-1 * x * z * y * z^-2 ] T36.90 : Triangle type {10,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^4 * x^-2 * z^4 ] T36.91 : Triangle type {10,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^4 * x^-1 * z^4 ] T36.92 : Triangle type {12,14,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x * y^-5 * x^5 * y^-2 ] T36.93 : Triangle type {12,21,28} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^2 * y^-3 * x^3 * z^-3 * x^4 ] T36.94 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-2 * z^4 * x^-4 * z^2 ] T36.95 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z^4 * x^-5 * z ] T36.96 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-6 ] T36.97 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * z^-2 * x^5 * y^-2 * x^4 ] T36.98 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, x^-1 * z^3 * x^-3 * z^3 ] T36.99 : Triangle type {13,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-5 * x^5 * y^-1 ] T36.100 : Triangle type {14,14,42} Group order 84 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T36.101 : Triangle type {14,14,42} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^3 ] T36.102 : Triangle type {14,14,42} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3 ] T36.103 : Triangle type {14,21,21} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, y * z^-1 * y * x^-1 * z * y, (z^-1 * x)^3 ] T36.104 : Triangle type {14,21,21} Group order 84 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x * z^-1 * x^3 * z^-1 * x * z^-1 ] T36.105 : Triangle type {14,21,21} Group order 84 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z * x^-2 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T36.106 : Triangle type {16,20,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, y^3 * x^-1 * y * x^-10 * y * x^-1 ] T36.107 : Triangle type {16,20,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, y^-1 * z^5 * y^-1 * z^3 ] T36.108 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-1 * z * y^-2 * x^4 * y^-4 ] T36.109 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-8 * z * y^-1 * x * y^-1 ] T36.110 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-2 * x^5 * z^-4 * x * z^-1 * x * z^-1 * x ] T36.111 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^6 * z^-2 * x^8 * z^-1 * x * z^-1 * x ] T36.112 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z^4 * x^-6 ] T36.113 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^3 * x^-5 * z ] T36.114 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * x^-1 * z^4 ] T36.115 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, y^-1 * z * y^-1 * z^9 ] T36.116 : Triangle type {19,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-19 ] T36.117 : Triangle type {20,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-1 * y^3 * z^-1 * y ] T36.118 : Triangle type {20,20,40} Group order 80 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^2 * z^-2 ] T36.119 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-6 * z, y^-1 * z^3 * y^-1 * x * y^-4 ] T36.120 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y^3 * x^-2 ] T36.121 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-3 * x^2 * z^-2 * x^5 * z^-4 * x * z^-1 * x * z^-2 ] T36.122 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^10 * z^-1 * x^2 * y^-1 * x^12 ] T36.123 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T36.124 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-9 * y ] T36.125 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, y^-1 * z^8 ] T36.126 : Triangle type {25,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-7 * x * y^-5 ] T36.127 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, y^-3 * x^-1 * z^2 ] T36.128 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^5 * y^-1 * z^-2 ] T36.129 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, z * x^-1 * z * x^-1 * z^3 ] T36.130 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, (y * z^-2)^2 ] T36.131 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^2 * z^-1 * y^2 * x^-1 * y^3 * z^-1 ] T36.132 : Triangle type {26,26,39} Group order 78 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^6 * y^-2 * z^4 * x^-1 * z * x^-1 ] T36.133 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-3 * x^4 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T36.134 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-3 * x^5 * z^-1 * x^3 ] T36.135 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-8 * y^2 ] T36.136 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-1 * z^5 * y^-3 * z ] T36.137 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^6 * x^-2 * z^4 ] T36.138 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^6 * x^-1 * z^4 ] T36.139 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, y^-2 * z^2 * y^-2 * x * y^-4 ] T36.140 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * x^2 * z^-9 ] T36.141 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * z * y^-3 * x^4 * y^-2 ] T36.142 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^3 * x^-3 * z^3 ] T36.143 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-9 * x * z^-9 ] T36.144 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-4 * x^4 * y^-5 * x * y^-1 * x ] T36.145 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-7 * z, y^4 * x^-1 * y^4 ] T36.146 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^5 * x^-2 * y^4 * z^-1 * y^2 ] T36.147 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-2 * z^4 * x * y^-4 ] T36.148 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-3 * z^4 * x^-6 ] T36.149 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^20 * x^-1 * z^4 ] T36.150 : Triangle type {37,74,74} Group order 74 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-37, y * z^-1 ] T36.151 : Triangle type {38,38,38} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^12 * x^-2 * y^6 ] T36.152 : Triangle type {38,38,38} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, (y^3 * z^-1 * y^3)^2 ] T36.153 : Triangle type {38,38,38} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, (x * y^-4)^2 ] T36.154 : Triangle type {38,38,38} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-5 * z, y^-1 * z^5 * y^-3 * z ] T36.155 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x^-2 * y^-1, y^31 * x^-1 * y^5, x * z^-1 ] T36.156 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-17 * x^2 * y^-6 ] T36.157 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 * x * y^-5 * x * y^-4 * x * y^-1 * x ] T36.158 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^12 ] T36.159 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-6 * x^5 * y^-2 ] T36.160 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-4 * y^5 ] T36.161 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, x^-7 * y^3 ] T36.162 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y, z^4 * x^-1 * z^4 ] T36.163 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^6 * x^-1 * z^4 ] T36.164 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z^4 * x^-5 * z ] T36.165 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-4 * x^2 * z^-5 * y * z^-4 ] T36.166 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z^3 * y^-1 * x * y^-4 ] T36.167 : Triangle type {73,73,73} Group order 73 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^4 * y^-3 * z ] Genus 37 T37.1 : Triangle type {2,3,8} Group order 1728 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z, z^2 * y * z^-1 * x * z^2 * y * z^-3 * x * z * y * x^2 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x, z * y * x * z * y * z^-1 * x * z * y * x * z^2 * y * x * z * y * x * z^2 * y^-1 * z^-3 * x ] T37.2 : Triangle type {2,3,12} Group order 864 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z * y * x * z^3 * y * x * z * y^-1 * x * y^-1 * z^-1 * x * z^2, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.3 : Triangle type {2,3,15} Group order 720 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1, z^-5 * x * z * y * x^2 * z * y^-1 * z^-9 ] T37.4 : Triangle type {2,3,18} Group order 648 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-1 * x * z * y * x * y^-1 * z^2 * y^-1 * z^-1 * x * z, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T37.5 : Triangle type {2,3,18} Group order 648 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^6 * y * x * y^-2 * z^-4 * x, z^2 * y * x * z^3 * y * x * y^-1 * x * z * y^-1 * z^-1 * x * z, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T37.6 : Triangle type {2,3,24} Group order 576 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-3 * x * z, z * y * x * z * y * z^-1 * x * z * y * x * z^7 ] T37.7 : Triangle type {2,3,24} Group order 576 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.8 : Triangle type {2,3,24} Group order 576 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-2 * x * z * y * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * z^-4 * x * y * z^-2 * x * z^7 ] T37.9 : Triangle type {2,4,6} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-2 ] T37.10 : Triangle type {2,4,8} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^-1 * z * y^-1 * z * y * z^-1 * x * y^-1 * z^3 * y^-1 * z ] T37.11 : Triangle type {2,4,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T37.12 : Triangle type {2,4,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-2 * x * z * y^2 * z^-1 * x * z^3 ] T37.13 : Triangle type {2,4,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x ] T37.14 : Triangle type {2,4,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T37.15 : Triangle type {2,4,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2 * y * z^-1)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.16 : Triangle type {2,4,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y^-1 * z)^6, z^-12 ] T37.17 : Triangle type {2,4,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, (y^-1 * z)^6 ] T37.18 : Triangle type {2,4,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y^-1 * z)^6, z^-4 * x * z^5 * y^-1 * z^-2 ] T37.19 : Triangle type {2,4,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^-1 * z^2 * y^-1 * z * y^-1 * z^-3 * x * z, (y^-1 * z)^6 ] T37.20 : Triangle type {2,4,20} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y^-1 * z)^6, x * z * y * x * z * y * x * y^-1 * z^-5 ] T37.21 : Triangle type {2,4,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-26 * x * z^5 * y * z^-2 * x * y^-1 * z^-5 ] T37.22 : Triangle type {2,4,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^10 * y * x * z * y^-1 * z^-4 ] T37.23 : Triangle type {2,4,76} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-68 * x * y * z^-7 ] T37.24 : Triangle type {2,4,148} Group order 296 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 * x * y^-1 * z^-7 ] T37.25 : Triangle type {2,6,6} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 ] T37.26 : Triangle type {2,6,6} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z * y^-1 * z^-2 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y * x ] T37.27 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T37.28 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.29 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T37.30 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2 ] T37.31 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^12 ] T37.32 : Triangle type {2,6,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-2 * x * z^3 * y^-1 * z^-6 ] T37.33 : Triangle type {2,6,15} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y * x * z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-5 * x * z^2 ] T37.34 : Triangle type {2,6,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z * y * x * y^-1 * z^-5 ] T37.35 : Triangle type {2,6,39} Group order 234 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^13 * y * x * z^15 * y * z^-1 * x * z^8 ] T37.36 : Triangle type {2,6,111} Group order 222 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^17 * y * z^-2 * x * z^7 * y^-1 * z^-8 * x * z ] T37.37 : Triangle type {2,8,8} Group order 288 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y^-2 * z * y^3 * x * y^-1 * z^-1 * x ] T37.38 : Triangle type {2,8,8} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T37.39 : Triangle type {2,8,8} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, (y^-1 * z)^6 ] T37.40 : Triangle type {2,9,18} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.41 : Triangle type {2,10,10} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x ] T37.42 : Triangle type {2,12,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^12 ] T37.43 : Triangle type {2,12,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y^-1 * z * y^-3 * z^-2 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.44 : Triangle type {2,12,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12 ] T37.45 : Triangle type {2,12,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^12 ] T37.46 : Triangle type {2,12,12} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z * y^-3 * z * y^-1 * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.47 : Triangle type {2,12,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, z * y^-4 * z * y^-1 * z^-1 * x ] T37.48 : Triangle type {2,12,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-2)^2 ] T37.49 : Triangle type {2,12,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^12 ] T37.50 : Triangle type {2,12,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12 ] T37.51 : Triangle type {2,20,20} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T37.52 : Triangle type {2,21,42} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-7 * y^11 * z^-1 ] T37.53 : Triangle type {2,27,54} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-1 * y^10 * z^-15 ] T37.54 : Triangle type {2,40,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-14 * y^11 * z^-1 * y^12 * z^-1 ] T37.55 : Triangle type {2,40,40} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^6 * z^-1 * y^8 * z^-2 ] T37.56 : Triangle type {2,75,150} Group order 150 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^61 * y^-12 * z ] T37.57 : Triangle type {2,76,76} Group order 152 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^62 * y^-13 ] T37.58 : Triangle type {2,148,148} Group order 148 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^60 * y^-12 * z ] T37.59 : Triangle type {3,3,4} Group order 864 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y * x * z^-1 * x^-1, x * z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y, z * y * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y^-1 * x ] T37.60 : Triangle type {3,3,4} Group order 864 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y * x * z^-1 * x^-1, x * z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y, z * y^-1 * z^-1 * x^-1 * z * y * x^-1 * z * y * x * z * y^-1 * z^-1 * x ] T37.61 : Triangle type {3,3,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, (x^-1 * y^-1 * z^-1 * x * z * y)^2 ] T37.62 : Triangle type {3,3,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x, (x^-1 * z^3 * y)^2 ] T37.63 : Triangle type {3,3,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z^-1 * x^-1 * y * x * z * y * x^-1 * y * x * z^-1 * x^-1 * y^-1 ] T37.64 : Triangle type {3,3,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, y * x^-1 * y * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T37.65 : Triangle type {3,3,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z * y)^2 ] T37.66 : Triangle type {3,3,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-3 ] T37.67 : Triangle type {3,3,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 ] T37.68 : Triangle type {3,3,21} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1, (y * x^-1 * z)^3 ] T37.69 : Triangle type {3,4,4} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-2 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.70 : Triangle type {3,4,4} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * x^-1 * y^-2 * x * z * y^-1 * z * y^-1 ] T37.71 : Triangle type {3,4,6} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x * z^-3 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T37.72 : Triangle type {3,4,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1 ] T37.73 : Triangle type {3,4,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y * x * z ] T37.74 : Triangle type {3,4,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * z^2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T37.75 : Triangle type {3,4,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x * z^-3 * x^-1 * y^-1 * x * z^2 * y^-1 * z^-1 ] T37.76 : Triangle type {3,4,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T37.77 : Triangle type {3,5,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^-5, z * y * z^-1 * x^-1 * z^2 ] T37.78 : Triangle type {3,5,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, y^-1 * z^-1 * y * x * z^2 ] T37.79 : Triangle type {3,6,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3 ] T37.80 : Triangle type {3,6,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * y)^3, y^-2 * z^-1 * y^2 * x * y^-1 * z * y * x^-1 ] T37.81 : Triangle type {3,6,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y * z^-1 * y ] T37.82 : Triangle type {3,6,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x^-1 * y^-1 * z * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 ] T37.83 : Triangle type {3,6,6} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^6, (z^-1 * y)^3 ] T37.84 : Triangle type {3,6,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z * y^2 * x^-1 * z^2, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x ] T37.85 : Triangle type {3,6,14} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-2 * x^-1 * z^3 ] T37.86 : Triangle type {3,6,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * x^-1 * z^2 * y^-1 ] T37.87 : Triangle type {3,6,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^-1 * y^2 * x^-1 * y^3 ] T37.88 : Triangle type {3,6,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T37.89 : Triangle type {3,6,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.90 : Triangle type {3,6,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.91 : Triangle type {3,8,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y ] T37.92 : Triangle type {3,8,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * z * y^-1 * z^-1 ] T37.93 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T37.94 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T37.95 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^2 * z^-2 * y^6 * z^-1 * y ] T37.96 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^-2 * z^2 * y^-2 * z * x^-1 * z^3 * y^-1 * z ] T37.97 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T37.98 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-1 * x * z * y, y^-1 * z * y^-5 * z * y^-1 * z^3 ] T37.99 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, y * x * y^-2 * x * y^-2 * z ] T37.100 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.101 : Triangle type {3,12,12} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.102 : Triangle type {3,14,42} Group order 126 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-1 * y^5 * z^-2 * y * z^-1 ] T37.103 : Triangle type {3,15,15} Group order 135 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-3 * y^2 * z^-1 * y^6 * z^-2 * y ] T37.104 : Triangle type {3,30,30} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^7 * z^-1 * y * z^-1 ] T37.105 : Triangle type {3,38,114} Group order 114 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-27 * z * y^-1 * z * y^-7 * z ] T37.106 : Triangle type {3,39,39} Group order 117 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-28 * z * y^-1 * z * y^-7 * z ] T37.107 : Triangle type {3,111,111} Group order 111 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-26 * z * y^-1 * z * y^-8 ] T37.108 : Triangle type {4,4,4} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x * z^-1 * y * x^-2 * z * y^2 * z^-1, y * z^-1 * y * x^-2 * y^-1 * z^2 * x^-1 ] T37.109 : Triangle type {4,4,4} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-1 * z^-1 * y * x^-2 * z * y^-1 * z^-1 * x, x * z * x^-1 * y * x^-1 * y * z^-1 * y * z^-1 ] T37.110 : Triangle type {4,4,4} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.111 : Triangle type {4,4,4} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.112 : Triangle type {4,4,5} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1 * x ] T37.113 : Triangle type {4,4,5} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.114 : Triangle type {4,4,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * x * z^-1 * x^-1 * z * y * x, z^-3 * x^-1 * z^2 * y^-1 ] T37.115 : Triangle type {4,4,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T37.116 : Triangle type {4,4,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, z^6, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * x^-1 * y^-1 ] T37.117 : Triangle type {4,4,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x ] T37.118 : Triangle type {4,4,10} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T37.119 : Triangle type {4,4,20} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x^2 * z * y * z^-1 ] T37.120 : Triangle type {4,4,20} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z * y^-1 * z^-2 ] T37.121 : Triangle type {4,4,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-11 * x * y^-1 * x * y^-1 * z^-7 ] T37.122 : Triangle type {4,4,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^3 * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * z ] T37.123 : Triangle type {4,4,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^7 * y * z^-4 * x^-1 * y^-1 * z^-7 * x ] T37.124 : Triangle type {4,4,38} Group order 152 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^25 * y * x^-1 * y * x^-1 * z^11 ] T37.125 : Triangle type {4,4,74} Group order 148 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^24 * y * x^-1 * z^12 ] T37.126 : Triangle type {4,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T37.127 : Triangle type {4,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, x^-1 * z * y * x * z * y ] T37.128 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * z^-1 * y * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T37.129 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T37.130 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-2 * y * x^-1 * y^-1 * z^-1, x * z * y^2 * z^-2 ] T37.131 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * x)^3 ] T37.132 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.133 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T37.134 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6 ] T37.135 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^4 * y^-1 * z^-3 * x * z^4 ] T37.136 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T37.137 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z * x^-1 ] T37.138 : Triangle type {4,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y * x * y^-1 * x * z^2, y^6 ] T37.139 : Triangle type {4,8,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x * y^-2 * x * z^-2 ] T37.140 : Triangle type {4,8,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y^-1 * z * y^-1 * x * z * x^-1 ] T37.141 : Triangle type {4,8,8} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T37.142 : Triangle type {4,8,8} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T37.143 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.144 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T37.145 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T37.146 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.147 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x^-1 * z^7 * y^-1 * x^-1 * z^4 ] T37.148 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z * y * x^-1 * z * y * x * z^4 ] T37.149 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.150 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.151 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.152 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.153 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^6 ] T37.154 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.155 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * z * y * x * z^4 ] T37.156 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^4 ] T37.157 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, y * z^-3 * x^-1 * z^4 ] T37.158 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y * z^-3 * x^-1 * z^4 ] T37.159 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T37.160 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.161 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^2 * y * z^-1 * x^-1 * z^4 ] T37.162 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^-3 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T37.163 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * z^-3 * x^-1 * z^4 ] T37.164 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, y * z^-3 * x^-1 * z^4 ] T37.165 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^8, (y * z^-1 * y^2)^2 ] T37.166 : Triangle type {4,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^8, (y * z^-1 * y^2)^2 ] T37.167 : Triangle type {4,14,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T37.168 : Triangle type {4,18,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-5 * z * y^-1 ] T37.169 : Triangle type {4,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T37.170 : Triangle type {4,50,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 * y^-1 * z ] T37.171 : Triangle type {5,10,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, x^-1 * y^-1 * x^2 * z * x^-1 ] T37.172 : Triangle type {5,10,22} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * y^-1 * z^-1, y^-2 * x^2 * z * y^-1 ] T37.173 : Triangle type {5,10,22} Group order 110 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^2 * y^-2, y * x^-1 * y^-1 * x * z^2 ] T37.174 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T37.175 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, (x * z * y)^2 ] T37.176 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6, y * x^-3 * z * x^-2 ] T37.177 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^6, y^6, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T37.178 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T37.179 : Triangle type {6,6,6} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.180 : Triangle type {6,6,15} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y * x^-1 * y * x^-1 * z^3 ] T37.181 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (z^-1 * y)^3 ] T37.182 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^-2 * x^2 * y^-2, (z^-1 * y)^3 ] T37.183 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, (z^-1 * y)^3 ] T37.184 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2 ] T37.185 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, (z^-1 * y)^3 ] T37.186 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (z^-1 * y)^3, y^-1 * z * y * x^-1 * y^-3 ] T37.187 : Triangle type {6,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3 ] T37.188 : Triangle type {6,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-1 * z * y^-2 ] T37.189 : Triangle type {6,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-3 * y^2 * z^-3 ] T37.190 : Triangle type {6,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^-1 * z^2 ] T37.191 : Triangle type {6,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2 ] T37.192 : Triangle type {6,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^4 * z^-3 ] T37.193 : Triangle type {6,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T37.194 : Triangle type {6,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z ] T37.195 : Triangle type {6,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-1 * z * y^-4 * z^7 ] T37.196 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T37.197 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T37.198 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, (x^-1 * z * y)^2 ] T37.199 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, (x^-1 * z * y)^2 ] T37.200 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^8 ] T37.201 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^8 ] T37.202 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-3 * z^2 ] T37.203 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^2 * z^-2 ] T37.204 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^8 ] T37.205 : Triangle type {8,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-2 ] T37.206 : Triangle type {8,22,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * x * y^-4 ] T37.207 : Triangle type {9,9,9} Group order 108 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y * x^-1 * z * x^-1 * y^-1 ] T37.208 : Triangle type {9,9,9} Group order 108 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, (x * z * y)^2 ] T37.209 : Triangle type {10,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3 ] T37.210 : Triangle type {10,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, (z^-1 * x)^3 ] T37.211 : Triangle type {10,15,30} Group order 90 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^10 ] T37.212 : Triangle type {12,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^-1 * y, (x * z * y)^2 ] T37.213 : Triangle type {12,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, (y * z^-1)^2 ] T37.214 : Triangle type {12,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T37.215 : Triangle type {12,12,12} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * x^4 * y^-3 ] T37.216 : Triangle type {12,21,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^2 * x^-4 * y^5 ] T37.217 : Triangle type {12,28,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-2 * z^2, y^-2 * z^2 * y^-2 * x^5 * y^-1 ] T37.218 : Triangle type {16,40,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-7 * z^2 * x^-5 * y^2 * x^-2 ] T37.219 : Triangle type {16,40,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-1 * z^5 * x * y^-4 ] T37.220 : Triangle type {16,40,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^3 * x^-5 * y^3 * z^-1 * y^3 ] T37.221 : Triangle type {16,40,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^6 * x^-2 * z^4 ] T37.222 : Triangle type {20,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^8 * x^-2 * z^4 ] T37.223 : Triangle type {20,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, x * z^-1 * x^3 * z^-3 ] T37.224 : Triangle type {20,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 * z^2 * x^-5 * y^2 * x^-2 ] T37.225 : Triangle type {20,40,40} Group order 80 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x * z^-1 * x^7 * y^-1 * x ] T37.226 : Triangle type {21,21,21} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-7 * x^3 * y^-2 ] T37.227 : Triangle type {21,21,21} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * z^-1 * x ] T37.228 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^4 * x^-2 * y * x^-1 * y^4 * x^-1 * y^5 * x^-1 * y * x^-1 ] T37.229 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z^8 ] T37.230 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z * y^-1 * z^9 ] T37.231 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y^-1 * z^3 * y^-1 * x * y^-4 ] T37.232 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * x^2 * z^-5 * y * z^-4 ] T37.233 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-2 * y^4 * z^-2 * y^4 ] T37.234 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^5 * x^-1 * z^4 ] T37.235 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z * y^-1 * z^5 * y^-4 ] T37.236 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z^3 * x^-6 ] T37.237 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-4 * z^4 * x^-5 * y * x^-1 ] T37.238 : Triangle type {26,39,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-10 * y * x^-2 * y * x^-1 * y * x^-11 ] T37.239 : Triangle type {27,27,27} Group order 81 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, x * y^-1 * x^2 * y^-2 ] T37.240 : Triangle type {27,27,27} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-4 * z * y^-5 * z^2 * y^-3 ] T37.241 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-2 * x * y^-4 ] T37.242 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-2 * y^7 ] T37.243 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-7 * z, y^-1 * z^5 * y^-2 * z^2 ] T37.244 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z^4 * x^-4 * z^2 ] T37.245 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-6 * y^3 * x^-1 ] T37.246 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, (y^4 * z^-1 * y^3)^2 ] T37.247 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z^5 * x * y^-4 ] T37.248 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y * x^-1 * y * x^-5 * y^6 ] T37.249 : Triangle type {38,76,76} Group order 76 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-38, y * z^-1 ] T37.250 : Triangle type {75,75,75} Group order 75 Reflexible action Defining relators: [ x^-2 * y^-1, y^32 * x^-1 * y^5, x * z^-1 ] T37.251 : Triangle type {75,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^3 * x^-4 * z^2 ] T37.252 : Triangle type {75,75,75} Group order 75 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-1 * z^3 * x^-4 * z^2 ] Genus 38 T38.1 : Triangle type {2,4,78} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-70 * x * y * z^-7 ] T38.2 : Triangle type {2,4,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-68 * x * y^-1 * z^-7 ] T38.3 : Triangle type {2,6,6} Group order 444 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-2 * z * y^-2 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y ] T38.4 : Triangle type {2,6,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^40 ] T38.5 : Triangle type {2,6,114} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^13 * y * x * z^14 * y * z^-8 * x * z ] T38.6 : Triangle type {2,8,15} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^2 * y * x * z^3 * y * z^-1 * x * y^-1 * z^-6 ] T38.7 : Triangle type {2,8,52} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z * y * x * y * x * y^-1 * z^-4 * x * y^-1 * z^-1 * x * z^5 ] T38.8 : Triangle type {2,10,95} Group order 190 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * x * y * z^-5 * x * z^4 ] T38.9 : Triangle type {2,12,32} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-5 * x * z * y * x * z * y * x * y^-1 * z^-6 ] T38.10 : Triangle type {2,28,42} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-2 * x * z * y^-1 * z^-3 * x, (y^-3 * z^3 * y^-1)^2 ] T38.11 : Triangle type {2,77,154} Group order 154 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^63 * y^-12 * z ] T38.12 : Triangle type {2,78,78} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^64 * y^-13 ] T38.13 : Triangle type {2,152,152} Group order 152 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^62 * y^-12 * z ] T38.14 : Triangle type {3,6,6} Group order 222 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x * z * y * x * z * y * x * z * y^-1 * z * y ] T38.15 : Triangle type {3,6,6} Group order 222 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y^2 * z^-2 * y * x^-1 * y^-1 * z^-1 * y * z^-1 * y * z^-1 ] T38.16 : Triangle type {3,40,40} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^27 * y^-3 * z * y^-7 * z ] T38.17 : Triangle type {3,114,114} Group order 114 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-27 * z * y^-1 * z * y^-6 * z^2 ] T38.18 : Triangle type {4,4,39} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * z * y * z^-1 ] T38.19 : Triangle type {4,4,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^26 * y * x^-1 * y * x^-1 * z^11 ] T38.20 : Triangle type {4,4,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^25 * y * x^-1 * z^12 ] T38.21 : Triangle type {4,8,9} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^4 * y^-1 * x^-1 * z^4 ] T38.22 : Triangle type {4,10,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^10 ] T38.23 : Triangle type {4,12,20} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^5 * y^-1 * x * z^4 ] T38.24 : Triangle type {4,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-2 * z * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T38.25 : Triangle type {4,15,15} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^2 * z^-1 * y * z^-3 * y^2 * z^-2 * y^4 ] T38.26 : Triangle type {4,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 * z^-2 * y^4 * z^-1 * y^13 * z^-1 * y ] T38.27 : Triangle type {5,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z^10 * y^-1 * z * y^-3 ] T38.28 : Triangle type {5,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^14 * y^-1 * z * y^-1 * z^2 ] T38.29 : Triangle type {6,6,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^8 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^5 ] T38.30 : Triangle type {6,6,57} Group order 114 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 * y * x * z^3 * y * x * z^2 * y * z^-1 * x^-1 * z ] T38.31 : Triangle type {6,32,32} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T38.32 : Triangle type {8,8,26} Group order 104 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^-1 * y * x^-2 * z^2 * y ] T38.33 : Triangle type {8,8,26} Group order 104 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^7 * y^-1 * x * y^-1 * x * z^4 ] T38.34 : Triangle type {8,44,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * y^-3 * z ] T38.35 : Triangle type {8,44,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z * y^-1 * z^9 ] T38.36 : Triangle type {10,18,45} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y^-5 * x^-1 * z^4 ] T38.37 : Triangle type {12,12,16} Group order 96 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x^4 * y^-1 * x * y^-1 * x, y^-1 * x * z * y^-1 * x * y^-1 * x * z^4 ] T38.38 : Triangle type {12,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-2 * z * x^-1 * z^4 * x^-4 * z^2 ] T38.39 : Triangle type {14,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x^-2 * z^4 * x^-4 * z^2 ] T38.40 : Triangle type {14,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^7 * z^-4 * x * z^-1 * x * z^-1 * x ] T38.41 : Triangle type {14,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y * x^-5 * y^3 * z^-1 * y ] T38.42 : Triangle type {15,18,18} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, y^4 * z^-2 ] T38.43 : Triangle type {20,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-6 * y * x^-1 * y * x^-8 * y * x^-1 * y * x^-1 ] T38.44 : Triangle type {20,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-2 * z^2, x * y^-4 * x^6 ] T38.45 : Triangle type {20,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y * x^-1 * y * z^-2 * y^8 ] T38.46 : Triangle type {21,28,28} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^5 * y^-1 * x * z^-1 ] T38.47 : Triangle type {21,28,28} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, z^-1 * x * z^-1 * x * z^-2 ] T38.48 : Triangle type {21,28,28} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1 ] T38.49 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^39, y * z^-1 ] T38.50 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^13 * x^-1 * y * x^-1 ] T38.51 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T38.52 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^2 * x^-7 ] T38.53 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-6 * x * z^-3 * x^2 * z^-9 ] T38.54 : Triangle type {39,78,78} Group order 78 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T38.55 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x^-2 * y^-1, y^33 * x^-1 * y^5, x * z^-1 ] T38.56 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-9 * y ] T38.57 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z^4 * x^-4 * z^2 ] T38.58 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-7 * x^5 * z^-4 * x * z^-1 * x * z^-2 ] T38.59 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-4 * y^6 ] T38.60 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-6 * y * x^-9 ] T38.61 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y, z^-5 * y * z^-5 * y * z^-1 * y * z^-2 ] T38.62 : Triangle type {77,77,77} Group order 77 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-1 * z^8 ] Genus 39 T39.1 : Triangle type {2,3,12} Group order 912 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z^2 * y * x * z * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T39.2 : Triangle type {2,4,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-26 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T39.3 : Triangle type {2,4,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-72 * x * y * z^-7 ] T39.4 : Triangle type {2,4,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-26 * x * z^5 * y * z^-2 * x * z^2 * y^-1 * z^-3 ] T39.5 : Triangle type {2,4,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-70 * x * y^-1 * z^-7 ] T39.6 : Triangle type {2,8,9} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * y * z^-4 ] T39.7 : Triangle type {2,8,28} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^16 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z^5 ] T39.8 : Triangle type {2,8,28} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-4 * x * z^4 * y * z^-2 * x * z^7 * y * x * y^-1 * z^-8 ] T39.9 : Triangle type {2,8,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-7 * x * z^8 * y * x * y^-1 * z^-9 ] T39.10 : Triangle type {2,8,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-5 * x * z^3 * y * z^-2 * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T39.11 : Triangle type {2,10,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, z^2 * y^3 * x * z * y^-1 ] T39.12 : Triangle type {2,12,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^9 * y * x * z^4 * y^-1 * z^-1 * x ] T39.13 : Triangle type {2,12,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^12 ] T39.14 : Triangle type {2,14,91} Group order 182 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * x * z^3 * y * z^-2 * x * y * z^-5 ] T39.15 : Triangle type {2,16,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^6 * y * z^-5 * x ] T39.16 : Triangle type {2,16,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z * y * x * y^-1 * z^-5 * x ] T39.17 : Triangle type {2,28,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-2 * y^10 * z^-3 * y^12 * z^-1 ] T39.18 : Triangle type {2,42,42} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-38 * z * y^-1 ] T39.19 : Triangle type {2,79,158} Group order 158 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^65 * y^-12 * z ] T39.20 : Triangle type {2,80,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-14 * y^11 * z^-1 * y^11 * z^-1 * y ] T39.21 : Triangle type {2,80,80} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^66 * y^-13 ] T39.22 : Triangle type {2,156,156} Group order 156 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^64 * y^-12 * z ] T39.23 : Triangle type {3,3,6} Group order 456 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z * y^-1 * z^-1 * x * z * y * x^-2 * z * y * x * z * y * x * z ] T39.24 : Triangle type {3,3,79} Group order 237 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-2 * x^-1 * z^3 * y^-1 * z^-1 * x^-1 ] T39.25 : Triangle type {3,4,10} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-3 * x^-1 * y^-1 * z^-3 ] T39.26 : Triangle type {3,4,12} Group order 228 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-2 * x^-1 * y * x * z^2 * y * x ] T39.27 : Triangle type {3,9,9} Group order 171 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y * x * y^-1, y * z^-1 * y * x^-1 * z^3 ] T39.28 : Triangle type {3,9,9} Group order 171 Chiral action Defining relators: [ x^3, x * y * z, z^-2 * y * x * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * z * y^2 ] T39.29 : Triangle type {3,9,9} Group order 171 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^-1 ] T39.30 : Triangle type {3,40,120} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-29 * z * y^-1 * z * y^-7 * z ] T39.31 : Triangle type {3,117,117} Group order 117 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-28 * z * y^-1 * z * y^-6 * z^2 ] T39.32 : Triangle type {4,4,21} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-15 * x^-1 * y^-1 * x * z * y * z^-3 ] T39.33 : Triangle type {4,4,40} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T39.34 : Triangle type {4,4,40} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * y^-1 * z^-1 ] T39.35 : Triangle type {4,4,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y * x * z^6 ] T39.36 : Triangle type {4,4,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-12 * x * z * y * z^-6 ] T39.37 : Triangle type {4,4,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^7 * y^-1 * z^-4 * x^-1 * y^-1 * z^-7 * x ] T39.38 : Triangle type {4,4,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-12 * x * y^-1 * z^-7 ] T39.39 : Triangle type {4,4,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^26 * y * x^-1 * z^12 ] T39.40 : Triangle type {4,8,32} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-3 * x^-1 * z^4 ] T39.41 : Triangle type {4,8,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x^-1 * z^7 * y^-1 * x * z^4 ] T39.42 : Triangle type {4,8,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^7 * y^-1 * z^-2 * x^-1 * z^6 ] T39.43 : Triangle type {4,9,9} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-6 * z ] T39.44 : Triangle type {4,10,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^10 ] T39.45 : Triangle type {4,12,30} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T39.46 : Triangle type {4,12,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T39.47 : Triangle type {4,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-2 * y * x * z^-1 * y ] T39.48 : Triangle type {4,27,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.49 : Triangle type {4,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z * y^-5 * z * y^-1 * z * y^-2 * z ] T39.50 : Triangle type {4,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.51 : Triangle type {4,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-24 * z * y^-2 * z ] T39.52 : Triangle type {4,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.53 : Triangle type {4,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T39.54 : Triangle type {6,10,10} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^3 * x * y^-1 * z^-1 ] T39.55 : Triangle type {6,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z^5 * x^-1 * z^5 * y^-1 * z^3 ] T39.56 : Triangle type {6,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-1 * z^3 ] T39.57 : Triangle type {6,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-1 * y^3 * z^-3 ] T39.58 : Triangle type {7,15,15} Group order 105 Chiral action Defining relators: [ x * y * z, y * x^2 * z, z * x^-2 * y * x^-1, z * y^-1 * z^3 * y^-2 * z * y^-6 * z ] T39.59 : Triangle type {7,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-3 * z * y^-4 * z^4 * y^-1 ] T39.60 : Triangle type {7,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 * z ] T39.61 : Triangle type {7,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z * y^-4 * x * y^-4 * z ] T39.62 : Triangle type {8,8,14} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y * z^-1 * x^-1 * y^-1 * z^-4 * x^-1 * y^-1 * x * z^4 ] T39.63 : Triangle type {8,8,14} Group order 112 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 * y^-1 * x^-1 * z^4 ] T39.64 : Triangle type {8,8,52} Group order 104 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x * z^4 ] T39.65 : Triangle type {8,8,52} Group order 104 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x * z * y^-1 * x * z^3 * y^-1 * z^-1 * x * z^4 ] T39.66 : Triangle type {8,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T39.67 : Triangle type {8,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^-3 * x^-1 * z * y * z^-1 ] T39.68 : Triangle type {8,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T39.69 : Triangle type {8,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^8 ] T39.70 : Triangle type {8,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * z^-1 * y * z^-2 ] T39.71 : Triangle type {8,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^2 * x^-1 * y^3 ] T39.72 : Triangle type {8,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^5 * y^-4 * z * y^-1 ] T39.73 : Triangle type {8,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T39.74 : Triangle type {9,30,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9, z^-5 * y^4 * z^-1 ] T39.75 : Triangle type {9,30,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9, y^-5 * x * z^4 * y^-1 ] T39.76 : Triangle type {12,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T39.77 : Triangle type {12,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T39.78 : Triangle type {12,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z * y^-1 * z * x^-1 * z^3 ] T39.79 : Triangle type {12,12,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T39.80 : Triangle type {12,16,16} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * y * z^-1 * y * x^2 * z^-1 * y * z^-1 ] T39.81 : Triangle type {12,16,16} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^6 * z^-2 ] T39.82 : Triangle type {14,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^2 * y^-5 * x^5 * y^-1 * x^2 ] T39.83 : Triangle type {14,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-5 * x^5 * y^-1 ] T39.84 : Triangle type {14,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^3 * y^-3 * x^3 * y^-3 * x^5 ] T39.85 : Triangle type {21,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-6 * y^4 ] T39.86 : Triangle type {21,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-5 * x^3 * y^-3 * z * y^-1 * x * y^-2 ] T39.87 : Triangle type {21,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-5 * x * y^-1 * x * y^-1 * x^8 * y^-1 * x^3 ] T39.88 : Triangle type {21,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-2 * z^4 * x^-6 ] T39.89 : Triangle type {21,28,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-1 * z * y^-1 * z^5 * y^-4 ] T39.90 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-27 ] T39.91 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^4 * x^-4 * z^2 ] T39.92 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^3 * x^-6 ] T39.93 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-1 * x * z^-4 * x^2 * z^-5 * y * z^-4 ] T39.94 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y^3 * x^-5 * y^5 * x^-1 * y ] T39.95 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-6 * x^2 * y^-1 * z^3 * y^-2 ] T39.96 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z * x^-1 * z^4 * x^-2 * z^4 ] T39.97 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^8 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T39.98 : Triangle type {27,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z * x^-1 * z^4 * x^-2 * z^4 ] T39.99 : Triangle type {28,28,42} Group order 84 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x^-3 * y * x^-1 * z ] T39.100 : Triangle type {28,28,42} Group order 84 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * x^-1 * z * x^-6 ] T39.101 : Triangle type {28,28,42} Group order 84 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * x * z^-5 * x * z^-1 * y * z^-1 * y * z^-1 ] T39.102 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-5 * y^3 * z^-1 * y^2 ] T39.103 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z^5 * y^-4 ] T39.104 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^22 * x^-1 * z^4 ] T39.105 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T39.106 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^40, y * z^-1 ] T39.107 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 * z^2 * x^-8 ] T39.108 : Triangle type {40,80,80} Group order 80 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-2 * z^2 * x^-7 ] T39.109 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x^-2 * y^-1, y^34 * x^-1 * y^5, x * z^-1 ] T39.110 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-18 * x^4 * y^-3 * x * y^-2 ] T39.111 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^6 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T39.112 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-4 * y^5 * x^-1 * y * x^-1 ] T39.113 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-3 * z * y^-3 * x^5 * y^-1 * x * y^-1 ] T39.114 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-5 * y^3 * z^-1 * y^2 ] T39.115 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^-5 * x * y^-4 ] T39.116 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^4 * x^-1 * z^4 ] T39.117 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^7 * x^-1 * z^4 ] T39.118 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z^4 * x^-5 * z ] T39.119 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-3 * z^4 * x^-6 ] T39.120 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-6, y^-1 * z^5 * y^-2 * z^2 ] T39.121 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-2 * y^6 * z^-1 * y^3 ] T39.122 : Triangle type {79,79,79} Group order 79 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-2 * z * y^-3 * x^4 * y^-2 ] Genus 40 T40.1 : Triangle type {2,3,12} Group order 936 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, z^-1 * x * z * y * x * z * y * x * z * y * x * z^2 * y^-2 * z^-1 * x * z * y^-1 * z^-1 ] T40.2 : Triangle type {2,4,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y * x * y^-2 * z^3 * y^-1 * z^-2 ] T40.3 : Triangle type {2,4,82} Group order 328 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-74 * x * y * z^-7 ] T40.4 : Triangle type {2,4,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-72 * x * y^-1 * z^-7 ] T40.5 : Triangle type {2,6,6} Group order 468 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-1 * x * z * y^-1 * z * y^2 * z^-1 * x * z * y^-1 * z^-1 ] T40.6 : Triangle type {2,6,6} Group order 468 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y^-1 * z^2 * y * x * z * y * z^-2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T40.7 : Triangle type {2,6,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T40.8 : Triangle type {2,6,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-2 * z^-1 * y * x * y^-1 * z^-1 ] T40.9 : Triangle type {2,6,16} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-6 * x * z^2 * y * z^-1 * x * y * z^-1 * x * z * y^-1 * z^-2 ] T40.10 : Triangle type {2,6,42} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * z * y * x * y^-1 * z^-4 ] T40.11 : Triangle type {2,6,42} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^15 * y * x * z^8 * y * x * z * y * z^-9 * x * z^6 ] T40.12 : Triangle type {2,6,42} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^31 * y * z^-8 * x * z^2 ] T40.13 : Triangle type {2,6,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-14 * x * z^15 * y * z^-1 * x * z^7 * y^-1 * z^-1 ] T40.14 : Triangle type {2,7,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^8, (z * y^-1 * z)^3 ] T40.15 : Triangle type {2,7,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, y * x * z * y^2 * x * y^-1 * z^-1, z^8 ] T40.16 : Triangle type {2,9,18} Group order 234 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-2 ] T40.17 : Triangle type {2,9,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T40.18 : Triangle type {2,10,22} Group order 220 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^7 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^5 ] T40.19 : Triangle type {2,12,18} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, z^2 * y^-3 * z^-1 * x * z^2 ] T40.20 : Triangle type {2,12,18} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^10 * y * x * y * z^-4 * x * z^2 ] T40.21 : Triangle type {2,12,18} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^5 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^3 ] T40.22 : Triangle type {2,12,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-9 * x * z^4 * y^-1 * z^-2 ] T40.23 : Triangle type {2,18,90} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-7 * z^3 * y^-5 * z^3 ] T40.24 : Triangle type {2,22,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-11 * z^3 * y^-5 * z^3 ] T40.25 : Triangle type {2,30,30} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^7 * z^-1 * y * z^-1 ] T40.26 : Triangle type {2,30,30} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-3 * y^10 * z^-3 * y^14 ] T40.27 : Triangle type {2,34,85} Group order 170 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-2 * x * z * y^-1 * z^-2 * x, y^-6 * z^3 * y^-6 * z^2 ] T40.28 : Triangle type {2,42,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-16 * y^11 * z^-1 * y^11 * z^-1 * y ] T40.29 : Triangle type {2,81,162} Group order 162 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^67 * y^-12 * z ] T40.30 : Triangle type {2,82,82} Group order 164 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^14 * z^-68 ] T40.31 : Triangle type {2,160,160} Group order 160 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^66 * y^-12 * z ] T40.32 : Triangle type {3,3,6} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, x * z * y * x * z * y * x^-1 * y * x * z^-1 * x * z^-1 ] T40.33 : Triangle type {3,3,42} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * z^-1 * x * z^5 ] T40.34 : Triangle type {3,4,5} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2 ] T40.35 : Triangle type {3,4,5} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * x^-1 * z^2, (x^-1 * z * y * z^-1 * y)^2 ] T40.36 : Triangle type {3,6,6} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T40.37 : Triangle type {3,6,6} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z ] T40.38 : Triangle type {3,6,6} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, x * z * y * z^-1 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T40.39 : Triangle type {3,6,6} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * y^2 * x^-1 * z * y^-1 * z^2 ] T40.40 : Triangle type {3,6,6} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * x^-1 * y^-1 * z^-2 * y * z^-1 * y ] T40.41 : Triangle type {3,6,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^2 ] T40.42 : Triangle type {3,6,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, y * x^-1 * y * x^-1 * z^3 ] T40.43 : Triangle type {3,6,28} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, y * z^-2 * y * x^-1 * z^3 ] T40.44 : Triangle type {3,12,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-2 * x^-1 * y^-1 * x * y^-2 * z^-1 ] T40.45 : Triangle type {3,12,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T40.46 : Triangle type {3,12,12} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * y ] T40.47 : Triangle type {3,12,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, z^-1 * x^-1 * z * y * x * z^2 * y ] T40.48 : Triangle type {3,12,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2 ] T40.49 : Triangle type {3,16,16} Group order 144 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^2 * z^-2 * y^5 * z^-3 * y^4 ] T40.50 : Triangle type {3,16,16} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, z^-1 * y^2 * z^-1 * y^6 * z^-2 * y^3 * z^-1 ] T40.51 : Triangle type {3,22,33} Group order 132 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^4 * y^-3 * z * y^-1 * z ] T40.52 : Triangle type {3,41,123} Group order 123 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-30 * z * y^-1 * z * y^-7 * z ] T40.53 : Triangle type {3,42,42} Group order 126 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-31 * z * y^-1 * z * y^-7 * z ] T40.54 : Triangle type {3,42,42} Group order 126 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^29 * y^-3 * z * y^-7 * z ] T40.55 : Triangle type {3,42,42} Group order 126 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-3 * y ] T40.56 : Triangle type {3,120,120} Group order 120 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-29 * z * y^-1 * z * y^-8 ] T40.57 : Triangle type {4,4,15} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * x^-1 * z^2 * y^-1 * z^-3 ] T40.58 : Triangle type {4,4,15} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * x^-1 * y * x^-1 * z^3 ] T40.59 : Triangle type {4,4,41} Group order 164 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * y^-1 * x * z^-3 * y ] T40.60 : Triangle type {4,4,41} Group order 164 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-28 * x^-1 * y^-1 * z^-12 ] T40.61 : Triangle type {4,4,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y * x^-1 * z^6 ] T40.62 : Triangle type {4,6,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, x * z * y^2 * z^-2 ] T40.63 : Triangle type {4,6,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x^-1 * z ] T40.64 : Triangle type {4,6,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^6, z^-2 * y * x * z * y ] T40.65 : Triangle type {4,6,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * x^-1 ] T40.66 : Triangle type {4,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * z^-1 * y * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T40.67 : Triangle type {4,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^6 ] T40.68 : Triangle type {4,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^4 * y^-1 * z^-3 * x^-1 * z^4 ] T40.69 : Triangle type {4,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T40.70 : Triangle type {4,7,7} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^3 * x^-1 * y^-1 * x * z ] T40.71 : Triangle type {4,7,7} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (y^-1 * x)^3, (z^-1 * x)^3 ] T40.72 : Triangle type {4,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2 ] T40.73 : Triangle type {4,12,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y^-1 * z^-2 * x * z^4 ] T40.74 : Triangle type {4,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-3 * y * z^-4 * y^2 * z^-4 ] T40.75 : Triangle type {4,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-2 * z * y^-9 * z * y^-1 ] T40.76 : Triangle type {4,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T40.77 : Triangle type {5,21,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^3 * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T40.78 : Triangle type {5,22,22} Group order 110 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-3 * z * y^-12 * z * y^-1 * z * y^-2 * z ] T40.79 : Triangle type {5,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-7 * z * y^-2 ] T40.80 : Triangle type {5,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-10 ] T40.81 : Triangle type {6,6,6} Group order 156 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^6, y^-1 * x * y^-1 * x^2 * y^-2 * x ] T40.82 : Triangle type {6,6,6} Group order 156 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, y * x^-1 * y * x^-1 * y * x * z ] T40.83 : Triangle type {6,6,8} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * x^2 * z^2, y^6 ] T40.84 : Triangle type {6,6,8} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^8 ] T40.85 : Triangle type {6,6,8} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^8 ] T40.86 : Triangle type {6,6,8} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, z^8 ] T40.87 : Triangle type {6,6,21} Group order 126 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * x * z^2 ] T40.88 : Triangle type {6,6,21} Group order 126 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, x^6, (y^-1 * x)^3 ] T40.89 : Triangle type {6,6,21} Group order 126 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^6, (y^-1 * x)^3 ] T40.90 : Triangle type {6,6,21} Group order 126 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^-2 * y * x * z^-2 ] T40.91 : Triangle type {6,6,21} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * z^-1 * x * z^3 ] T40.92 : Triangle type {6,6,21} Group order 126 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^10 * y^-1 * x * y * x^-1 * z^9 ] T40.93 : Triangle type {6,6,21} Group order 126 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 * y * x * y^-1 * z^-3 * x * z^7 ] T40.94 : Triangle type {6,6,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^10 * y^-1 * z^-4 * x^-1 * y * z^-1 * x^-1 * z^3 ] T40.95 : Triangle type {6,10,12} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^10 ] T40.96 : Triangle type {6,17,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-8 * z ] T40.97 : Triangle type {6,18,18} Group order 108 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^3 * x^-1 * y * z^-1 * y ] T40.98 : Triangle type {6,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^4 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T40.99 : Triangle type {6,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3 ] T40.100 : Triangle type {6,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3 ] T40.101 : Triangle type {6,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y^2 * z^-2, y * x^-3 * z * x^-2 ] T40.102 : Triangle type {6,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-1 * z * y^-12 * z * y^-1 * z^2 ] T40.103 : Triangle type {6,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-4 ] T40.104 : Triangle type {9,9,9} Group order 117 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x * z * y * x^-1 * y^-1 * z * y ] T40.105 : Triangle type {9,9,18} Group order 108 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, x * z * y^-1 * x * z^-2 ] T40.106 : Triangle type {9,9,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, (y^-1 * x)^3, (z^-1 * x)^3 ] T40.107 : Triangle type {9,11,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-4 * x * y^-4 ] T40.108 : Triangle type {9,12,12} Group order 108 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^4 * y^-1 * z^-1, y * z^-1 * y^3 * z^-3 * y * z^-1 * y^2 ] T40.109 : Triangle type {9,12,12} Group order 108 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * y^-2, z^-1 * y * x^2 * z^-2, z^-2 * x^2 * z * y^-1 ] T40.110 : Triangle type {9,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^-12 ] T40.111 : Triangle type {9,12,12} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-3 * z * x^-2, x^-9 ] T40.112 : Triangle type {9,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9, y * z^-3 * y * x^-1 * y^5 ] T40.113 : Triangle type {9,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9, y * z^-4 * y^4 * z^-1 ] T40.114 : Triangle type {10,10,11} Group order 110 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^10 ] T40.115 : Triangle type {10,10,11} Group order 110 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-2, y^-1 * z * x^-1 * z^2, x * y^-1 * x^5 * y^-3 ] T40.116 : Triangle type {10,10,11} Group order 110 Chiral action Defining relators: [ x * y * z, z * y * x * z, y * z^-1 * x^2 * z^-1 * y, x^10 ] T40.117 : Triangle type {10,10,11} Group order 110 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, y * x^-1 * y^-1 * x * z^2, x^-1 * y^2 * x^-4 * y * x^-2 ] T40.118 : Triangle type {10,10,11} Group order 110 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^6 * y^-1 * x^-1 * z^4 ] T40.119 : Triangle type {10,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y^-7 * z^2 ] T40.120 : Triangle type {10,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, z * y^-4 * x^-1 * z^4 ] T40.121 : Triangle type {10,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y * z^-8 ] T40.122 : Triangle type {11,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-11 ] T40.123 : Triangle type {11,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, (x^-2 * z^4)^2 ] T40.124 : Triangle type {11,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^4 * x^-2 * z^4 ] T40.125 : Triangle type {11,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z * x^-1 * z^4 * x^-3 * z^3 ] T40.126 : Triangle type {11,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-11 ] T40.127 : Triangle type {12,12,48} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z * y * z^-2 * x^-1 * z^4 ] T40.128 : Triangle type {15,18,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y^4 * x^-5 * y^2 * x^-4 ] T40.129 : Triangle type {15,18,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-2 * x^5 * y^-4 ] T40.130 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, (z^-1 * y)^3 ] T40.131 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, y^4 * z^-2 ] T40.132 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-4 * y^-1 * x * z, y^2 * x^-3 * y^4 ] T40.133 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-3 * y * x^-9 * z * x^-2 ] T40.134 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-1 * x * z^-1 * x^5 * z^-4 ] T40.135 : Triangle type {15,30,30} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-15 ] T40.136 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T40.137 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T40.138 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^9 * z^-4 * x * z^-1 * x^3 ] T40.139 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^17 ] T40.140 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, y^-1 * z^9 ] T40.141 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-1 * z^4 * x^-2 * z^4 ] T40.142 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^6 * x^-1 * z^4 ] T40.143 : Triangle type {17,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-4, x^-1 * z^4 * x^-5 * z ] T40.144 : Triangle type {18,18,45} Group order 90 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T40.145 : Triangle type {18,18,45} Group order 90 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * y^-1 * z^2 * x^-1 * z^4 ] T40.146 : Triangle type {21,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z * y^-2 * x^6 * y^-3 ] T40.147 : Triangle type {21,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-5 * x^4 * z^-4 * x * z^-1 * x * z^-2 ] T40.148 : Triangle type {21,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^9 * z^-1 * x^7 * y^-1 * x^4 ] T40.149 : Triangle type {22,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^4 * x^-1 * y * x^-2 * y * z^-1 * y^3 ] T40.150 : Triangle type {22,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-3 * x^2 * y^-3 ] T40.151 : Triangle type {22,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-2 * x * z^-1 * x * z^-3 ] T40.152 : Triangle type {22,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1 ] T40.153 : Triangle type {22,22,44} Group order 88 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^5 * x^-1 * z * x^-1 * z^4 ] T40.154 : Triangle type {28,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-10 * z^2 * y^-3 ] T40.155 : Triangle type {28,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * x^-1 * z^4 ] T40.156 : Triangle type {28,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^2 * x^-5 * y * z^-3 * y^3 ] T40.157 : Triangle type {28,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^16 * z^-1 * x^8 * y^-1 * x^3 ] T40.158 : Triangle type {28,42,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-6 * x^3 * z^-9 ] T40.159 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-6 * x * y^-1 * x * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T40.160 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^3 * z^-2 * x^10 ] T40.161 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-3 * x^5 * z^-1 * x^2 ] T40.162 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^5 * y^-3 * z ] T40.163 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T40.164 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-4 * z^5 * y^-1 * z^3 * y^-1 ] T40.165 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-4 * x * z^-5 * y * z^-1 * y * z^-2 ] T40.166 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-8 * y^2 ] T40.167 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-1 * y * z^-5 * y * z^-5 * y * z^-1 * y * z^-2 ] T40.168 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-4 * x^7 ] T40.169 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T40.170 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-3 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T40.171 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-6 * z * y^-8 * x^2 * y^-5 ] T40.172 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * y^-2 * z^2, y^-5 * x^5 * y^-1 ] T40.173 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^2 * x^-1 * z^4 * x^-2 * z^4 ] T40.174 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-2 * z * y^-3 * x^4 * y^-2 ] T40.175 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T40.176 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-4 * z^2 ] T40.177 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^22 * x^-2 * z^4 ] T40.178 : Triangle type {41,82,82} Group order 82 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^41, y * z^-1 ] T40.179 : Triangle type {42,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-14 * x^2 * y^-6 ] T40.180 : Triangle type {42,42,42} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^2 * x^-7, y^-1 * z^5 * y^-1 * z^3 ] T40.181 : Triangle type {81,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-2 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T40.182 : Triangle type {81,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, z^6 * x^-1 * z^4 ] T40.183 : Triangle type {81,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x * y^-5 * x^7 ] T40.184 : Triangle type {81,81,81} Group order 81 Reflexible action Defining relators: [ x^-2 * y^-1, y^35 * x^-1 * y^5, x * z^-1 ] T40.185 : Triangle type {81,81,81} Group order 81 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-4 * z * y^-3 * x^2 * y^-5 ] Genus 41 T41.1 : Triangle type {2,3,16} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1, z^4 * y * z^-1 * x * z * y * x * z^-1 * x * y^-1 * z^-2 * x * z^7 ] T41.2 : Triangle type {2,3,16} Group order 768 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.3 : Triangle type {2,4,6} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 ] T41.4 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-1 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T41.5 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, y * x * z^2 * y^-2 * z^-3 * y * z^-1 ] T41.6 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, (z^-1 * y)^5, x * z * y * x * z * y^-1 * z^2 * y^-1 * z^2 * y^-1 * z^-1 * y ] T41.7 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T41.8 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T41.9 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z ] T41.10 : Triangle type {2,4,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * x ] T41.11 : Triangle type {2,4,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-4 * x * y^-1 * z^-2 * y * z^-1 * y ] T41.12 : Triangle type {2,4,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-12, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T41.13 : Triangle type {2,4,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T41.14 : Triangle type {2,4,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y * z^-1 * y * x * z * y^2 * z^-1 * x * z^3, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T41.15 : Triangle type {2,4,20} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-3 * x * z^7 * y^-1 * x * z^2 * y^-1 * z^-4 * x * y^-1 * z^-1 ] T41.16 : Triangle type {2,4,20} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-2 * x * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-5 * y ] T41.17 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-8 * x * z^8 * y * x * z * y^-1 * z^-5 ] T41.18 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, z^-4 * x * z^5 * y^-1 * z^-2 ] T41.19 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^5 * y^-1 * z^-2 ] T41.20 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T41.21 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-10 * x * z^7 * y * x * z^2 * y^-1 * z^-3 ] T41.22 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z * y * z^-4 * x * z^4 * y^-1 * z^-1 * x ] T41.23 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T41.24 : Triangle type {2,4,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, x * z^5 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T41.25 : Triangle type {2,4,36} Group order 360 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z^5 * y * x * z^2 * y * x * z^7 * y^-1 * z^-1 ] T41.26 : Triangle type {2,4,44} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-29 * x * z^6 * y * z^-1 * x * z * y^-1 * z^-5 ] T41.27 : Triangle type {2,4,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-76 * x * y * z^-7 ] T41.28 : Triangle type {2,4,164} Group order 328 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-74 * x * y^-1 * z^-7 ] T41.29 : Triangle type {2,5,6} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 ] T41.30 : Triangle type {2,5,6} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, (y * z^-1)^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T41.31 : Triangle type {2,5,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1, z * y * z^-2 * y^2 * z^-2 * x * y^-1 ] T41.32 : Triangle type {2,5,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, (y * z^-2 * y * z^-1)^2 ] T41.33 : Triangle type {2,6,6} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1 * y * z^-1 * y)^2, z^-1 * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T41.34 : Triangle type {2,6,8} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T41.35 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T41.36 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8 ] T41.37 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z^8, (y * z^-1 * y)^4 ] T41.38 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T41.39 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T41.40 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-3 * z^-2 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.41 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T41.42 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, z * y * x * z * y^2 * z^-2 * y * x ] T41.43 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z, z * y * x * z * y^2 * z^-2 * y * x ] T41.44 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.45 : Triangle type {2,6,8} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T41.46 : Triangle type {2,6,33} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^5 * y * x * y * x * z * y^-1 * z^-2 * x ] T41.47 : Triangle type {2,6,123} Group order 246 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-15 * x * z^15 * y * z^-1 * x * y^-1 * z^-8 ] T41.48 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, z^-1 * y * z^-1 * y^3 * z^-3 * y ] T41.49 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-2 * z^-1 * x ] T41.50 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z ] T41.51 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T41.52 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.53 : Triangle type {2,8,8} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T41.54 : Triangle type {2,8,16} Group order 256 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y^-1 * z * y^-2 * z^-2 * x * z, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T41.55 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y * z^-6 ] T41.56 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T41.57 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T41.58 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T41.59 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T41.60 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T41.61 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, z^-1 * x * z * y * x * y^-1 * z^-4 ] T41.62 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z * y * z^-2 * x * y^-1 * z^-3 * x ] T41.63 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4 ] T41.64 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4 ] T41.65 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T41.66 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, x * z^3 * y^-1 * z^-4 ] T41.67 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-3 * z^-5 ] T41.68 : Triangle type {2,8,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^-2 * x * y^-3 * z^-5 ] T41.69 : Triangle type {2,8,24} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, x * z^2 * y^-2 * z * y^-1 * z^-2 ] T41.70 : Triangle type {2,8,24} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y * x * y^-1 * z^-2 * x ] T41.71 : Triangle type {2,8,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^16 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^4 ] T41.72 : Triangle type {2,8,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-3 * x * z^5 * y * z^-2 * x * z^7 * y * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T41.73 : Triangle type {2,12,12} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z * y^-2 * z^-1 ] T41.74 : Triangle type {2,12,12} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, y^12 ] T41.75 : Triangle type {2,12,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T41.76 : Triangle type {2,12,12} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * z * y^-3 * z * y^-1 * z^-2, z^-1 * y * x * y^-2 * z^-1 * y * z^-2, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T41.77 : Triangle type {2,14,14} Group order 224 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-2, y^-14 ] T41.78 : Triangle type {2,16,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^4 * y * z^-1 * x * z^6 ] T41.79 : Triangle type {2,16,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-7 * z^2, z^4 * y * z^-1 * x * z^6 ] T41.80 : Triangle type {2,16,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T41.81 : Triangle type {2,16,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-7 * z^2, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T41.82 : Triangle type {2,20,20} Group order 200 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * y * z^-1 * y^2 * z^-1 * y^9 * z^-3 * y ] T41.83 : Triangle type {2,20,20} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y^-1 * z^2 * y^-1 * z^4 * y^-9 * z * y^-1 * z ] T41.84 : Triangle type {2,20,20} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-1 * z^-1 * x * z * y * x * y^-5 * z^-5 * x ] T41.85 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-10 * y^9 * z^-2 * y ] T41.86 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^8 * z^-1 * y^2 * z^-1 ] T41.87 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^7 * z^-2 * y * z^-2 ] T41.88 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-8 * z * y^-2 * z ] T41.89 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^9 * z^-1 * y * z^-1 ] T41.90 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^10 * y^-1 * z * y^-10 * z ] T41.91 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^10 * z^-1 * y^7 * z^-2 * y ] T41.92 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-1 * y ] T41.93 : Triangle type {2,24,24} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^-1 * y^6 * z^-1 * y^2 * z^-2 ] T41.94 : Triangle type {2,36,36} Group order 180 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^-2 * y * z^-1 * y * z^-1 * y^7 * z^-5 ] T41.95 : Triangle type {2,44,44} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-17 * y^11 * z^-1 * y^14 ] T41.96 : Triangle type {2,83,166} Group order 166 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^68 * y^-14 ] T41.97 : Triangle type {2,84,84} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-68 * y ] T41.98 : Triangle type {2,164,164} Group order 164 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^14 * z^-67 * y ] T41.99 : Triangle type {3,3,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^8, y * x * z * y * x^-1 * z * y^-1 * x * z ] T41.100 : Triangle type {3,3,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^8 ] T41.101 : Triangle type {3,3,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^8, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.102 : Triangle type {3,4,4} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T41.103 : Triangle type {3,4,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, y * z^-2 * x^-1 * z^3 ] T41.104 : Triangle type {3,4,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, x^-1 * z * y^-1 * z^-2 * x * z^-4 ] T41.105 : Triangle type {3,5,5} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T41.106 : Triangle type {3,5,5} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, (x^-1 * z * y)^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T41.107 : Triangle type {3,6,6} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * x^-1 * y * x^-1 * y^-1 * x * z, y * z^-1 * y * x^-1 * y^-1 * z * y ] T41.108 : Triangle type {3,6,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y * x^-1 * z * y^-1 * x, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T41.109 : Triangle type {3,8,8} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T41.110 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, (z^-1 * y)^3, y^3 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.111 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T41.112 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T41.113 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-2 * y * x^-1 * z * y^2 ] T41.114 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, y^-1 * z * y^2 * x * z * y * x^-1 ] T41.115 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (z^-1 * y)^3, y^8 ] T41.116 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^8 ] T41.117 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^8, y * z^-1 * y^3 * x^-1 * y^-1 * z^4 ] T41.118 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T41.119 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.120 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^8 ] T41.121 : Triangle type {3,8,8} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, y^8 ] T41.122 : Triangle type {3,33,33} Group order 132 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-2 * y^5 * z^-2 * y ] T41.123 : Triangle type {3,123,123} Group order 123 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-30 * z * y^-1 * z * y^-6 * z^2 ] T41.124 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * z * y * x^-1, y * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z ] T41.125 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T41.126 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * x * z^-2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z * y ] T41.127 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T41.128 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * x * z^-2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.129 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * z * y * x * z ] T41.130 : Triangle type {4,4,4} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T41.131 : Triangle type {4,4,6} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, y * z^-1 * x^-2 * z^2 * x^-1, z * x^-1 * y * x^-1 * z^2 * y^-1 ] T41.132 : Triangle type {4,4,6} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^2 * y * x^-1 * y^-1 * z * x^-1 ] T41.133 : Triangle type {4,4,6} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 ] T41.134 : Triangle type {4,4,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T41.135 : Triangle type {4,4,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z * y^-1 ] T41.136 : Triangle type {4,4,10} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-5 * x^-1 * z^4 ] T41.137 : Triangle type {4,4,10} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-3 * x^-1 * z * y^-1 * z^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T41.138 : Triangle type {4,4,10} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^10 ] T41.139 : Triangle type {4,4,10} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * z^2 * x^-1 * y * z^-2 * x * z ] T41.140 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^2 * y * z^-3 * x^-1 * y * x * y^-1 * x * z^4 ] T41.141 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^12 ] T41.142 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-1 * x^-1 * z^3 ] T41.143 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z^2 * y^-1 ] T41.144 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^-3 * x^-1 * z^2 * y^-1 ] T41.145 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z * y * x^-1 * y^-1 * x * z^3 ] T41.146 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, y * z^-5 * x * z^6 ] T41.147 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, y^-1 * z^-6 * x^-1 * z^5 ] T41.148 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, (x * z^-1)^4 ] T41.149 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T41.150 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4 ] T41.151 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T41.152 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^12 ] T41.153 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, x * z^3 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-4 ] T41.154 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x * z * y * x * z^3 ] T41.155 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T41.156 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T41.157 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-6 * x * z^4 * y * z^-1 ] T41.158 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z * y^-1 * z^-5 * x^-1 * y * z^-4 * x ] T41.159 : Triangle type {4,4,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y * z^-4 ] T41.160 : Triangle type {4,4,18} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-3 * x * z * y * x * z * y^-1 * z^-2 ] T41.161 : Triangle type {4,4,22} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-3 * x^-1 * z * y * z^-6 * x ] T41.162 : Triangle type {4,4,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-29 * x^-1 * y^-1 * z^-12 ] T41.163 : Triangle type {4,4,82} Group order 164 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-28 * x^-1 * y * z^-12 ] T41.164 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.165 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * y^-2, y^6 ] T41.166 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T41.167 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-2 * y * x^-1 * y * z^-1 * y ] T41.168 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * z * y, (y * z^-2)^2, z^6 ] T41.169 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, z^-2 * y * x^-1 * y * z^-1 * y ] T41.170 : Triangle type {4,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z * y, y^6 ] T41.171 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2 ] T41.172 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-1 * y^2 * x^-1 * y^3 ] T41.173 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, y * x * z^-1 * x^-1 * y^-1 * x * z ] T41.174 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x * z^-1 * x * z * y^-1 ] T41.175 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2 ] T41.176 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^6, y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-2 * z^-1 * x ] T41.177 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T41.178 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y^6 ] T41.179 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T41.180 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z ] T41.181 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1, (z^-1 * x)^3 ] T41.182 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, z^6, z^-1 * y^2 * x^-1 * y^3 ] T41.183 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T41.184 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-1 * y^-1 * x * z * y, y^6 ] T41.185 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, (z^-1 * y)^3 ] T41.186 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T41.187 : Triangle type {4,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3 ] T41.188 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T41.189 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T41.190 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^8 ] T41.191 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^-1 * z * y * x^-1 * z * y^-1 * z ] T41.192 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8 ] T41.193 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x ] T41.194 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, y^8 ] T41.195 : Triangle type {4,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x * z^-1 * x^-1 * y * z^-1 * x ] T41.196 : Triangle type {4,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, y * z^-1 * y * x^-1 * z * y^-1 * z ] T41.197 : Triangle type {4,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, x^-1 * z * y * x * z * y ] T41.198 : Triangle type {4,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.199 : Triangle type {4,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.200 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (y^-4 * z * y^-1 * z * y^-1)^2 ] T41.201 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, z^-2 * y^3 * z^-2 * y ] T41.202 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^2 * z^-1 * y^2 * z^-3 ] T41.203 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T41.204 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^4 * z^-3 ] T41.205 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T41.206 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^5 * z^-1 * y * z^-1 ] T41.207 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (y * z^-2 * y)^2 ] T41.208 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z^2 * y^-3 * z * y^-1 ] T41.209 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^5 * z^-1 * y * z^-1 ] T41.210 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^5 * z^-1 * y * z^-1 ] T41.211 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T41.212 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3 ] T41.213 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2 ] T41.214 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2 ] T41.215 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3 ] T41.216 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-2 * y^3 * z^-2 * y ] T41.217 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, (y^-4 * z * y^-1 * z * y^-1)^2 ] T41.218 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y * z^-1 * y * z^-3 ] T41.219 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-2 * y^3 * z^-2 * y ] T41.220 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^2 * y * z^-1 * x^-1 * z^4 ] T41.221 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, y^4 * x^-1 * y^-3 * z ] T41.222 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, z^-4 * x^-1 * y * z^-3 ] T41.223 : Triangle type {4,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * y * z^-3 ] T41.224 : Triangle type {4,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^7 * z^-1 * y * z^-1 ] T41.225 : Triangle type {4,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y^2 * z^-2 ] T41.226 : Triangle type {4,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y^2 * x^-1 * y * z^-1 * y ] T41.227 : Triangle type {4,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-24 * z * y^-1 * z * y^-1 ] T41.228 : Triangle type {4,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T41.229 : Triangle type {5,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, (x * z * y)^2, z * y^-1 * z^-1 * x * z^2 ] T41.230 : Triangle type {5,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y^-5, z^-1 * y * x^-2 * y^2 * z^-1 ] T41.231 : Triangle type {5,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, (x * z * y)^2, y^-1 * z^-2 * x * z^2 ] T41.232 : Triangle type {5,5,10} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^-5, y^-1 * z^-2 * x * z^2 ] T41.233 : Triangle type {6,10,15} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2 ] T41.234 : Triangle type {6,12,12} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T41.235 : Triangle type {6,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-5 ] T41.236 : Triangle type {7,14,14} Group order 112 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, z^-2 * x^-1 * y^2 ] T41.237 : Triangle type {7,14,14} Group order 112 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * z * y^-1, (x * y^-1 * x)^2 ] T41.238 : Triangle type {7,14,14} Group order 112 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z * y, x^-7 ] T41.239 : Triangle type {8,8,8} Group order 128 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1 ] T41.240 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T41.241 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x, x^8 ] T41.242 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^8 ] T41.243 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-1 * y, x^8 ] T41.244 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T41.245 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T41.246 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2 ] T41.247 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, z * x^-3 * y^-3 ] T41.248 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * x^-1 * z * y, z * x^-3 * y^-3 ] T41.249 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T41.250 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * y^-1 * x)^2, z * y * x^2 * z * y^-1 ] T41.251 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * z * y^-1)^2, (x * z * y)^2, (y * z^-2)^2, y * x^-3 * y^-1 * z * y ] T41.252 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y ] T41.253 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T41.254 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T41.255 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T41.256 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2 ] T41.257 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, x^8 ] T41.258 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T41.259 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * z * y, x^8 ] T41.260 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^8 ] T41.261 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x, z^-1 * x^-3 * y * z^-2 ] T41.262 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, (x * z * y)^2 ] T41.263 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z * y)^2 ] T41.264 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x ] T41.265 : Triangle type {8,8,8} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2, z * y^2 * x^-1 * z * x^-1 ] T41.266 : Triangle type {8,8,12} Group order 120 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^-1 * y^-1 * z^-1, z^2 * x^-1 * z * y^-1 ] T41.267 : Triangle type {8,8,12} Group order 120 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x^2 * z^-1 * x^-1 ] T41.268 : Triangle type {8,8,28} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y^-1 * z^-3 * x * y^-1 * x^-1 * z^4 ] T41.269 : Triangle type {8,8,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^5 * y^-1 * z^-3 * x * y^-1 * x * z^4 ] T41.270 : Triangle type {8,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-1 * z^4 ] T41.271 : Triangle type {8,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-9 ] T41.272 : Triangle type {8,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-5 ] T41.273 : Triangle type {8,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^4 ] T41.274 : Triangle type {10,20,20} Group order 100 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y^-1 * x^4 * y^-3 ] T41.275 : Triangle type {10,20,20} Group order 100 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^10 ] T41.276 : Triangle type {10,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-4 * z^4 ] T41.277 : Triangle type {10,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1, x^10 ] T41.278 : Triangle type {10,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^3 * z^-1 * x^-1, x^2 * y^-1 * x^2 * y^-3 ] T41.279 : Triangle type {10,20,20} Group order 100 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^-2 * z * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 ] T41.280 : Triangle type {12,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-2 * y * z^-1 * y * z^-3 ] T41.281 : Triangle type {12,16,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^12 ] T41.282 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-12 ] T41.283 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^-4 * y * x^-1 * y ] T41.284 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, x^-4 * y * x^-1 * y ] T41.285 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2, z^-1 * x^4 * y^-2 * z^-1 ] T41.286 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * y^-1 * x^3 * y^-3, x * z^-1 * x^3 * z^-3 ] T41.287 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^12 ] T41.288 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-12 ] T41.289 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * z^-2 ] T41.290 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^12 ] T41.291 : Triangle type {12,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-1 * y^4 * z^-3 ] T41.292 : Triangle type {16,16,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T41.293 : Triangle type {16,16,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1 ] T41.294 : Triangle type {16,16,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z^3 ] T41.295 : Triangle type {16,16,24} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z * x^-1 * z^4 ] T41.296 : Triangle type {18,30,45} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y^3 * x^-9 * y^2 * x^-4 ] T41.297 : Triangle type {18,30,45} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-3 * x * z^-1 * x^9 * z^-1 ] T41.298 : Triangle type {22,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^3 * x^-7 * y^2 * z^-1 * y^2 ] T41.299 : Triangle type {22,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * z^-1 * y^6 * z^-1 * y^4 ] T41.300 : Triangle type {22,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-2 * z^2, x^-6 * y^4 ] T41.301 : Triangle type {22,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-2 * z^4 * x^-6 ] T41.302 : Triangle type {22,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^10 * z^-1 * x^7 * y^-1 * x^4 ] T41.303 : Triangle type {42,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * x^4 * y^-1 * z^3 * y^-2 ] T41.304 : Triangle type {42,84,84} Group order 84 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, (x * y^-4)^2 ] T41.305 : Triangle type {42,84,84} Group order 84 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^42, y * z^-1 ] T41.306 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x^-2 * y^-1, y^36 * x^-1 * y^5, x * z^-1 ] T41.307 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-20 * x^3 * y^-3 * x * y^-2 ] T41.308 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^6 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T41.309 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x * y^-13 * x * y^-2 ] T41.310 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x * y^-5 * x^5 * y^-1 * x * y^-1 ] T41.311 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-5 * x^7 ] T41.312 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^-5 * x^5 * y^-1 ] T41.313 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-7 * y^3 ] T41.314 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^5 * x^-1 * z^4 ] T41.315 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^6 * x^-1 * z^4 ] T41.316 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-6 * x^2 * z^-5 * y * z^-4 ] T41.317 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^4 * x^-2 * z^-5 * y * z^-1 * y^2 ] T41.318 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-2 * z^5 * y^-2 * z^2 ] T41.319 : Triangle type {83,83,83} Group order 83 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-2 * z * x^-1 * z^4 * x^-6 ] Genus 42 T42.1 : Triangle type {2,4,45} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-28 * x * z^9 * y^-1 * x * z * y^-1 * z^-5 ] T42.2 : Triangle type {2,4,86} Group order 344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-78 * x * y * z^-7 ] T42.3 : Triangle type {2,4,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-76 * x * y^-1 * z^-7 ] T42.4 : Triangle type {2,5,10} Group order 410 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z^2 * y * z^-1 * y^2 * z^-1 * y * z^-1 * x ] T42.5 : Triangle type {2,5,10} Group order 410 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z * y * z^-1 * y * x * y^-1 * z^-4 * x ] T42.6 : Triangle type {2,6,44} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^17 * y * x * z^8 * y * x * z * y * z^-9 * x * z^6 ] T42.7 : Triangle type {2,8,8} Group order 328 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * x * z * y^3 * x * y^-1 * z^-1 * y ] T42.8 : Triangle type {2,8,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^3 * y * x * z^3 * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T42.9 : Triangle type {2,8,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^12 * y * x * z * y^-1 * z^-11 * x * z^4 ] T42.10 : Triangle type {2,10,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^3 * y * z^-2 * x * z^15 ] T42.11 : Triangle type {2,14,16} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * y^-10 * z^-1 * y, z^4 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^2 ] T42.12 : Triangle type {2,26,91} Group order 182 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-3, y^-2 * z^3 * y^-4 * z^4 ] T42.13 : Triangle type {2,44,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-11 * z^3 * y^-6 * z * y^-1 ] T42.14 : Triangle type {2,45,45} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-41 * z * y^-1 ] T42.15 : Triangle type {2,58,87} Group order 174 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-1 * y^10 * z^-3 * y^13 * z^-1 ] T42.16 : Triangle type {2,85,170} Group order 170 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^69 * y^-14 * z ] T42.17 : Triangle type {2,86,86} Group order 172 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^16 * z^-70 ] T42.18 : Triangle type {2,168,168} Group order 168 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-69 ] T42.19 : Triangle type {3,43,129} Group order 129 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-32 * z * y^-1 * z * y^-7 * z ] T42.20 : Triangle type {3,44,44} Group order 132 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^31 * y^-3 * z * y^-7 * z ] T42.21 : Triangle type {3,126,126} Group order 126 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-31 * z * y^-1 * z * y^-8 ] T42.22 : Triangle type {4,4,43} Group order 172 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y * x * z^6 ] T42.23 : Triangle type {4,4,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-29 * x^-1 * y * z^-12 ] T42.24 : Triangle type {4,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^4 * y^-1 * x * z^4 ] T42.25 : Triangle type {4,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^6 * y * x * z^6 * y * x * z^4 ] T42.26 : Triangle type {4,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^7 * z^-1 * y * z^-1 ] T42.27 : Triangle type {4,29,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z^2 ] T42.28 : Triangle type {4,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^2 * z^-1 * y * z^-3 * y^2 * z^-3 * y^2 * z^-1 ] T42.29 : Triangle type {4,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-2 * z^2 * y^-1 * z * y^-10 * z * y^-5 * z * y^-5 ] T42.30 : Triangle type {4,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.31 : Triangle type {5,5,5} Group order 205 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, x * z^-1 * y * x^-1 * z * x^-1 * y ] T42.32 : Triangle type {5,5,5} Group order 205 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, y^-1 * z^-1 * x^-2 * z^2 * x^-1 ] T42.33 : Triangle type {5,22,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-3 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T42.34 : Triangle type {5,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T42.35 : Triangle type {5,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.36 : Triangle type {6,6,22} Group order 132 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-9 * x^-1 * y * x^-1 * y^-1 * x * z^4 * y^-1 * z^-6 ] T42.37 : Triangle type {6,10,20} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-1 * z * x^-1 * y^-1 * x^-1 * y^-1 * z^3 ] T42.38 : Triangle type {6,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-2 ] T42.39 : Triangle type {6,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 * z ] T42.40 : Triangle type {7,15,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * x * y^4 * z^-1 * y * z^-1 * y^3 ] T42.41 : Triangle type {7,16,16} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-16 ] T42.42 : Triangle type {7,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^4 * x^-2 * z^4 * y^-4 ] T42.43 : Triangle type {7,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 ] T42.44 : Triangle type {7,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-3 * z^5 * y^-1 * z * y^-1 * z ] T42.45 : Triangle type {8,8,15} Group order 120 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, z * x^-3 * y^-3, x^8 ] T42.46 : Triangle type {8,8,15} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^3 * y * x^-1 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^4 ] T42.47 : Triangle type {8,13,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T42.48 : Triangle type {8,14,14} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^-14 ] T42.49 : Triangle type {8,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * x * z^-4 ] T42.50 : Triangle type {8,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^3 * z^-1 ] T42.51 : Triangle type {9,9,13} Group order 117 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^-9 ] T42.52 : Triangle type {12,32,32} Group order 96 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y * z^-1 * y * z^-1 * y * z^-3 ] T42.53 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^13 ] T42.54 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^13 ] T42.55 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^13 ] T42.56 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-3 * x^5 * z^-4 ] T42.57 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-4, z^-1 * y * z^-1 * x^5 * z^-4 ] T42.58 : Triangle type {13,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^3 * y^-2 * x^-5 * z^2 ] T42.59 : Triangle type {15,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^2 * x^-7 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T42.60 : Triangle type {15,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-1 * x * y^-2 * x^6 * y^-3 ] T42.61 : Triangle type {15,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-2 * x^5 * y^-4 ] T42.62 : Triangle type {18,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, x^2 * y^-2 * x^6 * y^-3 ] T42.63 : Triangle type {18,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-2 * y * x^-9 * y^2 * x^-1 * y * x^-1 * y * x^-1 ] T42.64 : Triangle type {18,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-2 * x * z^-1 * x * z^-1 * x^9 * z^-1 ] T42.65 : Triangle type {22,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * x^-1 * z^4 ] T42.66 : Triangle type {22,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, (x^-2 * z^4)^2 ] T42.67 : Triangle type {22,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-4 * x * y^-10 * x * y^-2 ] T42.68 : Triangle type {22,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^5 * z^-1 * x^12 * z^-1 * x * z^-1 * x * z^-1 ] T42.69 : Triangle type {22,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-3 * z^4 * x^-6 ] T42.70 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^4 * z^-2 * y^2 * x^-1 * y^7 ] T42.71 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-5 * x * y^-4 ] T42.72 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^10 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T42.73 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-2 * z^3 * x^-6 ] T42.74 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-4 * y^6 ] T42.75 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-1 * x * y^-4, x^-1 * z^4 * x^-4 * z^2 ] T42.76 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-1 * z * y^-1 * z * y^-3 * x^3 * y^-5 ] T42.77 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-7 * y * z^-10 ] T42.78 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^16 * y^-1 * x^7 * z^-1 * x^5 ] T42.79 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-6 * z^2, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T42.80 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-6, y^-1 * z^2 * y^-2 * x * y^-4 ] T42.81 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-2 * z * y^-1 * z^5 * x^3 * y^-3 ] T42.82 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-5 * z^3 * x^-7 ] T42.83 : Triangle type {29,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^3 * z^-2 * x^6 * z^-1 * x^4 ] T42.84 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-12 * z * y^-9 ] T42.85 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-21 * x^3 * y^-3 * x * y^-2 ] T42.86 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-2 * x^9 * y^-2 ] T42.87 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^2 * y^-1 * x * y^-10 * x * y^-2 ] T42.88 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-2 * z^2 * x^-7 ] T42.89 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-6 * x^5 * y^-2 ] T42.90 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z * x^-1 * z^4 * x^-5 * z ] T42.91 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, y * x^-5 * y^3 * z^-1 * y ] T42.92 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^5 * x^-1 * z^-5 * y * z^-1 * y * z^-1 ] T42.93 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^2 * x^-7, y^-1 * z^5 * y^-2 * z^2 ] T42.94 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^8 * y^-1 * x^9 * z^-1 * x * z^-1 * x * z^-1 ] T42.95 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-3 * y^2 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.96 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-5 * z * y^-1 * z * y^-10 ] T42.97 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-4 * x^2 * z^-4 * x * z^-1 * x * z^-1 * x ] T42.98 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-2 * z^2 * y^-2 * x * y^-4 ] T42.99 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-3 * z, x^-1 * z^4 * x^-6 ] T42.100 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^2 * z^-3 * x^3 * z^-4 * x * z^-1 * x^3 ] T42.101 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T42.102 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z^5 * x * y^-4 ] T42.103 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T42.104 : Triangle type {43,86,86} Group order 86 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^43, y * z^-1 ] T42.105 : Triangle type {44,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * z * y^-1 * z^2 * y^-3 * x * y^-4 ] T42.106 : Triangle type {44,44,44} Group order 88 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-3 * x^2 * y^-3 ] T42.107 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x^-2 * y^-1, y^37 * x^-1 * y^5, x * z^-1 ] T42.108 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-1 * z^2 * y^-2 * x * y^-4 ] T42.109 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z * y^-1 * z * y^-1 * z^9 ] T42.110 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-20 * x^4 * y^-3 * x * y^-2 ] T42.111 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-2 * z^5 * y^-1 * z^3 ] T42.112 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z, y^-2 * z * y^-1 * z^5 * y^-4 ] T42.113 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-1 * z^4 * x^-6 ] T42.114 : Triangle type {85,85,85} Group order 85 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^8 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] Genus 43 T43.1 : Triangle type {2,3,9} Group order 1512 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z * y * x * z * y * z^-1 * x * z^2 * y * x * y^-1 * z^-2 * x * z, z^-2 * x * z * y * x * z * y * x * z^2 * y * x * z^2 * y^2 * z^-1 * x * z^2 * y^-1 * z^-1 ] T43.2 : Triangle type {2,3,9} Group order 1512 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^-1 * x * z^3 * y * z^-1 * x * z^2 * y * z^-2 * x * z * y^-1 * z^-1 ] T43.3 : Triangle type {2,3,12} Group order 1008 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y * x * z * y^-1 * z^-2 * x * z * y * x * z * y * x * z * y * x * z^2 * y * x * z * y^-2 * z^-2 * x * z * y^-1 * z^-1 * x ] T43.4 : Triangle type {2,3,20} Group order 720 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T43.5 : Triangle type {2,4,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2 * y * z^-1)^2, x * z * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 ] T43.6 : Triangle type {2,4,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T43.7 : Triangle type {2,4,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-80 * x * y * z^-7 ] T43.8 : Triangle type {2,4,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-30 * x * z^5 * y * z^-1 * x * y^-1 * z^-6 ] T43.9 : Triangle type {2,4,172} Group order 344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-78 * x * y^-1 * z^-7 ] T43.10 : Triangle type {2,6,9} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * z * y * x * y^-1 * z * y^-3 * z^-1 * y^2 * z^-1 * y ] T43.11 : Triangle type {2,6,9} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * z * y * x * z * y * x * y^-2 * z^-1 * y * x * z * y ] T43.12 : Triangle type {2,6,9} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, z * y * x * y^-1 * z * y^-2 * z^-1 * y * x * y^-2 * z^-1 * x ] T43.13 : Triangle type {2,6,12} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T43.14 : Triangle type {2,6,21} Group order 294 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^2 * y * x * y^-2 * z * y^-1 * z^-2 * x ] T43.15 : Triangle type {2,6,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^3 * y^-1 * z^-4 ] T43.16 : Triangle type {2,6,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T43.17 : Triangle type {2,6,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-3)^2 ] T43.18 : Triangle type {2,6,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T43.19 : Triangle type {2,6,45} Group order 270 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * x * z^5 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T43.20 : Triangle type {2,6,45} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-16 * x * z * y * x * z^15 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T43.21 : Triangle type {2,6,129} Group order 258 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^33 * y * z^-7 * x * z^2 ] T43.22 : Triangle type {2,8,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T43.23 : Triangle type {2,8,8} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, z^8, (y * z^-2 * y^2)^2 ] T43.24 : Triangle type {2,8,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, (y^-1 * z)^6 ] T43.25 : Triangle type {2,8,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, y^-1 * z * y * z^-2 * y * x * y^-1 * z^3 * y^-1 * z ] T43.26 : Triangle type {2,10,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, z * y * z^-1 * y^2 * z^-1 * x * y^-1, z * y * z^-1 * x * y^-1 * z^-2 * x ] T43.27 : Triangle type {2,12,15} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y * x * y^-3 * z^-1 * x * z^2 ] T43.28 : Triangle type {2,12,36} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-2 * y * z^-1, y^12 ] T43.29 : Triangle type {2,12,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^4 * y * x * z^4 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T43.30 : Triangle type {2,12,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-14 * x * z^2 * y^-1 * z^-1 ] T43.31 : Triangle type {2,15,30} Group order 210 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-2 * z^3 * y^-6 * z^3 * y^-1 ] T43.32 : Triangle type {2,24,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^9 * z^-1 * y * z^-1 ] T43.33 : Triangle type {2,24,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-4 * z^5 ] T43.34 : Triangle type {2,87,174} Group order 174 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^70 * y^-16 ] T43.35 : Triangle type {2,88,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-18 * y^11 * z^-1 * y^13 * z^-1 ] T43.36 : Triangle type {2,88,88} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-70 * y ] T43.37 : Triangle type {2,172,172} Group order 172 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^16 * z^-69 * y ] T43.38 : Triangle type {3,3,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T43.39 : Triangle type {3,3,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * y^-1 * x * y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * x * z * y * x * y^-1 * x * z ] T43.40 : Triangle type {3,3,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x ] T43.41 : Triangle type {3,4,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-2 * x * z^-1 * x * z^2 * y^-1 * z^-1 ] T43.42 : Triangle type {3,4,6} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T43.43 : Triangle type {3,4,6} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, (x * y^-1 * z^-1 * y)^2 ] T43.44 : Triangle type {3,4,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y * z^-2 * x^-1 * z * x^-1 * z * y * x * z * y^-1 * z^-1 ] T43.45 : Triangle type {3,8,24} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * x * z^2 * y, y^8 ] T43.46 : Triangle type {3,9,9} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^-9 ] T43.47 : Triangle type {3,9,9} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 ] T43.48 : Triangle type {3,9,9} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * x * z * y * x^-1 * y^-1 * z * y^-1 * z ] T43.49 : Triangle type {3,16,48} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * z^-2 * y^6 * z^-4 * y ] T43.50 : Triangle type {3,21,21} Group order 147 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^2 * y^-2 * x * y^-1 * z * y^-1 ] T43.51 : Triangle type {3,24,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T43.52 : Triangle type {3,24,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3 ] T43.53 : Triangle type {3,24,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T43.54 : Triangle type {3,24,24} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^4 * z^-3 ] T43.55 : Triangle type {3,44,132} Group order 132 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-33 * z * y^-1 * z * y^-7 * z ] T43.56 : Triangle type {3,45,45} Group order 135 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-3 * y^3 * z^-1 * y^5 * z^-2 * y ] T43.57 : Triangle type {3,45,45} Group order 135 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-34 * z * y^-1 * z * y^-7 * z ] T43.58 : Triangle type {3,129,129} Group order 129 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-32 * z * y^-1 * z * y^-8 ] T43.59 : Triangle type {4,4,4} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (z^-1 * x)^3, x * z * y * x^-1 * y^-1 * z^-1 * y ] T43.60 : Triangle type {4,4,4} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z * x^-1 * z * x^-1 * y^-1 * z * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T43.61 : Triangle type {4,4,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x^-1 * y * z^-6 * x ] T43.62 : Triangle type {4,4,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x^-1 * y * z^-6 * x^-1 ] T43.63 : Triangle type {4,4,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^44 ] T43.64 : Triangle type {4,4,86} Group order 172 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y * x^-1 * z^6 ] T43.65 : Triangle type {4,6,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T43.66 : Triangle type {4,6,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^-1 * z * y^2 * x * y^-2 * z^-1 ] T43.67 : Triangle type {4,8,10} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, y^-1 * z^-2 * x^-1 * z^3 ] T43.68 : Triangle type {4,8,10} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^-1 * z^-2 * x^-1 * z^3, y^8 ] T43.69 : Triangle type {4,8,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-3 ] T43.70 : Triangle type {4,8,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-4 * x^-1 * z * y * x * y^-1 * z^-3 ] T43.71 : Triangle type {4,9,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^9 ] T43.72 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^-12 ] T43.73 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-2 * z * x^-1 * y^-3 ] T43.74 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-1 * y^2 * z^-1 * y^2 * x^-1 * y^2 * z^-3 ] T43.75 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^7 * z^-3 ] T43.76 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T43.77 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T43.78 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y ] T43.79 : Triangle type {4,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-3 ] T43.80 : Triangle type {4,12,33} Group order 132 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^6 * y * x * z^4 ] T43.81 : Triangle type {4,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T43.82 : Triangle type {4,58,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T43.83 : Triangle type {6,6,6} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * x * y^-1 * x * z^-1 * x, y^-1 * z * y^-1 * x * y^-1 * z ] T43.84 : Triangle type {6,6,6} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * x * z * y * x * z ] T43.85 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z * y^-1 * z^-1 * x * z * y^-1 ] T43.86 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T43.87 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * z * x^-1 ] T43.88 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 ] T43.89 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^6, z^-1 * y^2 * x^-1 * y^3 ] T43.90 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, y^6, z^-1 * y^2 * x^-1 * y^3 ] T43.91 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, z * y * x^2 * z^-1 * x^-1 ] T43.92 : Triangle type {6,6,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^6 ] T43.93 : Triangle type {6,8,8} Group order 144 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T43.94 : Triangle type {6,8,8} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, x^-2 * y^-1 * x^2 * y^-1 * z^2 ] T43.95 : Triangle type {6,8,8} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, y^8 ] T43.96 : Triangle type {6,9,18} Group order 126 Chiral action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T43.97 : Triangle type {6,9,18} Group order 126 Chiral action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T43.98 : Triangle type {6,10,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^2 * x^-2 * y * z^-2 ] T43.99 : Triangle type {6,12,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^5 * y * x * z^4 ] T43.100 : Triangle type {6,15,15} Group order 120 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * x * z * y^-1 ] T43.101 : Triangle type {6,36,36} Group order 108 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y^2 * z^-1 * y ] T43.102 : Triangle type {6,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^6 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T43.103 : Triangle type {6,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z * y^-1 * z * x^-1 * y^-1 * z^2 ] T43.104 : Triangle type {6,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-13 * x * z * y^-1 * z * y^-2 ] T43.105 : Triangle type {9,12,36} Group order 108 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-1 * z^4 * y^-1 * z^2 * y^-4 ] T43.106 : Triangle type {9,12,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-3 * z * y^-4 * x * y^-4 ] T43.107 : Triangle type {9,12,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^-9 ] T43.108 : Triangle type {9,12,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^-3 * y^3 ] T43.109 : Triangle type {9,33,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-6 * z^2 ] T43.110 : Triangle type {9,33,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z * y^-1 * z * y^-4 * z^4 ] T43.111 : Triangle type {10,10,10} Group order 120 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x * z^-1 * x^-1 * z * y ] T43.112 : Triangle type {12,12,18} Group order 108 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^2 * z * y, y * x^-3 * y * z^-1 * x^-1 ] T43.113 : Triangle type {12,12,18} Group order 108 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y * x, y * x^3 * z^2, z^3 * x^-1 * z^2 * y^-1 ] T43.114 : Triangle type {12,12,18} Group order 108 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z^-1 * x * z^4 ] T43.115 : Triangle type {12,12,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T43.116 : Triangle type {12,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^12 ] T43.117 : Triangle type {12,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4, x^12 ] T43.118 : Triangle type {12,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^12 ] T43.119 : Triangle type {12,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-1 * y^3 * z^-3 ] T43.120 : Triangle type {15,15,15} Group order 105 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * x^-1, z^-1 * x^3 * z^-2, y^-3 * x^3 * y^-3 ] T43.121 : Triangle type {16,24,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-7 * z * y ] T43.122 : Triangle type {16,24,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * z * x^-10 * y * x^-3 ] T43.123 : Triangle type {16,24,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-7 * z * y ] T43.124 : Triangle type {16,24,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, x^2 * z^-2 * x^4 * z^-4 ] T43.125 : Triangle type {24,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T43.126 : Triangle type {24,24,24} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, y^3 * x^-1 * y * z^-1 * y ] T43.127 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^11 * y^-1 * x * y^-1 * x * y^-5 * x * y^-5 ] T43.128 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-5 * x^3 * z^-4 ] T43.129 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^7 * y^-2, z * y^-4 * x^-1 * z^4 ] T43.130 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-14 * y * x^-1 * y * x^-8 * y * x^-5 ] T43.131 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * y * x^-8 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T43.132 : Triangle type {30,45,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^5 * x^-2 * z^7 ] T43.133 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^9 ] T43.134 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-1 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T43.135 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x * y^-8 * z * y^-1 * x * y^-2 ] T43.136 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^21 * x^-2 * y^7 ] T43.137 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x * z^-4 * x^3 * z^-9 ] T43.138 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-2 * z^2, x^-6 * y^4 ] T43.139 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^9 * y^-1 * x * y^-1 ] T43.140 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^9 * x^-2 * z^3 ] T43.141 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^44, y * z^-1 ] T43.142 : Triangle type {44,88,88} Group order 88 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^10 * z^-1 * x^7 * z^-1 * x^4 ] T43.143 : Triangle type {87,87,87} Group order 87 Reflexible action Defining relators: [ x^-2 * y^-1, y^38 * x^-1 * y^5, x * z^-1 ] T43.144 : Triangle type {87,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^2 * x^-4 * y^5 ] T43.145 : Triangle type {87,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z * x^-1 * z^4 * x^-2 * z^4 ] T43.146 : Triangle type {87,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x * y^-1 * x * y^-10 * x * y^-2 ] T43.147 : Triangle type {87,87,87} Group order 87 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z * y^-1 * z * y^-1 * z^9 ] Genus 44 T44.1 : Triangle type {2,4,90} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-82 * x * y * z^-7 ] T44.2 : Triangle type {2,4,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-80 * x * y^-1 * z^-7 ] T44.3 : Triangle type {2,6,6} Group order 516 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, y * x * z * y * x * z^2 * y * z^-1 * x * z * y * z^-1 * y * z^-1 * x * z * y^-1 * z^2 ] T44.4 : Triangle type {2,6,46} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-24 * x * z^5 * y^-1 * z^-16 ] T44.5 : Triangle type {2,6,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^17 * y * x * z^15 * y * z^-8 * x * z^2 ] T44.6 : Triangle type {2,8,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^12 * y * x * z * y * x * z^15 ] T44.7 : Triangle type {2,10,24} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^3 * y * x * z * y * x * z * y * x * y * x * y^-1 * z^-7 * x * y^-1 * z^-3 * x * z^3 ] T44.8 : Triangle type {2,10,110} Group order 220 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-2 * x * z^6 * y^-1 * x * y^-1 * z^-8 * x * z^2 * y^-1 * z^-1 ] T44.9 : Triangle type {2,18,99} Group order 198 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y * z^-5 ] T44.10 : Triangle type {2,46,92} Group order 184 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-20 * y^11 * z^-1 * y^13 * z^-1 ] T44.11 : Triangle type {2,89,178} Group order 178 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^71 * y^-16 * z ] T44.12 : Triangle type {2,90,90} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^18 * z^-72 ] T44.13 : Triangle type {2,176,176} Group order 176 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-71 ] T44.14 : Triangle type {3,6,6} Group order 258 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T44.15 : Triangle type {3,6,6} Group order 258 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T44.16 : Triangle type {3,46,46} Group order 138 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^33 * y^-3 * z * y^-7 * z ] T44.17 : Triangle type {3,132,132} Group order 132 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-33 * z * y^-1 * z * y^-6 * z^2 ] T44.18 : Triangle type {4,4,45} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * x * z^6 ] T44.19 : Triangle type {4,4,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^45 ] T44.20 : Triangle type {4,4,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^31 * y^-1 * z^-4 * x * z^8 ] T44.21 : Triangle type {4,6,14} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-4 * x^-1 * z^3 * y * x^-1 * y * x * z * y * z^-3 ] T44.22 : Triangle type {4,8,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^6 * y * x * z^6 * y * x^-1 * z^4 ] T44.23 : Triangle type {4,12,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^6 * y * x^-1 * z^4 ] T44.24 : Triangle type {4,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-3 * z^2 * y^-1 * z * y^-10 * z * y^-5 * z * y^-5 ] T44.25 : Triangle type {5,23,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T44.26 : Triangle type {5,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^10 * z^-1 * y * z^-1 * y^7 * z^-4 ] T44.27 : Triangle type {5,24,24} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z * y^-3 * z * y^-1 * z * y^-5 ] T44.28 : Triangle type {5,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-2 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T44.29 : Triangle type {5,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-5 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T44.30 : Triangle type {6,6,23} Group order 138 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-23 ] T44.31 : Triangle type {6,6,66} Group order 132 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y * z^-3 * x * y^-1 * x * y^-1 * z^-3 * x * z^7 ] T44.32 : Triangle type {6,10,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * x^-1 * y^-1 * z^3 ] T44.33 : Triangle type {6,12,30} Group order 120 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * z^-2 * x^-1 * z * y^-1 * x^-1 * z^4 ] T44.34 : Triangle type {6,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y * z^-1 * y ] T44.35 : Triangle type {6,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-3 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-6 ] T44.36 : Triangle type {8,8,30} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * y^-1 * z^-1, z * y^-1 * x^2 * z^-1 * x ] T44.37 : Triangle type {8,8,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^3 * y * x^-1 * y * x^-1 * z^10 ] T44.38 : Triangle type {8,14,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y * z^-2 * y^3 * z^-2 * y * z^-2 * y * z^-2 ] T44.39 : Triangle type {8,26,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-6 * z^2 ] T44.40 : Triangle type {9,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-5 * z^3 ] T44.41 : Triangle type {9,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-8 ] T44.42 : Triangle type {10,10,12} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^7 * y^-1 * x^-1 * z^4 ] T44.43 : Triangle type {10,10,55} Group order 110 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^2 * y * z^-2 * x * z * y^-1 * x^-1 * z^4 ] T44.44 : Triangle type {10,10,55} Group order 110 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z * y * z^-4 * x * y^-1 * x * z^4 ] T44.45 : Triangle type {10,50,50} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-5 * z^3 ] T44.46 : Triangle type {10,50,50} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-7 * z ] T44.47 : Triangle type {12,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-2 * x * z^-2 * x^4 * z^-4 ] T44.48 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-2 * x^3 * y^-2 * z^2 * y^-2 ] T44.49 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * x^-4 * y^5 * x^-1 * y^3 ] T44.50 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x * z^-1 * x * z^-1 * x^7 * z^-2 ] T44.51 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^12 * x^-1 * y * x^-1 * y^3 ] T44.52 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^5 * z^-4 ] T44.53 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^7 * y^-4 ] T44.54 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-5, y^-1 * z^2 * y^-2 * x^7 * y^-3 ] T44.55 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x^6 * z^-3 ] T44.56 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-16 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T44.57 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-1 * z * y^-2 * x^4 * y^-4 ] T44.58 : Triangle type {23,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-23 ] T44.59 : Triangle type {24,32,32} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, z * x^-3 * z^3 ] T44.60 : Triangle type {24,32,32} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^-7 * z * y ] T44.61 : Triangle type {45,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-16 * x^2 * y^-3 * z * y^-2 ] T44.62 : Triangle type {45,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-1 * x * z^-1 * x^5 * z^-4 ] T44.63 : Triangle type {45,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^6 * y^-3, z^-1 * x * z^-1 * x^5 * z^-4 ] T44.64 : Triangle type {45,90,90} Group order 90 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 * y^2 * x^-4 ] T44.65 : Triangle type {45,90,90} Group order 90 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^45, y * z^-1 ] T44.66 : Triangle type {46,46,46} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^15 * x^-2 * y^7 ] T44.67 : Triangle type {46,46,46} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^6 * x^-1 * y^5 * x^-1 * y^3 ] T44.68 : Triangle type {46,46,46} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-1 * x^8 * y^-3 ] T44.69 : Triangle type {46,46,46} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-4 * x^2 * z^-4 ] T44.70 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x^-2 * y^-1, y^39 * x^-1 * y^5, x * z^-1 ] T44.71 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-1 * y^3 * x^-3 * y^7 ] T44.72 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-4 * y^4 * x^-1 * y^4 * x^-1 * y^5 * x^-1 * y^2 ] T44.73 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^15 * x^-1 * y^2 ] T44.74 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-1 * y * x^-5 * y^7 ] T44.75 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-5 * y^4 * x^-2 ] T44.76 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, x^-1 * y * x^-5 * y^4 * x^-1 ] T44.77 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, y^-5 * x * y^-4 ] T44.78 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^8 * x^-1 * z^4 ] T44.79 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-2 * z^5 * y^-4 ] T44.80 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z * x^-1 * z^4 * x^-4 * z^2 ] T44.81 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-3 * z * y^-3 * x^5 * y^-4 ] T44.82 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T44.83 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-5 * x^7 ] T44.84 : Triangle type {89,89,89} Group order 89 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x^9 * z^-2 * x^5 ] Genus 45 T45.1 : Triangle type {2,3,10} Group order 1320 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, z^2 * y * x * z^2 * y * x * z * y^2 * z^-1 * x * z * y^-1 * z^-1 * x, z * y * x * z * y * z^-1 * x * z * y * x * z * y * x * z * y^2 * z^-2 * x * z^3 ] T45.2 : Triangle type {2,3,10} Group order 1320 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z^5 * y * x * z * y^2 * z^-3 * x * z^2 ] T45.3 : Triangle type {2,3,22} Group order 726 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-21 * x ] T45.4 : Triangle type {2,3,28} Group order 672 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^3 * y * z^-1 * x * z * y * x * y^-1 * z^3 * y^-1 * z^-1 * x ] T45.5 : Triangle type {2,4,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^-7 * x * y * z^-7 ] T45.6 : Triangle type {2,4,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-8 * x * z^8 * y * x * z^4 * y^-1 * z^-2 ] T45.7 : Triangle type {2,4,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-30 * x * z^7 * y * x * y * x * y^-1 * z^-8 ] T45.8 : Triangle type {2,4,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-38 * x * y * z^-9 ] T45.9 : Triangle type {2,4,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-10 * x * z^7 * y * z^-1 * x * y^-1 * z^-4 ] T45.10 : Triangle type {2,4,92} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-84 * x * y * z^-7 ] T45.11 : Triangle type {2,4,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-82 * x * y^-1 * z^-7 ] T45.12 : Triangle type {2,5,6} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1, z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-1 * y ] T45.13 : Triangle type {2,5,6} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5 ] T45.14 : Triangle type {2,6,14} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-2 * x * y^-2 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T45.15 : Triangle type {2,8,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T45.16 : Triangle type {2,8,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, (y * z^-1)^4 ] T45.17 : Triangle type {2,8,32} Group order 256 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-1 * x * z^2 ] T45.18 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z^2 * y * x * z * y * x * y * x * z^15 ] T45.19 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^22 * y * z^-7 * x * z^2 ] T45.20 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z * y * x * z^5 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T45.21 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y^-1 * z^-1 * x * y^-1 * z^-4 ] T45.22 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T45.23 : Triangle type {2,8,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y * x * z * y^-1 * z^-4 ] T45.24 : Triangle type {2,8,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-4 * x * z^16 * y * x * y^-1 * z^-8 ] T45.25 : Triangle type {2,8,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^17 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T45.26 : Triangle type {2,11,22} Group order 242 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-11 ] T45.27 : Triangle type {2,12,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-2 * y^3 * z^-3, z * y^-1 * z * y^-2 * z^-2 * x * y^-1 ] T45.28 : Triangle type {2,12,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-1 * x * y^-2 * z^-3, (z^-1 * y)^5 ] T45.29 : Triangle type {2,12,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-20 ] T45.30 : Triangle type {2,14,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^2 * y^-7 * z^2, z^-9 * y * z^4 * y^-1 * z^-2 ] T45.31 : Triangle type {2,15,15} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^2 * z^-1, y^-15 ] T45.32 : Triangle type {2,15,15} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^-15 ] T45.33 : Triangle type {2,22,99} Group order 198 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y^-2 * z^5 ] T45.34 : Triangle type {2,32,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-4 * z^4 * y^-1 ] T45.35 : Triangle type {2,32,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-3 * y^11 * z^-2 * y^14 * z^-1 ] T45.36 : Triangle type {2,38,95} Group order 190 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-7 * z * y^-6 * z^4 * y^-1 ] T45.37 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T45.38 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-10 * y^11 * z^-1 ] T45.39 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-32 * z * y^-13 ] T45.40 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-21 * y^11 * z^-2 * y^13 * z^-1 ] T45.41 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-12 * z^2 * y^-8 * z^2 ] T45.42 : Triangle type {2,48,48} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^10 * z^-1 * y^8 * z^-2 ] T45.43 : Triangle type {2,62,93} Group order 186 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-4 * y^10 * z^-3 * y^12 * z^-2 ] T45.44 : Triangle type {2,91,182} Group order 182 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^72 * y^-18 ] T45.45 : Triangle type {2,92,92} Group order 184 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^19 * z^-72 * y ] T45.46 : Triangle type {2,180,180} Group order 180 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^18 * z^-71 * y ] T45.47 : Triangle type {3,3,5} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z, y^-1 * z^-1 * x^-1 * z * y * x * z * y * z^-1 * x^-1 ] T45.48 : Triangle type {3,3,5} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (x * z * y^-1 * z^-1)^2 ] T45.49 : Triangle type {3,3,11} Group order 363 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^5 * y^-1 * z^-1 * x^-1 * y * x * z^4 ] T45.50 : Triangle type {3,3,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-3 * x * z^3, z^-1 * x^-1 * z * y * x^-1 * z * y * x * y^-1 ] T45.51 : Triangle type {3,3,91} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, x * z^6 * x^-1 * z^-5 ] T45.52 : Triangle type {3,3,91} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, x * z^9 * y ] T45.53 : Triangle type {3,4,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-3 * x * z^-4 ] T45.54 : Triangle type {3,8,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z * y^2 * x^-1 * y^-1 * z^-1 * x, z^-3 * x^-1 * z^2 * y^-1 ] T45.55 : Triangle type {3,8,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-2 * z ] T45.56 : Triangle type {3,12,52} Group order 156 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-2 * x^-1 * z * y * z^-1 ] T45.57 : Triangle type {3,46,138} Group order 138 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-35 * z * y^-1 * z * y^-7 * z ] T45.58 : Triangle type {3,135,135} Group order 135 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-34 * z * y^-1 * z * y^-8 ] T45.59 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^4 * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-3 * x^-1 ] T45.60 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^4 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-4 * x ] T45.61 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y * z^-2 * x^-1 * z^3, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T45.62 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T45.63 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-18 * x * y * z^-5 ] T45.64 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^3 * y * z^-2 * x^-1 * y^-1 * x * y^-1 * x * z^4 ] T45.65 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^-1 * z^-3 * x^-1 * z^8 ] T45.66 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y^-1 * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x^-1 ] T45.67 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^8 ] T45.68 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-1 * x^-1 * z^2 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-5 ] T45.69 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * z^8 ] T45.70 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-18 * x * y * z^-5 ] T45.71 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-7 * x^-1 * z * y * z^-3 ] T45.72 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-6 * x^-1 * y * x^-1 * y^-1 * z^-4 ] T45.73 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y^-1 * z^-4 ] T45.74 : Triangle type {4,4,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y^-1 * z^-4 ] T45.75 : Triangle type {4,4,46} Group order 184 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^46 ] T45.76 : Triangle type {4,4,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^32 * y^-1 * z^-4 * x * z^8 ] T45.77 : Triangle type {4,6,8} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x * z^2 ] T45.78 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, (z^-1 * x)^3 ] T45.79 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, y * z^-2 * x^-1 * z * x^-1 * z ] T45.80 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, (z^-1 * x)^3, y * z^-1 * x^-2 * z^2 * x^-1 ] T45.81 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-2 * x^-1 * z * x^-1 * z ] T45.82 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (y * z^-1 * y)^2, x^-1 * y^2 * x^2 * z * x^-1 * z ] T45.83 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z ] T45.84 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y * x^-1 * z * y^-1 * z^-1 ] T45.85 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z^2 * y * x * z^2 * y ] T45.86 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y^2 * x * z * y^2 ] T45.87 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T45.88 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y * x^-1 * z^2 * y ] T45.89 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T45.90 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x * z^2, (z^-1 * x)^3 ] T45.91 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x * z^2, y * z^-1 * x^-2 * z^2 * x^-1, y * x * z^-1 * x^-1 * z^3 ] T45.92 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (z^-1 * x)^3 ] T45.93 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T45.94 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T45.95 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^2 * x^-2 * z * y * x^-1 ] T45.96 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3, x * z * y * x^2 * z * x^-1 * y^-1 ] T45.97 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T45.98 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z^8 ] T45.99 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, x^-1 * y^2 * x^-1 * y * x * z^-1 ] T45.100 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^8 ] T45.101 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^2 * y^-1 * z * y ] T45.102 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T45.103 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T45.104 : Triangle type {4,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^8, z^2 * y * x^-2 * z^3 * x^-1 ] T45.105 : Triangle type {4,8,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z^9 ] T45.106 : Triangle type {4,8,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z^6 * y^-1 * x * z^2 ] T45.107 : Triangle type {4,9,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^9 ] T45.108 : Triangle type {4,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1 ] T45.109 : Triangle type {4,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, x^-1 * z * y * x * z * y ] T45.110 : Triangle type {4,31,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T45.111 : Triangle type {4,32,32} Group order 128 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-2 * y^3 * z^-1 * y * z^-1 ] T45.112 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2 ] T45.113 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-4 * z^3 * y^-1 * z ] T45.114 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-6 * z^2 * y^-1 * z^4 * y^-1 * z * y^-16 ] T45.115 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-4 * z^4 * y^-1 ] T45.116 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z * y^-6 ] T45.117 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, y^-5 * z^4 * y^-7 ] T45.118 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T45.119 : Triangle type {4,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-5 * z * y^-2 * z ] T45.120 : Triangle type {4,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z^2 ] T45.121 : Triangle type {4,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T45.122 : Triangle type {5,5,31} Group order 155 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y * x^2 * z^2 ] T45.123 : Triangle type {5,5,31} Group order 155 Chiral action Defining relators: [ x * y * z, z * y * x * z, x^-5 ] T45.124 : Triangle type {6,6,7} Group order 168 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^-1 * z^2, x^6, x^-1 * y^2 * x^-1 * y^2 * z^-1 ] T45.125 : Triangle type {6,6,7} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, z * y^2 * x * y^-1 * z, (z^-1 * y)^3 ] T45.126 : Triangle type {6,12,60} Group order 120 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-3 * x * z^4 ] T45.127 : Triangle type {6,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y * x * z^-1 * y ] T45.128 : Triangle type {6,19,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-3 * x * y^-4 * z ] T45.129 : Triangle type {6,20,20} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y^3 * z^-1 * y * z^-1 * x^-1 * y^3 * z^-1 * y^7 * z^-1 * y ] T45.130 : Triangle type {6,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^4 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T45.131 : Triangle type {7,16,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T45.132 : Triangle type {7,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * x * y^4 * z^-1 * y * z^-1 * y * z^-2 ] T45.133 : Triangle type {7,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 ] T45.134 : Triangle type {7,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-5 * x * y^4 * z^-1 * y * z^-4 ] T45.135 : Triangle type {8,8,16} Group order 128 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, x * z * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T45.136 : Triangle type {8,8,16} Group order 128 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, z^-1 * y * x^2 * z^-1 * y, x^8 ] T45.137 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, (x * y^-1 * x)^2, x^8 ] T45.138 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * z^2, x^8 ] T45.139 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, z^-2 * y^2 * z^-2, x^8 ] T45.140 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^8 ] T45.141 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^-3 * x * y^-1 * x * z^2 * y^-1 * z^-1 ] T45.142 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T45.143 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T45.144 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-9 * x^-1 * y * x * y^-1 * z^-5 ] T45.145 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T45.146 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^2 * y * z^-1 * x^-1 * y * z^-4 ] T45.147 : Triangle type {8,8,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T45.148 : Triangle type {8,8,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y * z^-4 * x * z * y * z^-1 * x * z^2 ] T45.149 : Triangle type {8,8,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y * z^-4 * x^-1 * y * z^-1 * x^-1 * z^3 ] T45.150 : Triangle type {8,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^6 * z^-3 * y^3 * z^-1 * y ] T45.151 : Triangle type {8,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T45.152 : Triangle type {8,52,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-8 ] T45.153 : Triangle type {8,52,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-4 * z^4 ] T45.154 : Triangle type {9,9,39} Group order 117 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y^-2 * x * z^2 ] T45.155 : Triangle type {10,11,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-4 * x * y^-4 ] T45.156 : Triangle type {10,12,12} Group order 120 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, z * x^-2 * y * x, y^2 * z^-1 * y^3 * z^-1 * y^2 * z^-2 * y ] T45.157 : Triangle type {10,12,12} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^-4 * z * y^-6 * z ] T45.158 : Triangle type {10,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-6 * x * y^-4 ] T45.159 : Triangle type {10,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-6 * z^2 ] T45.160 : Triangle type {11,11,11} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * y^-1 * x^-1 * z^4, y^-3 * z * y^-3 * x * y^-4 ] T45.161 : Triangle type {11,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-2 * z^3, y^-1 * x * y^-4 * x^3 * y^-4 ] T45.162 : Triangle type {11,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-3 * x^-2 * z^3, y^-5 * x^3 * y^-4 ] T45.163 : Triangle type {11,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z^3, x^11 ] T45.164 : Triangle type {11,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * z^4, x^11 ] T45.165 : Triangle type {11,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x * y^-3, x^11 ] T45.166 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^5 * x^-6 * y^2 ] T45.167 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^14 ] T45.168 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^-3 * x^4 * y^-4 ] T45.169 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-1 * x * z^-2 * x^4 * z^-4 ] T45.170 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^14 ] T45.171 : Triangle type {14,49,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^-1 * x * y^-1 * x^7 * y^-5 ] T45.172 : Triangle type {15,15,35} Group order 105 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, z^-1 * x^-1 * y^-1 * x * y^-2, (z^-1 * x)^3 ] T45.173 : Triangle type {15,15,35} Group order 105 Chiral action Defining relators: [ x * y * z, y * x^-2 * z^2, z^-2 * x^-1 * y^2 ] T45.174 : Triangle type {16,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, x * z^-1 * x * z^-2 * x^5 * z^-3 ] T45.175 : Triangle type {16,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y^4 * x^-7 * y * x^-1 * y * x^-1 ] T45.176 : Triangle type {16,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * z * x^-10 * y * x^-3 ] T45.177 : Triangle type {16,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^3 * z^-4, y^-2 * x^5 * y^-4 ] T45.178 : Triangle type {16,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x * z^-1 * x * z^-1 * x * z^-2 * x^6 * z^-2 ] T45.179 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^4 * z^-3, y^-4 * x^2 * y^-1 * z^3 * y^-2 ] T45.180 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-4 * x * z^-2 * x^4 * z^-4 ] T45.181 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4, x * z^-1 * x * z^-2 * x^6 * z^-2 ] T45.182 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-4 * x^7 * y^-6 ] T45.183 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-4, y^-4 * x^3 * y^-2 * z^2 * y^-2 ] T45.184 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y^2 * x^-9 * z^2 * x^-6 ] T45.185 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-5 * x^3 * y^-5 ] T45.186 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, z^4 * x^-8 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T45.187 : Triangle type {19,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-2 * x^5 * z^-2, y * z^-5 * y^4 ] T45.188 : Triangle type {24,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-9 * y * x^-10 * y * x^-1 * y * x^-1 * y ] T45.189 : Triangle type {24,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x^8 * y^-3 ] T45.190 : Triangle type {24,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-8 * x^3 * z^-4 ] T45.191 : Triangle type {24,32,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y * z^-1 * y^2 * x^-7 * y^4 ] T45.192 : Triangle type {24,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-10 * z * x^-7 * y^2 * x^-1 * z * x^-4 ] T45.193 : Triangle type {24,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-9 * z * x^-2 * y ] T45.194 : Triangle type {24,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^2 * z^-1 * x * z^-2 * x^7 * z^-1 ] T45.195 : Triangle type {24,48,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^2 * z^-1 * x * y^-1 * x * y^-1 * x^5 * z^-1 * x ] T45.196 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-9 * y^6 * x^-3 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T45.197 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x * y^-3 * x^4 * y^-4 ] T45.198 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^7 * y^-1, z^3 * y^-4 * x * y^-4 * z ] T45.199 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^8 * z^-3 ] T45.200 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-4 * x * z^-11 ] T45.201 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-2 * x^2 * z^-3 * x * z^-4 * x^3 * z^-6 ] T45.202 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * z^4, x^2 * y^-3 * x^5 * y^-3 ] T45.203 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-8 * x^3 * y^-4 ] T45.204 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * x^2 * y^-4 ] T45.205 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-2 * x * z^-1 * x^7 * z^-6 ] T45.206 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-17 * y * x^-8 * z * x^-5 ] T45.207 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-8 * z, x^2 * y^-3 * x^8 ] T45.208 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y^3 * x^-5 ] T45.209 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * y^-1 * z * y^-4 * z^4 ] T45.210 : Triangle type {31,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T45.211 : Triangle type {32,32,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, y * x^-1 * y * x^-1 * y * z^-1 * y ] T45.212 : Triangle type {32,32,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^-5 * x * y^-2 * z * y^-2 * z ] T45.213 : Triangle type {32,32,48} Group order 96 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3 ] T45.214 : Triangle type {32,32,48} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * z^2 * x^-1 * z^4 ] T45.215 : Triangle type {32,32,48} Group order 96 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^8 * x^-2 * z^4 * x^-1 * z * x^-1 * z ] T45.216 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-5 * x^3 * y^-5 ] T45.217 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-1 * y^8 ] T45.218 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^2 * z^-1 * y * z^-5 * x * z^-4 * y ] T45.219 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-4 * x^2 * z^-4 ] T45.220 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-6 * y^3 ] T45.221 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x^8 * z^-1 ] T45.222 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-7 * y, z^-6 * x * z^-4 ] T45.223 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4, x^2 * z^-1 * x^6 * z^-3 ] T45.224 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x * z^-1 * x * z^-1 * x^5 * z^-4 ] T45.225 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^10 * x^-2 * y^6 * z^-1 * y ] T45.226 : Triangle type {46,92,92} Group order 92 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^46, y * z^-1 ] T45.227 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x^-2 * y^-1, y^40 * x^-1 * y^5, x * z^-1 ] T45.228 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-1 * x * z^-1 * x^6 * z^-5 ] T45.229 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^9, z * y^-4 * z^4 ] T45.230 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, z^3 * y^-1 * z * y^-10 * z^2 ] T45.231 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^20 * x^-2 * y^9 ] T45.232 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-4, x^8 * z^-3 ] T45.233 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 ] T45.234 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-11 * x^2 * z^-6 ] T45.235 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^10 * z^-1 * x^12 ] T45.236 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^6 * z^-4, y^-2 * x^5 * y^-4 ] T45.237 : Triangle type {91,91,91} Group order 91 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * z^-1, y^-5 * x * y^-4 ] Genus 46 T46.1 : Triangle type {2,3,8} Group order 2160 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-1 * x * z * y^-1 * z^-3 * x ] T46.2 : Triangle type {2,3,8} Group order 2160 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z^2 * y * x * z^2 * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * z^2 ] T46.3 : Triangle type {2,3,8} Group order 2160 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z ] T46.4 : Triangle type {2,3,36} Group order 648 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^8 * y * z^-1 * x * z^5 * y^-1 * z^-1 * x * z * y^-1 * z^-7 * x ] T46.5 : Triangle type {2,4,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, y^-1 * z^2 * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^2, (z^-2 * y * z^-1)^3 ] T46.6 : Triangle type {2,4,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5, z^2 * y * z^-1 * y * z^-2 * y * z^-2 * y * z^-1 * x ] T46.7 : Triangle type {2,4,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x, y * z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1 ] T46.8 : Triangle type {2,4,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * y * z^-4 ] T46.9 : Triangle type {2,4,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-4 * x * y * z^-4, z * y * z^-1 * x * z * y^2 * z^-2 * x * z * y^-1, x * z * y * x * z * y * z^-1 * y * z^-3 * y * z^-1 ] T46.10 : Triangle type {2,4,12} Group order 540 Chiral action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, z * y * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T46.11 : Triangle type {2,4,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z * y^-2 * z^-4 * y, x * z * y * z^-2 * x * z^5 * y^-1 * z^-2 ] T46.12 : Triangle type {2,4,94} Group order 376 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-86 * x * y * z^-7 ] T46.13 : Triangle type {2,4,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-84 * x * y^-1 * z^-7 ] T46.14 : Triangle type {2,6,8} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^8, (z * y^-1 * z)^3, z * y^-1 * z * y^3 * z^-1 * x * z^2 ] T46.15 : Triangle type {2,6,8} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, (y * z^-1 * y * z^-1 * y)^2 ] T46.16 : Triangle type {2,6,8} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T46.17 : Triangle type {2,6,12} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, x * z^3 * y^-1 * z^-4 ] T46.18 : Triangle type {2,6,18} Group order 324 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z * y^-1 * z^-1 * x ] T46.19 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-2 * x * z^8 * y * z^-2 * x * z * y^-1 * z^-3 ] T46.20 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-3 * x * z * y * z^-7 * x * y^-1 * x * z^3 * y^-1 * z^-1 ] T46.21 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3 * y)^2 ] T46.22 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1)^6 ] T46.23 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T46.24 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^6 * y * z^-6 * x * z^2 * y^-1 ] T46.25 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T46.26 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y^-2 * z * y^-2 * z * y^-1 * z^-2 * x ] T46.27 : Triangle type {2,6,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T46.28 : Triangle type {2,6,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-3 * x * z^7 * y^-1 * z^-5 ] T46.29 : Triangle type {2,6,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^28 * y * z^-2 * x * z^6 * y * x * y^-1 * z^-8 * x * z ] T46.30 : Triangle type {2,6,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^29 * y * x * z^3 * y * x * z * y * x * y^-1 * z^-6 * x * z^5 ] T46.31 : Triangle type {2,6,138} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-19 * x * z^7 * y * z^-2 * x * z^5 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T46.32 : Triangle type {2,9,9} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3, y^-9 ] T46.33 : Triangle type {2,9,9} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-1 * y * z^-2, y^-1 * z^2 * y^3 * x * z * y^-1 * z ] T46.34 : Triangle type {2,10,25} Group order 250 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^3 * z^-3 ] T46.35 : Triangle type {2,10,25} Group order 250 Chiral action Defining relators: [ x^2, x * y * z, y * z^-2 * y^2 * z^-1 * x * z ] T46.36 : Triangle type {2,10,25} Group order 250 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-3 * x * z * y * z^-3 * x * z^3 * y^-1 * z^-13 ] T46.37 : Triangle type {2,10,115} Group order 230 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^3 * y * z^-3 * x * y * z^-14 * x * z ] T46.38 : Triangle type {2,16,28} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^4 * x * y^-10 * z^-1 * y, z^-1 * x * z * y * x * z^3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T46.39 : Triangle type {2,18,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, (y^-6 * z^2 * y^-1)^2 ] T46.40 : Triangle type {2,18,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-6 * z^-1 * y^5, y^-1 * z^5 * y^-9 * z * y^-2 ] T46.41 : Triangle type {2,24,24} Group order 216 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z^-1 * y * z^-2, z^-1 * y^6 * z^-1 * y * z^-1 * y^2 ] T46.42 : Triangle type {2,33,66} Group order 198 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-6 * y^9 * z^-1 * y^2 * z^-13 * y ] T46.43 : Triangle type {2,93,186} Group order 186 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^73 * y^-18 * z ] T46.44 : Triangle type {2,94,94} Group order 188 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^20 * z^-74 ] T46.45 : Triangle type {2,184,184} Group order 184 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^19 * z^-73 ] T46.46 : Triangle type {3,3,4} Group order 1080 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * z^-1 * x^-1 * z * y * x * z * y^-1 * x * z * y ] T46.47 : Triangle type {3,3,4} Group order 1080 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x * z^-1, z * y^-1 * z^-2 * x^-1 * z * y * x * y^-1 * z^-1 * x * z^-1 * x ] T46.48 : Triangle type {3,3,4} Group order 1080 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T46.49 : Triangle type {3,3,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, x * z * y^-1 * z^-1 * x^-1 * z^3 * y ] T46.50 : Triangle type {3,3,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x * z^2 * y * z^-1 * x * z^4 * y * z^-1 ] T46.51 : Triangle type {3,3,93} Group order 279 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-4 * x^-1 * z^5 ] T46.52 : Triangle type {3,4,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, z^6, y * x^-1 * y^-2 * x * z * y^-1 * z^-1 ] T46.53 : Triangle type {3,4,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-2)^2, z^6 ] T46.54 : Triangle type {3,4,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T46.55 : Triangle type {3,4,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T46.56 : Triangle type {3,6,8} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * y^-1 * x * z^2 * y^-1 ] T46.57 : Triangle type {3,6,8} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, y^6, y * x^-1 * y^-2 * x * y^-1 * z * y ] T46.58 : Triangle type {3,6,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-4 * x^-1 * z^3 * y^-1 ] T46.59 : Triangle type {3,6,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^2 * y^2 * x^-1 * z^3 ] T46.60 : Triangle type {3,6,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y^-1 * z * y ] T46.61 : Triangle type {3,6,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * y)^3 ] T46.62 : Triangle type {3,6,62} Group order 186 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * x^-1 * y^-1 * z^-2 ] T46.63 : Triangle type {3,8,8} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-3, y^8 ] T46.64 : Triangle type {3,8,8} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, y^8 ] T46.65 : Triangle type {3,8,8} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * z * y, y^8 ] T46.66 : Triangle type {3,8,8} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, y^8 ] T46.67 : Triangle type {3,8,8} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^8 ] T46.68 : Triangle type {3,18,18} Group order 162 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^2 * z^-1 ] T46.69 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^3 * z^-1 * y^6 * z^-1 * y * z^-2 * y^2 ] T46.70 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-3 * y^11 * z^-3 ] T46.71 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^3 * z^-2 ] T46.72 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 ] T46.73 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * y)^3 ] T46.74 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T46.75 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-2 * y * x^-1 * z * y^-2 ] T46.76 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y * z^-1 * y * z^-1 * y^2 * z^-1 * y^3 * z^-1 * y^3 * z^-1 * y^2 * z^-1 ] T46.77 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^-1 * z * x^-1 * y^-1 * x * z^2 * y^-1 ] T46.78 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3, y * z^-2 * x^-1 * z^3 ] T46.79 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2 ] T46.80 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, (y * x^-1 * z)^3 ] T46.81 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, z * y * z^-1 * x^-1 * y^-3 ] T46.82 : Triangle type {3,18,18} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^5 * z^-1 * x^-1 * y^-2 * z * y * z^-1 * y ] T46.83 : Triangle type {3,47,141} Group order 141 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-36 * z * y^-1 * z * y^-7 * z ] T46.84 : Triangle type {3,48,48} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-37 * z * y^-1 * z * y^-7 * z ] T46.85 : Triangle type {3,48,48} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^35 * y^-3 * z * y^-7 * z ] T46.86 : Triangle type {3,48,48} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T46.87 : Triangle type {3,138,138} Group order 138 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-35 * z * y^-1 * z * y^-8 ] T46.88 : Triangle type {4,4,4} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * x^-1 * y^-1)^2, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, x^-1 * y^-1 * z * y^-1 * x * z * y^-1 * z ] T46.89 : Triangle type {4,4,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, x * z * y * x^2 * z * x^-1 * y^-1 ] T46.90 : Triangle type {4,4,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, z^-1 * x^-1 * y * x^2 * z * y * x, y * z^-1 * x * y^-1 * x * z^3 ] T46.91 : Triangle type {4,4,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * z * x^-1 * z, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T46.92 : Triangle type {4,4,47} Group order 188 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^47 ] T46.93 : Triangle type {4,4,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y^-1 * z^-4 * x * z^8 ] T46.94 : Triangle type {4,6,6} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, (z^-1 * x)^3, y^-1 * z^-1 * x^-2 * z * y^-2 ] T46.95 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T46.96 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y)^2, z^6 ] T46.97 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, (y * z^-2)^2 ] T46.98 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z^6 ] T46.99 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, z^6 ] T46.100 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^6, y * z^-1 * y * x^-1 * z^2 * y ] T46.101 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, z^-2 * y * x^-1 * z * y^-2 ] T46.102 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T46.103 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T46.104 : Triangle type {4,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, (z^-1 * x)^3 ] T46.105 : Triangle type {4,6,12} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x * z * y ] T46.106 : Triangle type {4,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^-2 * z * x^-1 * y^-3 ] T46.107 : Triangle type {4,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y^-1 * x * z^4 ] T46.108 : Triangle type {4,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T46.109 : Triangle type {4,14,28} Group order 140 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, z * y^-3 * x * z^2 * y^-1 ] T46.110 : Triangle type {4,16,16} Group order 144 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T46.111 : Triangle type {4,62,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^7 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T46.112 : Triangle type {5,6,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T46.113 : Triangle type {5,24,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T46.114 : Triangle type {5,25,25} Group order 125 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z * y^-1 * x * y^-2, y^-1 * z^-1 * y * x * z * x^-1 ] T46.115 : Triangle type {5,25,25} Group order 125 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x * y^-1 * z, y^-1 * z^-1 * y * x * z * x^-1 ] T46.116 : Triangle type {5,25,25} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T46.117 : Triangle type {5,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T46.118 : Triangle type {5,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T46.119 : Triangle type {6,6,9} Group order 162 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-1 * y^2 * x * y^-1 * z^-1 ] T46.120 : Triangle type {6,6,9} Group order 162 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z^-1 * x^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1 ] T46.121 : Triangle type {6,6,9} Group order 162 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y * x^2 * z^-2, y^6, y^-1 * z^-1 * y^2 * z^-1 * x ] T46.122 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^4 * y^-1 * x^-1 * z^4 ] T46.123 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, x^6, y^6, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * x * z ] T46.124 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, x^-1 * y * x^-1 * y * z^-1, y^6, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T46.125 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y ] T46.126 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T46.127 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^3 * y * z^-2 * x * z^3 ] T46.128 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-2 * x^-2 * y^-1 * z * y^-1 ] T46.129 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^3 * x^-1 * z^2 * y^-1 ] T46.130 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^4 * y^-1 * x^-1 * z^4 ] T46.131 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, (y^-1 * x)^3 ] T46.132 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^-1 * y^2 * x^2 * z^-1 * x^-1 * y^-1 ] T46.133 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, x^6, (y^-1 * x)^3 ] T46.134 : Triangle type {6,6,9} Group order 162 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^-1 * z^-1 * x^2 * z^-1 * x, (y^-1 * x)^3 ] T46.135 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T46.136 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * x * z^-1 * x^-1 ] T46.137 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^3 * y * x^-1 * z^4 ] T46.138 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z * y * x^2 * z^2, y^6 ] T46.139 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z * y * z^-2 * x^-1 * z^4 ] T46.140 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^24 ] T46.141 : Triangle type {6,6,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-12 * x * y^-1 * z^-3 * x * z * y * z^-6 ] T46.142 : Triangle type {6,6,69} Group order 138 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y^-1 * z^-4 * x * y^-1 * x * y^-1 * z^-3 * x * z^7 ] T46.143 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z^-1 * y, (z^-1 * y)^3 ] T46.144 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, x^-1 * z * y * x^-1 * z * x^-1 * z ] T46.145 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T46.146 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T46.147 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * z^-1 * x^-1 * z * y * x ] T46.148 : Triangle type {6,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-2, x^6, z * y^-1 * x^2 * z * y^-1 ] T46.149 : Triangle type {6,14,21} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3 ] T46.150 : Triangle type {6,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2, z^-1 * x * z^-1 * x * z * y^-1 ] T46.151 : Triangle type {6,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * z^4 ] T46.152 : Triangle type {6,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-3 * y^4 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T46.153 : Triangle type {8,12,24} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * y^-1 * x^2 * z * y^-1, x * z^-1 * x^2 * z^-2 ] T46.154 : Triangle type {8,12,24} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^-1 * y * z^-1, x^8 ] T46.155 : Triangle type {8,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z * y^-9 * x * z * y^-1 * z * y^-1 ] T46.156 : Triangle type {9,36,36} Group order 108 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^6 * z^-1 * y * z^-2 * y^2 ] T46.157 : Triangle type {9,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, x^2 * y^-1 * x^2 * y^-3 ] T46.158 : Triangle type {9,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-9 ] T46.159 : Triangle type {9,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * z^4 ] T46.160 : Triangle type {12,18,36} Group order 108 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2, y^3 * x^-1 * y * z^-1 * y ] T46.161 : Triangle type {12,18,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * x^-1 * z^4, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T46.162 : Triangle type {12,18,36} Group order 108 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^2 * y^-1 * x * y^-1 * x^4 * y^-1 * z^-1 * x * y^-1 * x ] T46.163 : Triangle type {12,18,36} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3 ] T46.164 : Triangle type {14,16,16} Group order 112 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x * z * y^-1 * z * y^-1 * x^2 * z * y^-1 * z * y^-1 ] T46.165 : Triangle type {15,21,35} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, x^2 * y^-4 * x^3 * y^-3 ] T46.166 : Triangle type {18,18,18} Group order 108 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-4 * y * x^-1 * z, y^3 * x^-1 * y * z^-1 * y ] T46.167 : Triangle type {18,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^7 * y^-1 * x * y^-1 ] T46.168 : Triangle type {18,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, x^-4 * y * x * z^-1, z^3 * x^-1 * z * x^-1 * z^4 ] T46.169 : Triangle type {18,18,18} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * y^-2, y^-1 * z * y^-1 * z * y^-4 * z^4 ] T46.170 : Triangle type {20,25,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x^11 * z^-3 ] T46.171 : Triangle type {20,25,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^3, x^2 * y^-4 * x^6 * y^-1 ] T46.172 : Triangle type {20,25,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-2 * x * y^-4 * x^3 * y^-4 ] T46.173 : Triangle type {20,25,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-5 * y^3 * x^-4 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.174 : Triangle type {24,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x * y^-5 * x * y^-4 * x * y^-5 * x * y^-1 ] T46.175 : Triangle type {24,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^7 * y^-4 ] T46.176 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^21 * y^-1 * x^8 * z^-1 * x^2 ] T46.177 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, y^-1 * x * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 ] T46.178 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-3 * x * z^-2 * x^4 * z^-4 ] T46.179 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^7, y^3 * z^-8 * y ] T46.180 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-2 * x^4 * z^-3, y^2 * z^-4 * x^-2 * y^3 ] T46.181 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-9 * x^2 * y^-6 ] T46.182 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-5 * x * z^-4 ] T46.183 : Triangle type {32,48,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^9 * x^-4 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T46.184 : Triangle type {33,33,33} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^7 * x^-2 * y^4 * x^-1 * y^4 ] T46.185 : Triangle type {33,33,33} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * x^3 * y^-4 ] T46.186 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^14 * x^-3 * y^8 ] T46.187 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^20 * x^-2 * y^10 ] T46.188 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-1 * x * y^-3 * x^4 * y^-4 ] T46.189 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-1 * y^3 * x^-7 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.190 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z * y^-1 * z * y^-5 * z^3 ] T46.191 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-6 * x^4 * y^-4 ] T46.192 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x * y^-2 * x^4 * y^-4 ] T46.193 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-10 * y^2 * z^-5 * y * z^-2 ] T46.194 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * y^-3 * x^-4 * z^3 ] T46.195 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^-1 * z * y^-6 * z^2 ] T46.196 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-1 * x * y^-3 * x^6 * y^-2 ] T46.197 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-4, y^-1 * z * y^-5 * z^3 ] T46.198 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T46.199 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-2 * x * y^-1 * x * y^-3 * x^4 * y^-4 ] T46.200 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^7, x^10 * z^-2 ] T46.201 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^5 * y^-1 * x^8 * y^-1 * x^2 ] T46.202 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^6 * x^-1 * y^4 * z^-1 * y * z^-1 * y^3 ] T46.203 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-1 * z * y^-8 ] T46.204 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x^7 * z^-6 ] T46.205 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^6 * x^-3 * z * x^-10 * z * x^-1 * z * x^-1 * z ] T46.206 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-2 * x^8, y^-1 * z * y^-7 * z ] T46.207 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T46.208 : Triangle type {47,94,94} Group order 94 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^47, y * z^-1 ] T46.209 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x^-2 * y^-1, y^41 * x^-1 * y^5, x * z^-1 ] T46.210 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y * x^-9 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.211 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^2 * y^-1 * x * y^-3 * x^6 * y^-2 ] T46.212 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * z^4, x^10 * z^-1 ] T46.213 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^4 * y^-3, x^7 * z^-4 ] T46.214 : Triangle type {93,93,93} Group order 93 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-5 * x^3 * y^-4 ] Genus 47 T47.1 : Triangle type {2,4,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-88 * x * y * z^-7 ] T47.2 : Triangle type {2,4,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-30 * x * z^5 * y * z^-2 * x * z^2 * y^-1 * z^-7 ] T47.3 : Triangle type {2,4,188} Group order 376 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-86 * x * y^-1 * z^-7 ] T47.4 : Triangle type {2,6,141} Group order 282 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-19 * x * z^9 * y * z^-1 * x * z^5 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T47.5 : Triangle type {2,8,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-4 * x * z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 ] T47.6 : Triangle type {2,8,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-3 * x * z^3 * y * x * z^2 * y^-1 * z^-8 ] T47.7 : Triangle type {2,8,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-8 * x * z^5 ] T47.8 : Triangle type {2,8,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^20 * y * z^-9 * x * z^2 ] T47.9 : Triangle type {2,12,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, z * y * z^-1 * y^2 * z^-1 * x * z ] T47.10 : Triangle type {2,95,190} Group order 190 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^93 * z^-2 ] T47.11 : Triangle type {2,96,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-20 * y^11 * z^-2 * y^14 ] T47.12 : Triangle type {2,96,96} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-93 ] T47.13 : Triangle type {2,188,188} Group order 188 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^20 * z^-73 * y ] T47.14 : Triangle type {3,4,7} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^3 * y^-1 * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y^-1 ] T47.15 : Triangle type {3,141,141} Group order 141 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-36 * z * y^-1 * z * y^-6 * z^2 ] T47.16 : Triangle type {4,4,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^48 ] T47.17 : Triangle type {4,4,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x ] T47.18 : Triangle type {4,4,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x^-1 ] T47.19 : Triangle type {4,4,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-17 * x * z^2 * y * z^-4 ] T47.20 : Triangle type {4,4,94} Group order 188 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^34 * y^-1 * z^-4 * x * z^8 ] T47.21 : Triangle type {4,5,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^6, z^-2 * y * x^-1 * y * z^-1 * y ] T47.22 : Triangle type {4,6,28} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-4 * x^-1 * z^3 * y * x^-1 * y * x * y^-1 * z^-4 ] T47.23 : Triangle type {4,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z^-2 * y * x^2 * z * y * z^-1 ] T47.24 : Triangle type {4,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, x^-1 * z * y^2 * x^-1 * z^3 ] T47.25 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x^-1 * z^4 ] T47.26 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-4 * x^-1 * z * y * x^-1 * z * y * z^-2 ] T47.27 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * x * z * y * z^-2 * x * z^2 ] T47.28 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^6 * y^-1 * z^-3 * x * y^-1 * z^-8 ] T47.29 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 ] T47.30 : Triangle type {4,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x * z^4 ] T47.31 : Triangle type {4,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^4 * z^-1 * y * z^-1 ] T47.32 : Triangle type {4,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-5 * z^3 * y^-7 * z^3 ] T47.33 : Triangle type {4,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z^4 * y^-1 * z^3 * y^-1 * z^2 * y^-5 * z * y^-1 ] T47.34 : Triangle type {4,33,44} Group order 132 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-1 * z * y^-5 * z ] T47.35 : Triangle type {4,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-7 * z^2 * y^-1 * z^4 * y^-1 * z * y^-15 * z ] T47.36 : Triangle type {4,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T47.37 : Triangle type {6,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-6 ] T47.38 : Triangle type {6,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, z * y^-2 * x * y^-1 * z ] T47.39 : Triangle type {6,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-7 * z ] T47.40 : Triangle type {8,8,9} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^4 * y^-1 * x^-1 * z^4 ] T47.41 : Triangle type {8,8,9} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^9 ] T47.42 : Triangle type {8,8,32} Group order 128 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T47.43 : Triangle type {8,8,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-9 * x^-1 * y * x^-1 * y * z^-5 ] T47.44 : Triangle type {8,15,24} Group order 120 Chiral action Defining relators: [ x * y * z, z * y^-1 * x * y^-1, y * x * z^-1 * x^-1 * z * y^2, x^8 ] T47.45 : Triangle type {8,15,24} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * z * y, x^8 ] T47.46 : Triangle type {8,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^6 * z^-3 * y^4 * z^-1 ] T47.47 : Triangle type {8,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-7 * z ] T47.48 : Triangle type {10,12,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-1 * z^-1 * y, x^10 ] T47.49 : Triangle type {10,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-4 * z^4 ] T47.50 : Triangle type {15,21,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T47.51 : Triangle type {20,50,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-7 * y^2 * x^-6 * z^2 * x^-5 ] T47.52 : Triangle type {20,50,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-3 * x^6 * z^-7 ] T47.53 : Triangle type {20,50,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^5 * y^-2, z^3 * y^-4 * x^-2 * z^3 ] T47.54 : Triangle type {20,50,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-7 * y^4 * x^-1 * y^4 ] T47.55 : Triangle type {48,96,96} Group order 96 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^48, y * z^-1 ] T47.56 : Triangle type {48,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-10 * z * x^-8 * z * x^-5 ] T47.57 : Triangle type {48,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^3 * z^-2 * x^8 ] T47.58 : Triangle type {48,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-2 * z^2 * y^-3 * x^4 * y^-4 * z^3 ] T47.59 : Triangle type {48,96,96} Group order 96 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-6 * x * z^-4 ] T47.60 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x^-2 * y^-1, y^42 * x^-1 * y^5, x * z^-1 ] T47.61 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^4 * z^-3, y^-4 * x^3 * y^-4 ] T47.62 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y, y^2 * z^-5 * y^2 * z^-2 ] T47.63 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-4 * y^7 ] T47.64 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^2 * z^-1 * x * z^-2 * x^8 ] T47.65 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^3 * z^-4 * x^-2 * y^4 ] T47.66 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * z^-1 * x^9 ] T47.67 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-5 * y^9 * x^-2 * y^4 * x^-1 * y * x^-1 * y ] T47.68 : Triangle type {95,95,95} Group order 95 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x^9 ] Genus 48 T48.1 : Triangle type {2,4,51} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-35 * x * z^8 * y^-1 * z^-7 ] T48.2 : Triangle type {2,4,98} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-98 ] T48.3 : Triangle type {2,4,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-88 * x * y^-1 * z^-7 ] T48.4 : Triangle type {2,6,50} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^38 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^5 ] T48.5 : Triangle type {2,8,34} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-12 * x * z^3 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-14 ] T48.6 : Triangle type {2,10,26} Group order 260 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^4 * y * x * z^2 * y * x * z * y * x * y * x * z^15 ] T48.7 : Triangle type {2,10,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^7 * y * z^-16 ] T48.8 : Triangle type {2,12,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-5 * x * z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T48.9 : Triangle type {2,14,18} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-1 * z^-1 * x * y^-1 * z * y * x * z * y * x * y^-6 * z^-1 * x, z^-2 * x * z^9 * y^-1 * z^-6 ] T48.10 : Triangle type {2,14,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-3 * z^4)^2, z^9 * y * x * z^6 ] T48.11 : Triangle type {2,26,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-14 * z^2 * y^-7 * z^2 * y^-1 ] T48.12 : Triangle type {2,34,102} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-5 * y^11 * z^-2 * y^12 * z^-3 ] T48.13 : Triangle type {2,50,100} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-22 * y^11 * z^-1 * y^14 * z^-1 ] T48.14 : Triangle type {2,51,51} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-37 * y^11 * z^-1 ] T48.15 : Triangle type {2,97,194} Group order 194 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^94 * z^-2 * y ] T48.16 : Triangle type {2,98,98} Group order 196 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-93 * z ] T48.17 : Triangle type {2,192,192} Group order 192 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-92 * z ] T48.18 : Triangle type {3,3,97} Group order 291 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * x^-1 * z^7 * y^-1 * z^-2 ] T48.19 : Triangle type {3,14,28} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-3 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^2 * z^-1 ] T48.20 : Triangle type {3,26,39} Group order 156 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-5 * z * y^-1 * z^4 * y^-1 * z ] T48.21 : Triangle type {3,49,147} Group order 147 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-38 * z * y^-1 * z * y^-7 * z ] T48.22 : Triangle type {3,50,50} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^37 * y^-3 * z * y^-7 * z ] T48.23 : Triangle type {3,144,144} Group order 144 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-37 * z * y^-1 * z * y^-6 * z^2 ] T48.24 : Triangle type {4,4,49} Group order 196 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-49 ] T48.25 : Triangle type {4,4,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^35 * y^-1 * z^-4 * x * z^8 ] T48.26 : Triangle type {4,6,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-4 * x * z^4 * y * z^-5 ] T48.27 : Triangle type {4,10,16} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^4 * y^-1 * x * z^3, y^10 ] T48.28 : Triangle type {4,20,35} Group order 140 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y * x * z^3 ] T48.29 : Triangle type {4,33,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^12 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T48.30 : Triangle type {4,34,34} Group order 136 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-16 ] T48.31 : Triangle type {4,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z^2 * y^-1 ] T48.32 : Triangle type {4,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T48.33 : Triangle type {5,26,26} Group order 130 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-3 * z^2 * y^-1 * z * y^-1 * z * y^-14 * z ] T48.34 : Triangle type {5,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T48.35 : Triangle type {5,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T48.36 : Triangle type {6,6,25} Group order 150 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^25 ] T48.37 : Triangle type {6,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * x * y^-2 * z * y^-1 ] T48.38 : Triangle type {6,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^4 * z^-1 * y * z^-1 * x^-1 * y^3 * z^-1 * y^8 * z^-1 ] T48.39 : Triangle type {7,17,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^4 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 ] T48.40 : Triangle type {7,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z * y^-5 * z^2 ] T48.41 : Triangle type {7,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, z * x^-2 * y * x, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-5 * z * y^-2 ] T48.42 : Triangle type {7,18,18} Group order 126 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-2 * z * y^-1 * z * y^-10 * z * y^-1 * z ] T48.43 : Triangle type {7,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T48.44 : Triangle type {7,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T48.45 : Triangle type {7,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 * y^-1 ] T48.46 : Triangle type {8,8,17} Group order 136 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^8, (x * y^-1 * x^2)^2 ] T48.47 : Triangle type {8,8,17} Group order 136 Chiral action Defining relators: [ x * y * z, z * y * x * z, x^8, (x * y^-1 * x^2)^2 ] T48.48 : Triangle type {8,8,17} Group order 136 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^2 * y * x * z^2, x^8 ] T48.49 : Triangle type {8,8,17} Group order 136 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x * z^5 ] T48.50 : Triangle type {8,15,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1, x^8 ] T48.51 : Triangle type {9,13,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z^4 * y^-2 * z^4 ] T48.52 : Triangle type {9,14,14} Group order 126 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^12 * z^-2 ] T48.53 : Triangle type {9,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.54 : Triangle type {9,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T48.55 : Triangle type {9,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T48.56 : Triangle type {10,10,13} Group order 130 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^8 * y * x * z^4 ] T48.57 : Triangle type {10,10,60} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^3 * y * x^-1 * z^3 * y^-1 * x * z^4 ] T48.58 : Triangle type {10,10,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z * y^-1 * z^-1 * x^-1 * z^2 * y^-1 * z^-2 * x * z^4 ] T48.59 : Triangle type {10,12,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^10 ] T48.60 : Triangle type {10,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x * z^2, (y * z^-1 * y)^2, (z^-1 * x)^3 ] T48.61 : Triangle type {10,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^2 * z^-2, (x * y^-1)^4 ] T48.62 : Triangle type {10,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3 ] T48.63 : Triangle type {12,12,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * z * y^-1 * z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T48.64 : Triangle type {12,27,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^2 * y^-4 ] T48.65 : Triangle type {12,27,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^4, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T48.66 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^4 * y^-3 * x^4 * z^-3 * x^2 ] T48.67 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-2 * x^4 * z^-6 ] T48.68 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z * x^-1 * z^5 * x^-6 * z^2 ] T48.69 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x * y^-4 * x^2 * y^-4 ] T48.70 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x * y^-4 * x^3 * y^-3 ] T48.71 : Triangle type {13,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^4 * y^-3 * x^4 * z^-3 * x^2 ] T48.72 : Triangle type {14,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z * y * z^-2 * x^-1 * z^4 ] T48.73 : Triangle type {14,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^4 ] T48.74 : Triangle type {14,14,56} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, z^3 * y * x^-1 * z^4 ] T48.75 : Triangle type {15,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, x * y^-1 * x * y^-4 * x^4 * y^-2 ] T48.76 : Triangle type {15,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^5 * y^-3 * x^4 * z^-3 * x^3 ] T48.77 : Triangle type {15,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^-7 * y^4 * x^-1 * y * x^-1 * y^2 ] T48.78 : Triangle type {16,16,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z * y * x^-1 * y * x^-1 * z^4 ] T48.79 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T48.80 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.81 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-8 * x * y^-4 ] T48.82 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x * z^-1 * x^7 * z^-5 * x^2 ] T48.83 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^13 * y^-1 * x * z^-1 * x^2 ] T48.84 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x^7 * z^-5 * x^3 ] T48.85 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, x * y^-1 * x * y^-4 * x^5 * y^-1 ] T48.86 : Triangle type {17,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * y^-3 * x^4 * y^-3 * x^4 ] T48.87 : Triangle type {18,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * x * y^-1 ] T48.88 : Triangle type {18,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, z^-1 * x^5 * z^-1 * x * z^-1 * x ] T48.89 : Triangle type {18,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * z^3 ] T48.90 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x^3 * y^-2, x^7 * z^-4 ] T48.91 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^5 * x^-4 * y^-3 * z^4 ] T48.92 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-4 * x^7 ] T48.93 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, (x^-9 * z * x^-1 * z * x^-1)^2 ] T48.94 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^5 * x^-4 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T48.95 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y^2 * x^-6 * y^2 * x^-5 ] T48.96 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-3, x^-1 * z^4 * x^-7 ] T48.97 : Triangle type {25,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-4 * x * y^-4 * x^3 * y^-4 ] T48.98 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-4 * x^2 * y^-2 * z * y^-4 * x * y^-1 ] T48.99 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-2 * x^4 * y^-4 ] T48.100 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-2, y^5 * z^-1 * y * z^-1 ] T48.101 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, z^-4 * x^2 * z^-4 ] T48.102 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^8 * y^-2 ] T48.103 : Triangle type {26,26,52} Group order 104 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^4 * x^-1 * z * x^-1 * z^4 * y^-1 * z * x^-1 * z ] T48.104 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^5 * y^-7 * z^3 ] T48.105 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x^7 * z^-7 ] T48.106 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-5 * x^3 * y^-4 ] T48.107 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, x^-12 * z * x^-1 * z^5 * x^-3 * z^4 * x^-1 * z^2 ] T48.108 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-19 * z * x^-8 * y * x^-5 ] T48.109 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z^3, x^3 * y^-3 * x^7 ] T48.110 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^12 * x^-2 * z^4 * x^-1 * z^2 ] T48.111 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-4 * x^3 * y^-4 ] T48.112 : Triangle type {33,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.113 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 ] T48.114 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y * x^-1 * y * x^-1 * y * z^-1 * y ] T48.115 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x * z^2, x^5 * y^-1 * z^-2 ] T48.116 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * z * y, (z * x^-1 * z^3)^2 ] T48.117 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, x^-4 * z^3 ] T48.118 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^5 * z^-1 * x * z^-1 ] T48.119 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * x^-6 * y * x^-1 * z^3 * y ] T48.120 : Triangle type {34,34,51} Group order 102 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * x * z^-5 * x * z^-4 * y * z^-1 * y * z^-1 ] T48.121 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^15 * x^-1 * z^9 ] T48.122 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-2 * x^8 ] T48.123 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * y * x^-7 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T48.124 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-2 * x * z^-2 * x^4 * z^-4 ] T48.125 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-5 * x^3 * y^-5 ] T48.126 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-10 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 ] T48.127 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-16 * z * y^-3 ] T48.128 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 ] T48.129 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^3 * z^-4, y^2 * z^-5 * x^-3 * y^3 ] T48.130 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y * z^-9 ] T48.131 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 ] T48.132 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^3 * z^-2 * x^8 ] T48.133 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-28 * x * z^-4 ] T48.134 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-4 * z * y^-3 * x^3 * y^-4 * z * y^-3 ] T48.135 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^49, y * z^-1 ] T48.136 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^3 * z^-3 * y * z^-4 * y^3 ] T48.137 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-8 * x * z^-4 ] T48.138 : Triangle type {49,98,98} Group order 98 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^3 * z^-4, y^-4 * x^3 * y^-4 ] T48.139 : Triangle type {50,50,50} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * z^-1 * y^3 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T48.140 : Triangle type {50,50,50} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-8 * x^2 * y^-4 ] T48.141 : Triangle type {50,50,50} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-16 * x^2 * z^-8 ] T48.142 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x^-2 * y^-1, y^43 * x^-1 * y^5, x * z^-1 ] T48.143 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-25 * x^2 * y^-6 ] T48.144 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-7 * x * y^-1 * x * y^-1 * x * y^-4 * x^3 * y^-5 * x * y^-1 ] T48.145 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^3 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 ] T48.146 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y^5 * x^-7 * y * x^-1 * y * x^-1 ] T48.147 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x^7 * y^-5 ] T48.148 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x^7 * y^-4 ] T48.149 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4, x^11 * y^-1 ] T48.150 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^-5 * x * z^-4 ] T48.151 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x * z^-1 * x * z^-2 * x^8 ] T48.152 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^4 * z^-3, y^-3 * x^4 * y^-4 ] T48.153 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x * z^-1 * x * z^-1 * x * z^-2 * x^8 ] T48.154 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^9 * y^-4 * z^8 ] T48.155 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^2 * z^-1 * y^3 * x^-5 * y^3 * z^-1 * y ] T48.156 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x * z^-2 * x^4 * z^-4 ] T48.157 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-7 * x^2 * y^-6 ] T48.158 : Triangle type {97,97,97} Group order 97 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-4 * x^3 * z^-4 ] Genus 49 T49.1 : Triangle type {2,3,10} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * x * z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-3 * x, z^-1 * x * z^4 * y * x * z^2 * y * x * z * y^2 * z^-2 * x * y^-1 * z^-2 ] T49.2 : Triangle type {2,3,12} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, z * y * z^-1 * x * z * y * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z ] T49.3 : Triangle type {2,3,14} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x, x * z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 ] T49.4 : Triangle type {2,3,14} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^5 * y * x * z * y^-1 * x * z^2 * y^-1 * z^-1 * x, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T49.5 : Triangle type {2,4,5} Group order 1920 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, y * x * z * y^-1 * z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * y * z^-2 * y * z^-1, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T49.6 : Triangle type {2,4,5} Group order 1920 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^6, z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.7 : Triangle type {2,4,6} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-2 * y * z^-1 * y^2 * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T49.8 : Triangle type {2,4,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-1)^6 ] T49.9 : Triangle type {2,4,7} Group order 896 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, (y * z^-1)^4, (y * z^-2)^4 ] T49.10 : Triangle type {2,4,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z^10, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T49.11 : Triangle type {2,4,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^10, z^-1 * x * z * y^-1 * z * y^-1 * z^-3 * y * z^-1 ] T49.12 : Triangle type {2,4,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^10, z * y * z^-3 * x * y^-1 * z^-4 * x ] T49.13 : Triangle type {2,4,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^12 ] T49.14 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, z^-1 * x * z^4 * y * z^-2 * x * y * z^-7 ] T49.15 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, x * z^3 * y * z^-4 * x * z^2 * y^-1 * z^-5 ] T49.16 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-2 * z^-4 * y, z^6 * y * x * z^2 * y^-1 * x * z^3 * y^-1 * z^-1 * x * z ] T49.17 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z ] T49.18 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T49.19 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z * y * z^-2 * x * y^-1 * z^-3 * x ] T49.20 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.21 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^3 * y^-2 * z^-4 * y ] T49.22 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T49.23 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y^-1 * z * y * z^-1 * x * y^-1 * z^2 * y^-1 * z * y^-1 ] T49.24 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.25 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.26 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-9 * y * z^-1 * y^2 * z^-1 * y * z^-5 ] T49.27 : Triangle type {2,4,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-1 * y * z^-1 * y * z^-2 ] T49.28 : Triangle type {2,4,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-4)^2, z^-2 * y * x * z * y^2 * z^-2 * x * y^-1 * z^-1 ] T49.29 : Triangle type {2,4,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.30 : Triangle type {2,4,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-14 * x * z^4 * y * z^-1 * x * z^3 * y^-1 * z^-4 ] T49.31 : Triangle type {2,4,52} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-37 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T49.32 : Triangle type {2,4,100} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-100 ] T49.33 : Triangle type {2,4,196} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-8 * x * y^-1 * z^-89 ] T49.34 : Triangle type {2,5,5} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (y * z^-1)^6, y * z^-2 * y * x * y^-2 * z^-1 * y * x * y^-1 * z^-2 ] T49.35 : Triangle type {2,5,5} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-1)^6 ] T49.36 : Triangle type {2,5,6} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.37 : Triangle type {2,6,6} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-1 * y)^4, (y * z^-2 * y * z^-1 * y)^2, y * x * y^-1 * z^2 * y^2 * z^-2 * x * z^2 ] T49.38 : Triangle type {2,6,6} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, z^-1 * y^2 * x * y^-2 * z^2 * y^-1 * z^-2 ] T49.39 : Triangle type {2,6,6} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.40 : Triangle type {2,6,6} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y^-1 * z^2 * y^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.41 : Triangle type {2,6,6} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2, (y * z^-1 * y)^4 ] T49.42 : Triangle type {2,6,6} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-2 * y * z^-1 * y)^2 ] T49.43 : Triangle type {2,6,6} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T49.44 : Triangle type {2,6,12} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, y * z^-1 * x * z * y^2 * x * z * y^-1 * z ] T49.45 : Triangle type {2,6,12} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T49.46 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, (y * z^-1 * y)^4 ] T49.47 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * y^-1 * z, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T49.48 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-3 * z^-3 * y * z^-1 ] T49.49 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * y^-1 * z, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T49.50 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^2 * y^-3 * z^-3 * y^2 ] T49.51 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y^-3 * z^-3 * y^2 ] T49.52 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z * y * z^-3 * x * y^-1 * z^-4 * x ] T49.53 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.54 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, (y * z^-1 * y)^4 ] T49.55 : Triangle type {2,6,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-1 * x * y^-2 * z^-2 * y * z^-1 * y, (y * z^-1 * y)^4 ] T49.56 : Triangle type {2,6,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^2 * z^-1 * y * x ] T49.57 : Triangle type {2,6,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^4 * y^-1 * z^-5, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 ] T49.58 : Triangle type {2,6,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-8 * x * y * z^-6 ] T49.59 : Triangle type {2,6,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y^-2 * z)^3 ] T49.60 : Triangle type {2,6,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y^-2 * z)^3 ] T49.61 : Triangle type {2,6,39} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z^4 * y * x * y^-1 * z^-5 ] T49.62 : Triangle type {2,6,51} Group order 306 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^40 * y * x * y * z^-7 * x * z^2 ] T49.63 : Triangle type {2,6,147} Group order 294 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-21 * x * z^16 * y * z^-1 * x * y^-1 * z^-9 ] T49.64 : Triangle type {2,7,7} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^-3 * x * y * z^-3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T49.65 : Triangle type {2,7,14} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T49.66 : Triangle type {2,8,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, (y^-1 * z)^6 ] T49.67 : Triangle type {2,8,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z ] T49.68 : Triangle type {2,9,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.69 : Triangle type {2,10,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * y^-1 * z * y^-2 * z^-2 * y * z^-1, y^10 ] T49.70 : Triangle type {2,10,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-3 * y, z^-2 * x * y^-2 * z * y^-1 * z^-1 * y, y^10 ] T49.71 : Triangle type {2,10,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^10, (y * z^-1 * y^3)^2, (y * z^-1 * y * z^-1 * y)^2 ] T49.72 : Triangle type {2,10,10} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-1 * x * z, y^10, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T49.73 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T49.74 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T49.75 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^2 * x * z * y^2 * x * z^3, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T49.76 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^12 ] T49.77 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^12, y^2 * z^-1 * y^4 * z^-1 * y^2 * z^-2 ] T49.78 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T49.79 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-4 * x * z^5 * y^-1 * z^-2 ] T49.80 : Triangle type {2,12,12} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, z^-12 ] T49.81 : Triangle type {2,12,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-1 * x * z^8 * y * z^-4 * x * z * y^-1 * z^-4 ] T49.82 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z^9 * y^-1 * z^-6, y * x * y^-1 * z^-1 * x * y^-1 * z * y * x * z * y * x * y^-6 * z^-1 * y ] T49.83 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-1 * x * z^8 * y * z^-6 ] T49.84 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^5 * y * z^-4 * x * z^2 * y^-1 * z^-3, (y^-4 * z^3 * y^-1)^2 ] T49.85 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-2 * x * z^7 * y^-1 * z^-6 ] T49.86 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y^-3 * z^-1 * x * z^3 ] T49.87 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^-1 * z * y^-1 * z^3 * y^-7 * z^2 * y^-1 ] T49.88 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T49.89 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, x * z * y * x * z * y^3 * x * z^2 * y^-1 * z^-1 ] T49.90 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4 ] T49.91 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^-1 * z * y^-1 * z^3 * y^-7 * z^2 * y^-1 ] T49.92 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z * y * x * z * y^3 * x * y^-1 * z^-3 * x ] T49.93 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, (y * z^-1)^4, (y * z^-3)^2 ] T49.94 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, (y * z^-3)^2 ] T49.95 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1 * y^2)^2, (y * z^-3)^2 ] T49.96 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-2 * y)^2, (y * z^-3)^2 ] T49.97 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^-2 * z * y^-2 * z^2 * y^-6 * z * y^-2 ] T49.98 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T49.99 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T49.100 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, (y * z^-1)^4 ] T49.101 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, (y * z^-1)^4 ] T49.102 : Triangle type {2,16,16} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, (y^3 * z^-1 * y * z^-1 * y^2)^2 ] T49.103 : Triangle type {2,16,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * z^6 * y^-1 * z^-5, y^-4 * z^4 * y^-3 * z^4 * y^-1 ] T49.104 : Triangle type {2,16,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * z^10 * y^-1 * z^-1 ] T49.105 : Triangle type {2,20,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, (y * z^-2 * y)^2 ] T49.106 : Triangle type {2,20,20} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-4 * z^-4, y^-1 * z * y^-3 * z^-1 * y * x * y^-1 ] T49.107 : Triangle type {2,27,54} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-27 ] T49.108 : Triangle type {2,28,28} Group order 224 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y * z^-1, y^-1 * z * y^-1 * z^10 * y^-15 ] T49.109 : Triangle type {2,28,28} Group order 224 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-3 * y, y^-10 * z^2 * y^-1 * z ] T49.110 : Triangle type {2,28,28} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-11 * z^3 * y^-10 * z^2 ] T49.111 : Triangle type {2,30,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^2 * y^-4 * z^5 ] T49.112 : Triangle type {2,36,36} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^-8 * y^11 * z^-4 * y * z^-12 ] T49.113 : Triangle type {2,52,52} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-24 * y^11 * z^-2 * y^12 * z^-2 ] T49.114 : Triangle type {2,99,198} Group order 198 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^95 * z^-4 ] T49.115 : Triangle type {2,100,100} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^4 * y^-95 ] T49.116 : Triangle type {2,196,196} Group order 196 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-94 ] T49.117 : Triangle type {3,3,5} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, z * y * z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 * x, z^-1 * x^-1 * y * x * z * y * x^2 * y^-1 * x * z^2 * y ] T49.118 : Triangle type {3,3,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, (x * z * y)^4 ] T49.119 : Triangle type {3,3,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z ] T49.120 : Triangle type {3,3,7} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^3 * y^-1 * x^-1 * z^3, (z^-1 * x^-1 * y^-1)^3, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x ] T49.121 : Triangle type {3,3,7} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z^2 * y^-1 * x * z^3, z^3 * y^-1 * x^-1 * z^3, z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x ] T49.122 : Triangle type {3,4,4} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, (y * z^-1)^4, z^-1 * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1 ] T49.123 : Triangle type {3,4,4} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (y * z^-1)^4, (y * x^-1 * z)^3 ] T49.124 : Triangle type {3,4,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x * y^-1 * x * z * y * z^-1 ] T49.125 : Triangle type {3,4,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * x * z ] T49.126 : Triangle type {3,4,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * x * z ] T49.127 : Triangle type {3,4,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, (x^-1 * z^2 * y)^2 ] T49.128 : Triangle type {3,4,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, (x^-1 * z^2 * y)^2 ] T49.129 : Triangle type {3,4,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * z^-1 * x^-1 ] T49.130 : Triangle type {3,4,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y^-1 * x * z ] T49.131 : Triangle type {3,4,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T49.132 : Triangle type {3,4,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-4 * x^-1 * z^3 * y^-1 ] T49.133 : Triangle type {3,4,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T49.134 : Triangle type {3,5,5} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, (z^-1 * y)^3 ] T49.135 : Triangle type {3,5,15} Group order 240 Chiral action Defining relators: [ x^3, x * y * z, y^-5, (x * z * y)^2, y * x^-1 * y * x^-1 * y * z^-2 ] T49.136 : Triangle type {3,6,6} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T49.137 : Triangle type {3,6,6} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, z^6, y * z^-1 * x^-1 * y^-1 * x * z^2 * y ] T49.138 : Triangle type {3,6,6} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * z * y^-1 * z * y ] T49.139 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, (z^-1 * y)^3, z^6 ] T49.140 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, y * z^-2 * x^-1 * y * z^-2 ] T49.141 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y, x * z * y * x^-1 * y * z^-1 * y ] T49.142 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T49.143 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (x^-1 * y^-1 * z^-1)^4 ] T49.144 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^2 * z^-1 * y * x^-1 * z * y^-1 * z^2 ] T49.145 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * z * y^-2 * z^-1 ] T49.146 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T49.147 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (z^-1 * y)^3, z^6 ] T49.148 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.149 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y * z^-1 * y^2 * x^-1 * y^-2 * z^-1 * y * z^-2 * y^2 * z^-1 ] T49.150 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3 ] T49.151 : Triangle type {3,6,6} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T49.152 : Triangle type {3,6,10} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * z * y^-1 * z^-1, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x ] T49.153 : Triangle type {3,8,24} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T49.154 : Triangle type {3,12,12} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * y^-2 * z^-1 ] T49.155 : Triangle type {3,12,12} Group order 192 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, y * z^-2 * x^-1 * y^-2 * z ] T49.156 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.157 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^2 * x * z^2 * y ] T49.158 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^3 * x^-1 * y^-1 * z * y ] T49.159 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x * z * y)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.160 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-2 * x^-1 * y^-1 * x * y^-3 ] T49.161 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * y^-1 * z * y, z * y^-1 * z^-1 * x^-1 * y^-2 * z ] T49.162 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, (y * z^-1)^4 ] T49.163 : Triangle type {3,12,12} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^4, z^-1 * y^4 * x^-1 * y^-1 * z^-1 * y^3 ] T49.164 : Triangle type {3,14,42} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^14 ] T49.165 : Triangle type {3,15,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-3 * y * z^-2 * y^3 * z^-1 * y^4 ] T49.166 : Triangle type {3,15,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x * y^-1 * z^-1, z * y^-1 * z^-1 * x * z^2 ] T49.167 : Triangle type {3,15,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^5 * x^-1 * y^-2 * z * y * z^-1, y^-1 * z^2 * y^-2 * x^-1 * z * y^-1 * z^2 ] T49.168 : Triangle type {3,15,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (x^-1 * z * y)^2 ] T49.169 : Triangle type {3,15,15} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z * x^-1 * y^-1 * x * y^-1 * x ] T49.170 : Triangle type {3,39,39} Group order 156 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-1 * z^2 * y^-1 * z * y^-4 * z^2 * y^-2 ] T49.171 : Triangle type {3,50,150} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-39 * z * y^-1 * z * y^-7 * z ] T49.172 : Triangle type {3,51,51} Group order 153 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-40 * z * y^-1 * z * y^-7 * z ] T49.173 : Triangle type {3,147,147} Group order 147 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-38 * z * y^-1 * z * y^-8 ] T49.174 : Triangle type {4,4,5} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^2 * y * x^-1 * y^-1 * z^-1 * x, (x * y^-1)^4 ] T49.175 : Triangle type {4,4,5} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^2 * y^-1 * x^-1 * z^2, (x * y^-1)^4 ] T49.176 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x^-1 * z^2, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T49.177 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x^-1 * z^2, (y * z^-1)^4 ] T49.178 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * z * y * z^-1 ] T49.179 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-2)^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T49.180 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^2 * y * x^-1 * z * y^-1 * x, y * x * z^-1 * x^-1 * z * x^-1 * z ] T49.181 : Triangle type {4,4,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, z^2 * y * x^-1 * z * y^-1 * x ] T49.182 : Triangle type {4,4,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^6 ] T49.183 : Triangle type {4,4,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T49.184 : Triangle type {4,4,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 ] T49.185 : Triangle type {4,4,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2, z^8 ] T49.186 : Triangle type {4,4,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1, (y * z^-1)^4 ] T49.187 : Triangle type {4,4,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * z * y, (x * z^-1 * y)^2 ] T49.188 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T49.189 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T49.190 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1)^4, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T49.191 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T49.192 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^8 ] T49.193 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T49.194 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, z^-2 * y * x^-1 * z * y^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T49.195 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T49.196 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2 ] T49.197 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-1)^4 ] T49.198 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T49.199 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4, z^-1 * x * z^-1 * y * x * z * y * z^-1 ] T49.200 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T49.201 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T49.202 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-3 * y * x^2 * z^3 * y ] T49.203 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^8 ] T49.204 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-2 * z^3 ] T49.205 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2, z^8 ] T49.206 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.207 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, (y * z^-1)^4 ] T49.208 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T49.209 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.210 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^8 ] T49.211 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z^-1 * y * z^-1 * y * x^-1 * z^2 * y * z^-1 ] T49.212 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.213 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T49.214 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T49.215 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.216 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T49.217 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z * y)^2 ] T49.218 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T49.219 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T49.220 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x^-1 * z * y)^2 ] T49.221 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, z^8, y^-1 * z * y * z^-1 * x^-1 * y^-1 * z^3 ] T49.222 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^8 ] T49.223 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * z^-1 ] T49.224 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^2 * y * x^-2 * z^3 * x^-1, z^-1 * x * z^-2 * x^-1 * z * y^-1 * z^-1 * x ] T49.225 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x * z^-1 * x^-2 * z^2 * y * z^-1 ] T49.226 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, z^8 ] T49.227 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T49.228 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1 ] T49.229 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, (x * z^-3)^2, z^8 ] T49.230 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T49.231 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y ] T49.232 : Triangle type {4,4,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T49.233 : Triangle type {4,4,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z * y)^2 ] T49.234 : Triangle type {4,4,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, (x * z^-2)^2, (y * z^-2)^2, z * x^-1 * y * x^2 * z * y * x^-1 ] T49.235 : Triangle type {4,4,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T49.236 : Triangle type {4,4,14} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-4 * x * z * y * x * y^-1 * x * y^-1 * z^-3 * x^-1 * z^2 * y^-1 ] T49.237 : Triangle type {4,4,26} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * x^-1 * z^3 * y^-1 * z^4 ] T49.238 : Triangle type {4,4,26} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y^-1 * x * z * y * z^-7 * x^-1 ] T49.239 : Triangle type {4,4,50} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T49.240 : Triangle type {4,4,50} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y^-1 * x^-1 * z^13 ] T49.241 : Triangle type {4,4,98} Group order 196 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-42 * x * y^-1 * z^-6 ] T49.242 : Triangle type {4,6,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x * z * y^-1, (z^-1 * x)^3 ] T49.243 : Triangle type {4,6,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x * z * y^-1, y * x^-1 * y * x^-1 * z * y * z^-1, z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 ] T49.244 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2, z^2 * y * x^-1 * z^2 * x^-1 ] T49.245 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T49.246 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1 ] T49.247 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^-2 * y * x^-1 * y * z^-1 * y ] T49.248 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, y * z^-2 * x^-1 * z^3 ] T49.249 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2 ] T49.250 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T49.251 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (z^-1 * x)^3, (y * z^-2)^2, y * z^-1 * y * x^-1 * y * x * z ] T49.252 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z, x * z^-2 * x^-1 * z * y * z^-1 ] T49.253 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1 ] T49.254 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (z^-1 * x)^3 ] T49.255 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z * y * x^-1 * z * y^-1 * z^-3 * x * z * y^-1 * z^-1 * x^-1 ] T49.256 : Triangle type {4,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T49.257 : Triangle type {4,6,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-4 * x * z^7 * y * z^-2 ] T49.258 : Triangle type {4,8,40} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * y^-1 * z, (x^-1 * z * y)^2 ] T49.259 : Triangle type {4,8,40} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^8 ] T49.260 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-4 * x * z^2 ] T49.261 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-2 * x * z^4 ] T49.262 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-4 * x^-1 * z^2 ] T49.263 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z^4 ] T49.264 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^6 * y^-1 * z^-3 * x * z * y * z^-7 ] T49.265 : Triangle type {4,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * z^-1 * x * z^5 ] T49.266 : Triangle type {4,10,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^10 ] T49.267 : Triangle type {4,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y^5 * z^-1 * y^2 ] T49.268 : Triangle type {4,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-7 * y^6 * z^-1 * y^4 ] T49.269 : Triangle type {4,20,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y * x^-1 * z^3 ] T49.270 : Triangle type {4,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-1 * y^2 * z^-1 * y^2 * x^-1 * y^3 * z^-1 * y ] T49.271 : Triangle type {4,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^8 * z^-1 * y ] T49.272 : Triangle type {4,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T49.273 : Triangle type {4,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T49.274 : Triangle type {4,28,35} Group order 140 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^-4 * x^-1 * z * y^-1 * z ] T49.275 : Triangle type {4,28,35} Group order 140 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-3 * x * z^3 ] T49.276 : Triangle type {4,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-15 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T49.277 : Triangle type {4,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^14 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T49.278 : Triangle type {5,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (x * y^-2)^2, (y * z^-1 * y)^2 ] T49.279 : Triangle type {5,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, (y * z^-1 * y)^2, z * y^-1 * z^-1 * x * z^2 ] T49.280 : Triangle type {5,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, (x * z * y)^2 ] T49.281 : Triangle type {5,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^3 * x^-1 * y^-1 * z ] T49.282 : Triangle type {6,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, z * y * x^-2 * y * x^2 ] T49.283 : Triangle type {6,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, y^-1 * z^-1 * x^-2 * y * x * y^-1 ] T49.284 : Triangle type {6,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^2 * x^2 * z^2, y^6 ] T49.285 : Triangle type {6,6,6} Group order 192 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * z * y^-1 * x * y^-1 * z ] T49.286 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.287 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, x^6, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * x^-1 * y^-1 * x * z * x^-1 * z ] T49.288 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, (x * z * y)^2, z^6, y * x^-3 * z * x^-2 ] T49.289 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^6, (x * z * y)^2 ] T49.290 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, z^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x ] T49.291 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^6, z^6, z * y * x^-2 * z * y * x ] T49.292 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^6, (y * z^-1)^4 ] T49.293 : Triangle type {6,6,6} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, (y * z^-1)^4 ] T49.294 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z^-2 * x^2 * z * y ] T49.295 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, y^2 * x^2 * z^-1 * y ] T49.296 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * x * z^-1 * x * z^-2 ] T49.297 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^8 ] T49.298 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^3 ] T49.299 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T49.300 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y * z^-2 * x^-1 * z^3, y^8 ] T49.301 : Triangle type {6,8,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^3 ] T49.302 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3 ] T49.303 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z^3 * y^-8 ] T49.304 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.305 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y * z^-2 * x^-1 * y * z^-2 ] T49.306 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2 ] T49.307 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z^2 * y^-1 * z * y^-3 * z^3 ] T49.308 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * y^2 * x^-1 * z * x^-1, (z^-1 * y)^3 ] T49.309 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z * y, (z^-1 * y)^3 ] T49.310 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (x^-1 * z * y)^2 ] T49.311 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T49.312 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y^2 * x^-1 * z * y^-1 * z, z^-1 * y^4 * z^-3 ] T49.313 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T49.314 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, x^6, y^-1 * z * y^-1 * z^2 * y^-2 * z * y^-3 * z ] T49.315 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y^3 * x^-1 * y^-2 * z ] T49.316 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T49.317 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y^-6 * z * y^-1 * z^2 ] T49.318 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y * z^-1 * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T49.319 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T49.320 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^12 ] T49.321 : Triangle type {6,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^3 * x * z * y^3 * x * y^-3 * z^-1 * y ] T49.322 : Triangle type {6,18,63} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-2 * x * z^3 ] T49.323 : Triangle type {6,18,63} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^3 ] T49.324 : Triangle type {6,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-12 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T49.325 : Triangle type {6,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * y^-1 * z * y^-1 ] T49.326 : Triangle type {6,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-4 * z * y^-1 * z ] T49.327 : Triangle type {6,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 * z^2 ] T49.328 : Triangle type {6,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^6 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T49.329 : Triangle type {7,7,7} Group order 168 Reflexible action Defining relators: [ x * y * z, (y^-1 * x)^3, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (z^-1 * x)^3 ] T49.330 : Triangle type {8,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T49.331 : Triangle type {8,8,12} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1 ] T49.332 : Triangle type {8,15,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-4 * z^2 ] T49.333 : Triangle type {8,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, y * z^-1 * x^2 * z^-1 * y, x^8 ] T49.334 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, z^-1 * y^4 * z^-3 ] T49.335 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y^3 * z^-2 * y ] T49.336 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^2 * z^-1 * y^2 * z^-3 ] T49.337 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^4 * z^-3 ] T49.338 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, (y * z^-1)^4 ] T49.339 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T49.340 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y * z^-1 * y, z * x^-3 * y^-1 * z^2 ] T49.341 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1, x^8 ] T49.342 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T49.343 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-1 * y^2 * x^-1 * y * z^-1 * y * z^-1 ] T49.344 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^14 * z^-2 ] T49.345 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^6 * z^-2 ] T49.346 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2, x^8 ] T49.347 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^8, y * x^-4 * z * x^-3 ] T49.348 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, (x^-1 * z * y)^2 ] T49.349 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (x^-1 * z * y)^2 ] T49.350 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (x^-1 * z * y)^2 ] T49.351 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.352 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1 ] T49.353 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T49.354 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1 ] T49.355 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4 ] T49.356 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^-3 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T49.357 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-4 * x^-1 * z^2 * y * z^-1 ] T49.358 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, (x * z * y)^2 ] T49.359 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T49.360 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T49.361 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T49.362 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2 ] T49.363 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, (x^-1 * z * y)^2 ] T49.364 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2 ] T49.365 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T49.366 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1 ] T49.367 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, z * y^2 * x^-1 * z * x^-1 ] T49.368 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, z * y^2 * x^-1 * z * x^-1 ] T49.369 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^8 ] T49.370 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T49.371 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-3 * y^3 * z^-2 ] T49.372 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-1 * y^3 * z^-3 ] T49.373 : Triangle type {8,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^4 * x^-1 * y^3 * z^-1 ] T49.374 : Triangle type {8,24,30} Group order 120 Chiral action Defining relators: [ x * y * z, y * x^-2 * y * z^-1, y^2 * x^2 * z^2, z * x^-3 * z^2 * x^-1 ] T49.375 : Triangle type {8,24,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z^3 * x^-1 * z^2 * y^-1 ] T49.376 : Triangle type {8,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 ] T49.377 : Triangle type {8,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-8 ] T49.378 : Triangle type {8,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^4 ] T49.379 : Triangle type {9,9,9} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, y * z^-1 * x^-1 * y^-1 * x * z * x^-1 * z ] T49.380 : Triangle type {9,14,18} Group order 126 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y * z^-1, z * y * x^2 * z * y^-1, x^9 ] T49.381 : Triangle type {10,12,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T49.382 : Triangle type {10,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y^-3 * x^2 * y^-3 ] T49.383 : Triangle type {10,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^10 ] T49.384 : Triangle type {10,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T49.385 : Triangle type {10,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^3 * y^-4 * x^-1 * z^4 ] T49.386 : Triangle type {10,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-5 * z^3 ] T49.387 : Triangle type {10,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-7 * z ] T49.388 : Triangle type {12,12,30} Group order 120 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * x^-1 * z^3 ] T49.389 : Triangle type {12,12,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T49.390 : Triangle type {12,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, z^5 * x^-1 * z^4 ] T49.391 : Triangle type {12,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T49.392 : Triangle type {14,16,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x * y^-1 * x * y^-1 * x * y^-4 * x^4 * y^-2 ] T49.393 : Triangle type {14,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^5 * z^-1 * y * z^-1 ] T49.394 : Triangle type {14,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-4 * x^2 * y^-4 ] T49.395 : Triangle type {14,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-3 * y * x^-7 * z * y * x^-1 * z * x^-1 ] T49.396 : Triangle type {15,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-1 * x^7 * z^-6 ] T49.397 : Triangle type {15,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^3 * y^-3, x^-1 * z^4 * x^-3 * z^3 ] T49.398 : Triangle type {16,16,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^3 * y * x^-1 * z^3 ] T49.399 : Triangle type {16,16,56} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * z^-1 * x * z^3 ] T49.400 : Triangle type {16,16,56} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, z^3 * x^-2 * z^4 ] T49.401 : Triangle type {18,36,36} Group order 108 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^-4 * y * x^-1 * z ] T49.402 : Triangle type {18,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-5 * z * y * x^-8 * y * x^-2 * z * x^-1 ] T49.403 : Triangle type {18,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * z^-2 * x^6 * y^-2 * x^4 ] T49.404 : Triangle type {18,36,36} Group order 108 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-4 * z * x^-1 * z ] T49.405 : Triangle type {21,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y * x^-3 * y * x^-8 * z^2 * x^-6 ] T49.406 : Triangle type {21,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^7 * y^-1 * x^-6 * z^2 ] T49.407 : Triangle type {21,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-2 * x * y^-4 * x^2 * y^-4 ] T49.408 : Triangle type {21,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^5 * y^-1, z^4 * y^-2 * x^-1 * z^4 ] T49.409 : Triangle type {21,35,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T49.410 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-8 * x^2 * y^-4 ] T49.411 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-6 * x * y^-4 * x * y^-3 * z * y^-1 * x * y^-1 ] T49.412 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^8 * z^-4 * x^2 ] T49.413 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^2 * y^-4 * x^6 ] T49.414 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T49.415 : Triangle type {26,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-8 * z * x^-5 ] T49.416 : Triangle type {27,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-1 * z^-1, y^2 * x^2 * z^2, z^-1 * y^3 * z^-2 ] T49.417 : Triangle type {27,27,27} Group order 108 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-1 * z * y * x^-8 * y * x^-3 ] T49.418 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-2 * y^13 ] T49.419 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^7 * y^-3 * x^-2 * z^5 ] T49.420 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-4 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T49.421 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-8 * x^2 * y^-4 ] T49.422 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^4, x^3 * y^-3 * x^7 ] T49.423 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^-1 * z^3 * x^-8 ] T49.424 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-1 * x * z^-1 * x^10 * y^-1 * x * z^-1 * x * z^-1 ] T49.425 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^2 * y^-4 * x^4 * y^-2 ] T49.426 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^7, z^5 * x^-1 * z^4 ] T49.427 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-5 * x^2 * y^-4 ] T49.428 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * y^-3 * x^-1 * z^4 ] T49.429 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^7 * x^-5 * z^2 ] T49.430 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^12 * x^-2 * z^4 * x^-1 * z * x^-1 * z ] T49.431 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-14 * y * x^-3 * y * x^-9 * y * x^-6 ] T49.432 : Triangle type {34,51,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, x * y^-1 * x * y^-4 * x^2 * y^-4 ] T49.433 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^50, y * z^-1 ] T49.434 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x * y^-4 * x^7 ] T49.435 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x^9 * z^-2 ] T49.436 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^7 * x^-5 * z^3 ] T49.437 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^6 * z^-1, x^3 * y^-1 * x^6 * z^-3 * x ] T49.438 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^4 * y^-4 * z^4 ] T49.439 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^18 * x^-1 * y^3 * x^-4 * y^9 ] T49.440 : Triangle type {50,100,100} Group order 100 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^2 * y^-1 * z^3 * x^-6 * z^4 ] T49.441 : Triangle type {99,99,99} Group order 99 Reflexible action Defining relators: [ x^-2 * y^-1, y^44 * x^-1 * y^5, x * z^-1 ] T49.442 : Triangle type {99,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^11 * z^-1 * y^5 ] T49.443 : Triangle type {99,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-1 * z * x^-6 * y^4 * x^-4 ] T49.444 : Triangle type {99,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^7, x^8 * z^-5 ] T49.445 : Triangle type {99,99,99} Group order 99 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y, z^5 * y^-1 * z * y^-1 * z * y^-1 * z^4 * x^-1 * y^-3 * z^2 * y^-1 * z ] Genus 50 T50.1 : Triangle type {2,3,13} Group order 1092 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^-1 * z^3 * y^-1 * z^-1 * x, z^2 * y * z^-1 * x * z^4 * y * x * z * y^-1 * x * z * y^-1 * z^-2 * x ] T50.2 : Triangle type {2,4,6} Group order 1176 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y^-2 * z^-1 * y * z^-2 * y ] T50.3 : Triangle type {2,4,102} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-102 ] T50.4 : Triangle type {2,4,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y^-1 * z^-90 ] T50.5 : Triangle type {2,6,6} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y^-1 * z * y^-1 * z^3 * y * z^-1 * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T50.6 : Triangle type {2,6,6} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * z^-1 * x * z * y^2 * x * y^-1 * z^2 ] T50.7 : Triangle type {2,6,6} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-1 ] T50.8 : Triangle type {2,6,6} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, x * z * y^-1 * z^2 * y^-1 * z^2 * y * z^-1 * x * z^2 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T50.9 : Triangle type {2,6,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * z * y^-1, z^3 * y * x * y^-1 * z^-3 * x ] T50.10 : Triangle type {2,6,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T50.11 : Triangle type {2,6,52} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-30 * x * z^3 * y * x * z * y * x * y^-1 * z^-15 ] T50.12 : Triangle type {2,6,150} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-20 * x * z * y * x * z^16 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-1 ] T50.13 : Triangle type {2,8,8} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * y * x * y^-2 * z^-1 * y * z^-2 ] T50.14 : Triangle type {2,8,68} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-12 * x * z^3 * y * x * z * y * z^-16 ] T50.15 : Triangle type {2,12,22} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-3 * x * z * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T50.16 : Triangle type {2,12,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, x * z^9 * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T50.17 : Triangle type {2,15,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y * z^-2 * x * y^-1 * z^-3 ] T50.18 : Triangle type {2,18,18} Group order 252 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y * x * y^-1 * z^-2 * x, y^2 * z^-1 * y^2 * z^-1 * y^8 * z^-1 * y^2 * z^-1 ] T50.19 : Triangle type {2,20,24} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z^5 * y * x * y^-3 * z^-1 * x * y^-1 * z^-1 * x ] T50.20 : Triangle type {2,22,110} Group order 220 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-10 * z^2 * y^-7 * z^2 * y^-1 ] T50.21 : Triangle type {2,42,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-9 * z^2 * y^-6 * z^3 * y^-1 ] T50.22 : Triangle type {2,52,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-14 * z^2 * y^-8 * z^2 ] T50.23 : Triangle type {2,101,202} Group order 202 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^96 * z^-4 * y ] T50.24 : Triangle type {2,102,102} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^5 * y^-95 * z ] T50.25 : Triangle type {2,200,200} Group order 200 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^4 * y^-94 * z ] T50.26 : Triangle type {3,3,4} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y * x, x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z * y * x^-1 * z * y * z^-1 ] T50.27 : Triangle type {3,3,4} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y * x, x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-2 ] T50.28 : Triangle type {3,3,52} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T50.29 : Triangle type {3,4,4} Group order 588 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, y * z^-1 * x^-1 * y^-2 * x * z * y^-1 * z^2 ] T50.30 : Triangle type {3,4,4} Group order 588 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 * z^-1 ] T50.31 : Triangle type {3,4,4} Group order 588 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * x^-1 * z * y * x^-1 * z * y * x * y^-1 ] T50.32 : Triangle type {3,6,6} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * x * y * z^-1 * y * z^-1 * y * z^-1 ] T50.33 : Triangle type {3,6,6} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y^-2 * z^-1 * x^-1 * y^-1 * z^2 ] T50.34 : Triangle type {3,6,6} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-1 * y * x^-1 * y^-2 * z^-1, z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^-1 ] T50.35 : Triangle type {3,6,6} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z * x^-1 * z * y * x * z * y * x * y^-1 * x * z * y * x ] T50.36 : Triangle type {3,6,6} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^2 * z^-1 * y * z^-1 * y ] T50.37 : Triangle type {3,6,6} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T50.38 : Triangle type {3,21,28} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * z * y^-1 * z ] T50.39 : Triangle type {3,24,24} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T50.40 : Triangle type {3,24,24} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z * y^-1 * z, y * z^-1 * y^3 * z^-3 ] T50.41 : Triangle type {3,52,52} Group order 156 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^39 * y^-3 * z * y^-7 * z ] T50.42 : Triangle type {3,150,150} Group order 150 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-39 * z * y^-1 * z * y^-6 * z^2 ] T50.43 : Triangle type {4,4,4} Group order 392 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y * x^-1 * z * y * x^-1 * y * z^-1 * x^-1 * z, x^-1 * y^-1 * z * y * x^-1 * z * x^-1 * y^-1 * z ] T50.44 : Triangle type {4,4,4} Group order 392 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-1 * z^-1 * y * x^-2 * z * y^-1 * x * z, y^-1 * z * x^-1 * y * x^-1 * z * y^-1 * z * x^-1 ] T50.45 : Triangle type {4,4,51} Group order 204 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x * z^-1 * y * z^-2 ] T50.46 : Triangle type {4,4,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^37 * y^-1 * x^-1 * z^13 ] T50.47 : Triangle type {4,4,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y^-1 * x * z^13 ] T50.48 : Triangle type {4,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z^2 * y ] T50.49 : Triangle type {4,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-5 * y * z^-2 * y^2 * z^-1 * y * z^-2 * y^4 ] T50.50 : Triangle type {4,28,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-3 * x^-1 * z^3 ] T50.51 : Triangle type {4,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-14 * z * y^-1 ] T50.52 : Triangle type {5,26,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T50.53 : Triangle type {5,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T50.54 : Triangle type {5,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^3 * z^-1 ] T50.55 : Triangle type {6,6,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * z^-2, z * y^-2 * x * z * x^-1, x * z * y^-1 * x * y^-1 * z^-1 ] T50.56 : Triangle type {6,6,12} Group order 168 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T50.57 : Triangle type {6,6,12} Group order 168 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y * x^-1 * y * x^-1 * y * x * z ] T50.58 : Triangle type {6,6,26} Group order 156 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^6, (x * y^-1 * x)^2 ] T50.59 : Triangle type {6,6,26} Group order 156 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, x^6, y^6, y * x^-3 * z * x^-2 ] T50.60 : Triangle type {6,6,26} Group order 156 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^26 ] T50.61 : Triangle type {6,6,75} Group order 150 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-12 * x * y^-1 * x * y^-1 * z^-3 * x * z * y * z^-6 ] T50.62 : Triangle type {6,22,22} Group order 132 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^14 * z^-1 * y * z^-1 * y^2 * z^-1 ] T50.63 : Triangle type {6,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-5 * z ] T50.64 : Triangle type {8,8,34} Group order 136 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, y^2 * x^-2 * z^3 ] T50.65 : Triangle type {8,8,34} Group order 136 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x^-1 * y * x^-1 * z^4 ] T50.66 : Triangle type {8,24,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^8 ] T50.67 : Triangle type {8,24,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^2 ] T50.68 : Triangle type {8,30,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-2, x^8 ] T50.69 : Triangle type {9,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, y^2 * x^2 * z^2, x^-9 ] T50.70 : Triangle type {9,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z * y^-1, z^-1 * y^3 * z^-2 ] T50.71 : Triangle type {9,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, z^-2 * y^2 * z^-1 * y ] T50.72 : Triangle type {9,18,18} Group order 126 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-2 * y^2 * z^-1 * y, x^-9 ] T50.73 : Triangle type {10,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z * y * z^-1 * x^-1 * z^3 ] T50.74 : Triangle type {10,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-3 * x^-1 * y * z^-2 ] T50.75 : Triangle type {10,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^2 * z^-3 ] T50.76 : Triangle type {10,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, y * z^-3 * y^2 * z^-1 * y^2 * z^-1 * y^2 ] T50.77 : Triangle type {10,24,24} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z * y^-3 * z * y^-3 * x * z * y^-1 * z * y^-1 ] T50.78 : Triangle type {11,12,12} Group order 132 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^10 * z^-2, x^2 * z^-1 * y * z^-1 * y * z^-1 * x^-2 * y^-1 * z * y^-1 * z * y^-1 * x^2 ] T50.79 : Triangle type {11,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x^2 * y^-4, z^4 * y^-2 * x^-1 * z^4 ] T50.80 : Triangle type {11,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^3, x^11 ] T50.81 : Triangle type {11,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-1 * z^4, x^11 ] T50.82 : Triangle type {11,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-3 * x^-1 * z^4, y^-2 * x * y^-4 * x^2 * y^-4 ] T50.83 : Triangle type {11,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x^11 ] T50.84 : Triangle type {12,12,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, y * x * z^2 * y^-1 * z^-2 * x * z^4 ] T50.85 : Triangle type {12,20,20} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * z * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 ] T50.86 : Triangle type {14,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^5 * z^-1 * y * z^-1 ] T50.87 : Triangle type {14,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y * x^-1 * y * x^-1 * y * x^-1 * z ] T50.88 : Triangle type {14,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-2 * x * z^-1 * x * z^-3 ] T50.89 : Triangle type {14,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * y^2 * z^-2 ] T50.90 : Triangle type {14,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^-5 * z^3 * y ] T50.91 : Triangle type {15,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z * x^-1, y * z^-1 * x^-1 * y * z^-1 ] T50.92 : Triangle type {15,15,20} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T50.93 : Triangle type {18,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^5 * y^-3 * x^-1 * z^4 ] T50.94 : Triangle type {18,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^3 * z^-1 * x^10 * y^-1 * x^4 ] T50.95 : Triangle type {18,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-8 * x^2 * y^-4 ] T50.96 : Triangle type {21,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-6 * x * y^-4 ] T50.97 : Triangle type {21,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-4 * y * x^-9 * z * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.98 : Triangle type {21,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x * y^-1 * x * y^-4 * x^6 ] T50.99 : Triangle type {22,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x * y^-1 * x * y^-1 * x * z^2 * y^-1 ] T50.100 : Triangle type {22,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T50.101 : Triangle type {22,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^2 * y^-1 * x * z^2 ] T50.102 : Triangle type {22,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^5 * z^-1 * x * z^-1 ] T50.103 : Triangle type {22,22,55} Group order 110 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-1 * y * z^-3 * x^3 * z^-1 * y * z^-3 ] T50.104 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * y^-4 * x^-3 * z^3 ] T50.105 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^6, y^-1 * z * y^-1 * z * y^-5 * z^3 ] T50.106 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^6 * x^-2 * z * x^-1 * z * x^-1 * z * x^-10 * z * x^-1 * z * x^-1 * z ] T50.107 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^8 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T50.108 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * y^-2 * z^6 ] T50.109 : Triangle type {26,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^3 * y^-1 * x * y^-4 * x^5 * z^-1 * x ] T50.110 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^14 * x^-2 * y^4 * x^-1 * y^6 ] T50.111 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x * y^-1 * x * y^-4 * x^3 * y^-3 ] T50.112 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7 * z, x^-1 * z^4 * x^-6 ] T50.113 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y^5 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T50.114 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^3 * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T50.115 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.116 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y^-1 * z * y^-1 * z * y^-7 * z ] T50.117 : Triangle type {51,102,102} Group order 102 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-51, y * z^-1 ] T50.118 : Triangle type {52,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.119 : Triangle type {52,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-1 * x * y^-1 * x^3 * y^-4 ] T50.120 : Triangle type {52,52,52} Group order 104 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-2, z^-3 * x^2 * z^-3 ] T50.121 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x^-2 * y^-1, y^-45 * x * y^-5, x * z^-1 ] T50.122 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-1 * y^3 * x^-3 * y^11 ] T50.123 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-5 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.124 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^8 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.125 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-6 * y^4 * x^-1 * y^5 ] T50.126 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.127 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x * y^-4 * x^2 * y^-4 ] T50.128 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-4 * x^5 * y^-1 ] T50.129 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-2 * x^8, y^-2 * z * y^-8 ] T50.130 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-2 * z * y^-1 * z * y^-5 * z^3 ] T50.131 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x * z^-1 * x^7 * z^-5 * x * z^-1 ] T50.132 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z^2, x^-1 * z^4 * x^-5 * y * x^-1 ] T50.133 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^7 * y^-6 * z^4 ] T50.134 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-4 * z^4, x * y^-1 * x * y^-4 * x^4 * y^-2 ] T50.135 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, x^2 * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.136 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-6 * y * x^-7 * y^2 * x^-6 ] T50.137 : Triangle type {101,101,101} Group order 101 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^4 * y^-2 * x^4 * z^-4 * x^3 ] Genus 51 T51.1 : Triangle type {2,3,12} Group order 1200 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12, z^3 * y * x * z^4 * y * x * z * y^2 * z^-3 * x * z^2 ] T51.2 : Triangle type {2,3,12} Group order 1200 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z^3 * y * z^-1 * x * z * y * x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T51.3 : Triangle type {2,3,30} Group order 750 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^6 * y * x * z * x * y^-1 * z^-4 ] T51.4 : Triangle type {2,4,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-3 * y * z^-1 * x * z * y^-1 * z^2 ] T51.5 : Triangle type {2,4,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * z^-1 * x ] T51.6 : Triangle type {2,4,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 * y * x ] T51.7 : Triangle type {2,4,8} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T51.8 : Triangle type {2,4,8} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y ] T51.9 : Triangle type {2,4,12} Group order 600 Chiral action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-3 * y * x * y^-1 * z^3 * y^-1 * z^-1 ] T51.10 : Triangle type {2,4,12} Group order 600 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T51.11 : Triangle type {2,4,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, z * y^-1 * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T51.12 : Triangle type {2,4,20} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, (z^-1 * y)^5 ] T51.13 : Triangle type {2,4,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-6 * x * z^5 * y * z^-2 * x * y^-1 * z^-9 ] T51.14 : Triangle type {2,4,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x, z^5 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T51.15 : Triangle type {2,4,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^-1 * x * z * y * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-2 ] T51.16 : Triangle type {2,4,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z^-3 * x * z * y^-1 * z^-4 * y ] T51.17 : Triangle type {2,4,44} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-1 * x * z^2 * y * x * z^8 * y * z^-3 * x * z^4 * y^-1 * z^-1 ] T51.18 : Triangle type {2,4,54} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-38 * x * z^8 * y^-1 * z^-7 ] T51.19 : Triangle type {2,4,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-104 ] T51.20 : Triangle type {2,4,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-37 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T51.21 : Triangle type {2,4,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-10 * x * y^-1 * z^-91 ] T51.22 : Triangle type {2,6,8} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^-1 ] T51.23 : Triangle type {2,6,8} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-2 * z * y^-1 * z^-2 * y ] T51.24 : Triangle type {2,6,28} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-2 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-4 ] T51.25 : Triangle type {2,8,8} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^3 * y^3 * x * y^-1 * z^-1 * x ] T51.26 : Triangle type {2,8,8} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y ] T51.27 : Triangle type {2,8,8} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1)^4, z^8, y * z^-1 * x * y^-3 * z^3 * y^-1 * z^-1 ] T51.28 : Triangle type {2,8,8} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y ] T51.29 : Triangle type {2,8,8} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-1 * y ] T51.30 : Triangle type {2,8,8} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T51.31 : Triangle type {2,8,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T51.32 : Triangle type {2,8,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T51.33 : Triangle type {2,8,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^7 * y * x * z^2 * y * z^-6 * x * z ] T51.34 : Triangle type {2,8,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-4 * x * z^7 * y * z^-1 * x * y^-1 * z^-4 ] T51.35 : Triangle type {2,8,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^17 * y * x * z^3 * y * x * z * y^-1 * z^-5 * x * y^-1 * z^-1 * x * z^5 ] T51.36 : Triangle type {2,8,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^16 * y * z^-2 * x * z^6 * y * x * y^-1 * z^-8 * x * z ] T51.37 : Triangle type {2,8,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-8 * x * z^7 * y * z^-1 * x * z^4 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T51.38 : Triangle type {2,8,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-7 * x * z^8 * y * z^-1 * x * z^4 * y * z^-9 * x * z^2 * y^-1 ] T51.39 : Triangle type {2,12,12} Group order 300 Chiral action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * y^-3 * z^4 ] T51.40 : Triangle type {2,12,12} Group order 300 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, x * z * y^2 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y ] T51.41 : Triangle type {2,12,12} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 ] T51.42 : Triangle type {2,14,119} Group order 238 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^3 * y^-5 * z^3, z^-1 * x * z^5 * y * z^-10 ] T51.43 : Triangle type {2,15,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^11 * z^-1 * y^2 * z^-1 ] T51.44 : Triangle type {2,20,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * y^5 * z^-2 * y * z^-1 ] T51.45 : Triangle type {2,24,24} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-6 * z * y^-3 * z^2 * y^-5 * z * y^-1 * z * y^-2 * z * y^-1 ] T51.46 : Triangle type {2,24,24} Group order 240 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T51.47 : Triangle type {2,28,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-15 * z^4 * y^-5 * z^4 ] T51.48 : Triangle type {2,28,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^10 * y^-1 * z^4 * y^-10 * z^2 ] T51.49 : Triangle type {2,44,44} Group order 220 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z * y^-2 * z * y^-1 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z^2 ] T51.50 : Triangle type {2,54,54} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-40 * y^11 * z^-1 ] T51.51 : Triangle type {2,70,105} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-6 * y^11 * z^-2 * y^14 * z^-1 ] T51.52 : Triangle type {2,103,206} Group order 206 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^97 * z^-6 ] T51.53 : Triangle type {2,104,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-24 * y^11 * z^-2 * y^14 ] T51.54 : Triangle type {2,104,104} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^6 * y^-97 ] T51.55 : Triangle type {2,204,204} Group order 204 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^5 * y^-96 ] T51.56 : Triangle type {3,3,6} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-2 * x^-1 * y * x * z * y^-1 * z^-2 * x ] T51.57 : Triangle type {3,3,6} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x * z^2 * x^-1 * z^2 * y * x^-1 * z ] T51.58 : Triangle type {3,3,6} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x ] T51.59 : Triangle type {3,3,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T51.60 : Triangle type {3,3,28} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-6 * x^2 * z^3 * y^-1 * z^-2 ] T51.61 : Triangle type {3,3,103} Group order 309 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x * z^2 * y * z^-1 * x * y * z^-4 ] T51.62 : Triangle type {3,4,12} Group order 300 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, y * x^-1 * y^-2 * x * z * y * z^-1 ] T51.63 : Triangle type {3,4,12} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y * z^-1 ] T51.64 : Triangle type {3,8,8} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T51.65 : Triangle type {3,8,8} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-1 * y * x^-1 * y^-1 * x * z * y^-2 ] T51.66 : Triangle type {3,21,42} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-2 * x * z^2 * y^-1 ] T51.67 : Triangle type {3,28,28} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-4 * z^2 ] T51.68 : Triangle type {3,52,156} Group order 156 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-41 * z * y^-1 * z * y^-7 * z ] T51.69 : Triangle type {3,153,153} Group order 153 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-40 * z * y^-1 * z * y^-8 ] T51.70 : Triangle type {4,4,4} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, y^-1 * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 * y * x^2 * z * x^-1 * z * y^-1 * x ] T51.71 : Triangle type {4,4,4} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1, (y * z^-1)^4 ] T51.72 : Triangle type {4,4,4} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, (x * y^-1)^4, y * z^-1 * x * z^-1 * x * z * y * z^-1 ] T51.73 : Triangle type {4,4,4} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x * z^-2 * y * x^-1 * z * y * z^-1 ] T51.74 : Triangle type {4,4,4} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-2 * y * z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 * z^-1 ] T51.75 : Triangle type {4,4,4} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y * z^-1 * y * x^-1 * y^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z ] T51.76 : Triangle type {4,4,4} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T51.77 : Triangle type {4,4,4} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x * z * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T51.78 : Triangle type {4,4,6} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * z^-1 * x^-1 * y * z^-1 * x ] T51.79 : Triangle type {4,4,6} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * x^-2 * z * y^-1 * z^-1 ] T51.80 : Triangle type {4,4,6} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z * y * x * z^-1 * y * x^-2 * y^2 * x * y^-1 ] T51.81 : Triangle type {4,4,6} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z * x^-1 * y * x^-2 * y^-1 * x * y^-1 * x * y^-1 ] T51.82 : Triangle type {4,4,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T51.83 : Triangle type {4,4,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-3 ] T51.84 : Triangle type {4,4,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^5 * y * x * y^-1 * x * z^4 * y^-1 * x ] T51.85 : Triangle type {4,4,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * x * z^2 * y ] T51.86 : Triangle type {4,4,22} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, x^-1 * z^4 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T51.87 : Triangle type {4,4,27} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^19 * y^-1 * x * z * y * z^-4 * x * z ] T51.88 : Triangle type {4,4,52} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * y^-1 * z^-2 ] T51.89 : Triangle type {4,4,52} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z * x^-1 * z^3 ] T51.90 : Triangle type {4,4,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y * x * z * y * z^-7 * x^-1 ] T51.91 : Triangle type {4,4,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y * x * z * y * z^-7 * x ] T51.92 : Triangle type {4,4,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^38 * y^-1 * x^-1 * z^13 ] T51.93 : Triangle type {4,4,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^37 * y^-1 * x * z^13 ] T51.94 : Triangle type {4,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T51.95 : Triangle type {4,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * z * y * z^-1 ] T51.96 : Triangle type {4,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y^6, (x * z * y)^2, z^6 ] T51.97 : Triangle type {4,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T51.98 : Triangle type {4,6,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^3 * y * x^-1 * z^6 * y * x^-1 * z^5 ] T51.99 : Triangle type {4,6,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T51.100 : Triangle type {4,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * z * y * x, y^3 * x^2 * y^-2 * z^-1 ] T51.101 : Triangle type {4,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x^-1 * z * y^-1 * z ] T51.102 : Triangle type {4,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y^-1 * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T51.103 : Triangle type {4,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z ] T51.104 : Triangle type {4,8,8} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z^2 * y ] T51.105 : Triangle type {4,8,8} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-1 ] T51.106 : Triangle type {4,10,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T51.107 : Triangle type {4,10,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * z * y * z^-2, y^10 ] T51.108 : Triangle type {4,12,14} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-4 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-4 ] T51.109 : Triangle type {4,12,39} Group order 156 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z^-1 * y * x^-2 * z * y * z^-1 ] T51.110 : Triangle type {4,12,39} Group order 156 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y * z^-1 * x * z^4 ] T51.111 : Triangle type {4,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^-1 * z^2, (y * z^-1 * y^2)^2 ] T51.112 : Triangle type {4,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z * y^-1, (y * z^-1 * y^2)^2 ] T51.113 : Triangle type {4,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z * y^-1 * z^4 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.114 : Triangle type {4,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z^4 * y^-1 * z^3 * y^-1 * z^2 * y^-3 * z^2 * y^-2 ] T51.115 : Triangle type {4,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-5 * z^3 * y^-10 ] T51.116 : Triangle type {4,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^6 * z^-1 * y^3 * z^-1 ] T51.117 : Triangle type {4,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-8 * z * y^-3 * z * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.118 : Triangle type {4,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-1 * y^21 * z^-1 * y^5 * z^-1 * y * z^-5 ] T51.119 : Triangle type {4,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-14 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T51.120 : Triangle type {4,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-15 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.121 : Triangle type {6,6,14} Group order 168 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^3 ] T51.122 : Triangle type {6,6,14} Group order 168 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^3 * x^-1 * z * y^-1 * z ] T51.123 : Triangle type {6,6,14} Group order 168 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, y^-1 * x * z * y * x^-1 * z^4 ] T51.124 : Triangle type {6,9,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1 ] T51.125 : Triangle type {6,9,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * z^2 * y^-1 ] T51.126 : Triangle type {6,10,15} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * x * z^2 ] T51.127 : Triangle type {7,18,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z * y^-3 ] T51.128 : Triangle type {7,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^5 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 ] T51.129 : Triangle type {7,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 * z ] T51.130 : Triangle type {7,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^5 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y^2 ] T51.131 : Triangle type {8,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T51.132 : Triangle type {8,8,8} Group order 160 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T51.133 : Triangle type {8,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, x * z * y^-1 * z^-2 * x * y * z^-4 ] T51.134 : Triangle type {8,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-4 * x^-1 * y * x * y^-1 * z^-3 ] T51.135 : Triangle type {8,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, x^-1 * z^4 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T51.136 : Triangle type {8,8,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-11 * x^-1 * y * x * y^-1 * z^-5 ] T51.137 : Triangle type {8,8,68} Group order 136 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^5 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T51.138 : Triangle type {8,8,68} Group order 136 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x * z^4 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T51.139 : Triangle type {8,30,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^2 * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T51.140 : Triangle type {8,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, z * x^-1 * z * x^-1 * z^3 ] T51.141 : Triangle type {8,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^8 ] T51.142 : Triangle type {9,9,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y^2 * x^-1 * z^2 ] T51.143 : Triangle type {9,39,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z^4 * y^-5 * z ] T51.144 : Triangle type {9,39,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-3 * z^4 * y^-2 * x * y^-4 ] T51.145 : Triangle type {10,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-1 * x^4 * y^-3 ] T51.146 : Triangle type {10,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^10 ] T51.147 : Triangle type {10,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x ] T51.148 : Triangle type {10,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y ] T51.149 : Triangle type {10,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y ] T51.150 : Triangle type {12,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-3 * z^3, x^3 * y^-5 * x * z^-5 * x^3 ] T51.151 : Triangle type {12,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * y^-1 * z^-2, x * y^-1 * x^3 * y^-2 * z^-1 ] T51.152 : Triangle type {12,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^-2 * y^2 * x^-2 * y^2 * x^-6 ] T51.153 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z^-2 * x^7 * z^-5 * x * z^-1 ] T51.154 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^5 * z^-1 * y * z^-1 ] T51.155 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-2 * x^4 * z^-6 ] T51.156 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-4 * x^2 * y^-4 ] T51.157 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^5 * y^-4 * x^2 * y^-4 * x^3 ] T51.158 : Triangle type {14,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * z * x^-1 * z * x^-7 * z^2 * x^-2 ] T51.159 : Triangle type {15,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, y^2 * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T51.160 : Triangle type {15,15,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, z^2 * x^-3 * z^4 ] T51.161 : Triangle type {15,20,20} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^2 * z^-1 * y, z * y^2 * x^-1 * z * y^-1 * z ] T51.162 : Triangle type {15,20,20} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y * x^-3 * y^3 ] T51.163 : Triangle type {16,28,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-9 * z^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T51.164 : Triangle type {16,28,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^3 * y^-3, z^6 * x^-5 * z ] T51.165 : Triangle type {18,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z * x^-1 * z^5 * x^-9 ] T51.166 : Triangle type {18,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x * y^-4 * x^5 * y^-1, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T51.167 : Triangle type {18,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^3 * y^-1 * x * y^-1 * x * y^-4 * x^8 ] T51.168 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^7 * z^-4 * x ] T51.169 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-7 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x ] T51.170 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^4 * y^-4 * x^-1 * z^4 ] T51.171 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * z^-1 * y^3 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T51.172 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-2 * x * z^-4 * y^2 * z^-8 ] T51.173 : Triangle type {27,36,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^3 * y^-1 * x^5 * z^-5 * x^2 ] T51.174 : Triangle type {28,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-3 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T51.175 : Triangle type {28,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, (y^2 * x^-1 * y * x^-1 * y^3)^2 ] T51.176 : Triangle type {28,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-3 * x^2 * y^-3 ] T51.177 : Triangle type {28,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^6, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T51.178 : Triangle type {28,28,28} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-3 * x * y^-1 * x * y^-4 ] T51.179 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-8 * x * z^-1 * x * z^-4 * x^3 * z^-5 * x * z^-1 * x * z^-2 ] T51.180 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * y^-4 * x^-3 * z^3 ] T51.181 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 * y^3 * x^-6 ] T51.182 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-1 * y^14 ] T51.183 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-35 ] T51.184 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, x^-1 * z^4 * x^-5 * y * x^-1 ] T51.185 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-2 * x^5 * y * z^-6 ] T51.186 : Triangle type {35,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^2 * y^-3 * x^7 ] T51.187 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-2 * x^7 * z^-5 * x * z^-1 ] T51.188 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-1 * z^4, x * y^-2 * x^8 ] T51.189 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-3 * z * y^-1 * x * y^-1 ] T51.190 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-23 * x * y^-4 * x^3 * y^-5 ] T51.191 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, z^4 * y^-2 * x^-1 * z^4 ] T51.192 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-8 ] T51.193 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z * y^-1 * z * y^-8 ] T51.194 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z * x^-1 * z * x^-1 * z^5 * x^-7 * z^3 ] T51.195 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * z^-1 * y^6 * x^-2 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T51.196 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-6 * x * y^-4 ] T51.197 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-52, y * z^-1 ] T51.198 : Triangle type {52,104,104} Group order 104 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-8 * y * x^-5 ] T51.199 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x^-2 * y^-1, y^-46 * x * y^-5, x * z^-1 ] T51.200 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-2 * y^11 ] T51.201 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-7 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T51.202 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y^5 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T51.203 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T51.204 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-7 * y^4 * x^-1 * y * x^-1 * y^2 ] T51.205 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-4 * x^6 ] T51.206 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-4 * x^3 * y^-3 ] T51.207 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^6, z^5 * x^-1 * z^4 ] T51.208 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^6 * x^-1 * z^4 ] T51.209 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * y^-8 * z^2 ] T51.210 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z * x^-1 * z^5 * x^-6 * z^3 ] T51.211 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-7 * x^2 * y^-4 ] T51.212 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^-1 * z^4 * x^-5 * z ] T51.213 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-2 * z^3 * x^-9 ] T51.214 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^11 * x^-4 * z^4 * x^-1 * z * x^-1 * z ] T51.215 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-3 * z^3 * x^-10 ] T51.216 : Triangle type {103,103,103} Group order 103 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, z^4 * y^-3 * x^-1 * z^4 ] Genus 52 T52.1 : Triangle type {2,3,8} Group order 2448 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z^-1 * x * z^3 * y * z^-1 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T52.2 : Triangle type {2,3,8} Group order 2448 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z^2 * y * x * z^2 * y * z^-3 * x * z * y^-1 * z^-1 * x * z^2 ] T52.3 : Triangle type {2,4,106} Group order 424 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-106 ] T52.4 : Triangle type {2,4,208} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-11 * x * y^-1 * z^-92 ] T52.5 : Triangle type {2,6,20} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-5 * x * z * y * z^-2 * x * z * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T52.6 : Triangle type {2,6,54} Group order 324 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z^4 * y * x * y^-1 * z^-6 * x * z^2 * y^-1 ] T52.7 : Triangle type {2,6,54} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-36 * x * y^-1 * z^-6 * x * y^-1 * z^-10 ] T52.8 : Triangle type {2,6,54} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-25 * x * z^16 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-2 ] T52.9 : Triangle type {2,6,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^23 * y * x * z^16 * y * z^-1 * x * y * z^-7 * x * z^2 ] T52.10 : Triangle type {2,10,28} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-3 * x * z * y * x * z * y * x * z * y * x * z * y * x * y * z^-9 * x * y^-1 * z^-6 ] T52.11 : Triangle type {2,10,130} Group order 260 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * x * y * z^-16 * x ] T52.12 : Triangle type {2,12,16} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, x * z * y * z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T52.13 : Triangle type {2,16,16} Group order 272 Chiral action Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-2 * y ] T52.14 : Triangle type {2,16,16} Group order 272 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-2 * y ] T52.15 : Triangle type {2,18,117} Group order 234 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-10 ] T52.16 : Triangle type {2,24,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-3 * x * z * y^-1 * z^-5 ] T52.17 : Triangle type {2,28,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^4 * y^-2 * z^4 * y^-1 ] T52.18 : Triangle type {2,54,108} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-26 * y^11 * z^-2 * y^15 ] T52.19 : Triangle type {2,105,210} Group order 210 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^98 * z^-6 * y ] T52.20 : Triangle type {2,106,106} Group order 212 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^7 * y^-97 * z ] T52.21 : Triangle type {2,208,208} Group order 208 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^6 * y^-96 * z ] T52.22 : Triangle type {3,9,63} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * z^3, y^-9 ] T52.23 : Triangle type {3,9,63} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y * x * z^2 ] T52.24 : Triangle type {3,9,63} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-2, z^2 * y * z^-1 * y * z^-2 * x^-1 ] T52.25 : Triangle type {3,15,30} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y^4 * z^-3 * y^2 ] T52.26 : Triangle type {3,20,20} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-1 * y^10 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y ] T52.27 : Triangle type {3,24,56} Group order 168 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^2 * z^-1 * x^-1 * z^3, y * z^-2 * y^2 * z^-3 ] T52.28 : Triangle type {3,28,42} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z * y^-1 * x * z * y^-1 * z ] T52.29 : Triangle type {3,53,159} Group order 159 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-42 * z * y^-1 * z * y^-7 * z ] T52.30 : Triangle type {3,54,54} Group order 162 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-4 * y^11 * z^-1 * y * z^-1 ] T52.31 : Triangle type {3,54,54} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-43 * z * y^-1 * z * y^-7 * z ] T52.32 : Triangle type {3,54,54} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-2 * y^6 * z^-1 * y * z^-2 * y * z^-1 ] T52.33 : Triangle type {3,54,54} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^41 * y^-3 * z * y^-7 * z ] T52.34 : Triangle type {3,156,156} Group order 156 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-41 * z * y^-1 * z * y^-8 ] T52.35 : Triangle type {4,4,53} Group order 212 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * x^-1 * z * y^-1 * z^4 ] T52.36 : Triangle type {4,4,53} Group order 212 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^39 * y^-1 * x^-1 * z^13 ] T52.37 : Triangle type {4,4,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^38 * y^-1 * x * z^13 ] T52.38 : Triangle type {4,5,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-5, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T52.39 : Triangle type {4,6,9} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1 ] T52.40 : Triangle type {4,6,9} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * x * z^-1 * x^-1 * z * x^-1 * z, z^9 ] T52.41 : Triangle type {4,6,12} Group order 204 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x * z^-1 * x^-2 * z * y * z^-1 * x ] T52.42 : Triangle type {4,8,22} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z^4 * y^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * z^6 ] T52.43 : Triangle type {4,10,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * y^-1 * z^-3, y^10 ] T52.44 : Triangle type {4,12,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y * z^-1 * x^-1 * z^4 ] T52.45 : Triangle type {4,16,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 ] T52.46 : Triangle type {4,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-5 * y * z^-2 * y^5 * z^-1 * y^4 ] T52.47 : Triangle type {4,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-12 * z^3 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T52.48 : Triangle type {5,6,15} Group order 180 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^2, (z^-1 * x)^3 ] T52.49 : Triangle type {5,27,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T52.50 : Triangle type {5,28,28} Group order 140 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, z * y^-11 * z * y^-3 * z * y^-6 * z * y^-1 * z^3 ] T52.51 : Triangle type {5,28,28} Group order 140 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z^-1 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^6 * z^-1 * y^7 * z^-1 * y * z^-1 * y^2 ] T52.52 : Triangle type {5,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^3 * z^-1 ] T52.53 : Triangle type {5,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^3 * z^-1 ] T52.54 : Triangle type {6,6,10} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, y * z^-5 * x * z^4 ] T52.55 : Triangle type {6,6,10} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^4 * y * z^-1 * x * z^4 ] T52.56 : Triangle type {6,6,27} Group order 162 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, x * z^3 * y^-1 * z^-1 * x^-1 * y^-1 * z^-3 ] T52.57 : Triangle type {6,6,27} Group order 162 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^3 * y^-1 * z^-2 * x^-1 * z^3 ] T52.58 : Triangle type {6,6,27} Group order 162 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-13 * x^-1 * y^-1 * x * z * y * z^-3 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T52.59 : Triangle type {6,6,27} Group order 162 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-14 * x * y * z^-12 ] T52.60 : Triangle type {6,6,78} Group order 156 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-9 * x * z * y^-1 * z^-1 * x * z^5 * y * x * z * y * z^-3 * x * z * y * z^-1 ] T52.61 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * z * x^-1 * z^3 ] T52.62 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^2 * z^-2 ] T52.63 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, z * y^3 * x * z * y * x^-1 ] T52.64 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * z^-2 * x^-1 * z^3 * y * x * z^4 ] T52.65 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^6, z^-2 * x^-2 * z * y^-1 * x ] T52.66 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, z * y^3 * x * y^-1 * z^-1 * x^-1 ] T52.67 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, x * z^5 * y^-1 * x^-1 * z * y * z^-4 ] T52.68 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^2 * z^-2, z^2 * y * x * z^-1 * x^-1 ] T52.69 : Triangle type {6,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^6, (z^-1 * y)^3 ] T52.70 : Triangle type {6,16,16} Group order 144 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * y^4 * z^-2 * y ] T52.71 : Triangle type {6,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, y^2 * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T52.72 : Triangle type {6,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 ] T52.73 : Triangle type {6,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-12 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T52.74 : Triangle type {6,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-5 * y * z^-1 * y * z^-1 * y^11 * z^-1 ] T52.75 : Triangle type {8,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, y^-1 * z * y * x^-1 * y^-3 ] T52.76 : Triangle type {8,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T52.77 : Triangle type {8,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y * z^-1 * x^-1 * y^-1 * x * z^3, z^-1 * y^3 * x * z * x^-1 * y^-1 ] T52.78 : Triangle type {8,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 ] T52.79 : Triangle type {8,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-6 ] T52.80 : Triangle type {9,14,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-5 * y^5 * z^-4 ] T52.81 : Triangle type {9,18,42} Group order 126 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y * z^-1, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y * x^-1 * z * x^-1 ] T52.82 : Triangle type {9,18,42} Group order 126 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^-1 * z * y, x * y^-2 * x * z * y, x^-1 * z * x^-2 * z^3 ] T52.83 : Triangle type {9,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z^4 * y^-3 * z^3 ] T52.84 : Triangle type {9,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^2 * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T52.85 : Triangle type {10,10,14} Group order 140 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^9 * y * x * z^4 ] T52.86 : Triangle type {10,10,65} Group order 130 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^6 * y * z^-2 * x^-1 * z^4 ] T52.87 : Triangle type {10,10,65} Group order 130 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-3 * x^-1 * y^-1 * z^-4 * x^-1 * y * z^-4 ] T52.88 : Triangle type {10,24,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z^4 * y^-5 * z ] T52.89 : Triangle type {10,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^10 ] T52.90 : Triangle type {10,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^10 ] T52.91 : Triangle type {10,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, z^-2 * x * z^-1 * x * z^-3 ] T52.92 : Triangle type {12,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-3 * x^-1 * y^-1 * z^3 ] T52.93 : Triangle type {12,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-7 ] T52.94 : Triangle type {14,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^3 * y^-3 ] T52.95 : Triangle type {14,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^5 * y^-4 * x^2 * y^-4 * x^2 ] T52.96 : Triangle type {14,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^-1 * z^4 * x^-2 * z^4 ] T52.97 : Triangle type {15,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x * z^-1 * x^2 * z * y^-1 ] T52.98 : Triangle type {15,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (y^-1 * x)^3, x^-1 * z * y * x * z^2 ] T52.99 : Triangle type {15,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, y * x^-3 * y^3 ] T52.100 : Triangle type {15,24,24} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * z * x^-2 * y * z^-1 * x^-1, y^-1 * z * y^-3 * x * z * y^-2 ] T52.101 : Triangle type {15,24,24} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, z^-1 * y^4 * z^-3 ] T52.102 : Triangle type {16,56,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-1 * x^7 * z^-6 ] T52.103 : Triangle type {16,56,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T52.104 : Triangle type {16,56,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^2 * z^-1 * x^7 * z^-5 * x * z^-1 * x ] T52.105 : Triangle type {16,56,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, x * y^-1 * x * y^-4 * x^4 * y^-2 ] T52.106 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-6 * x^2 * y^-4 ] T52.107 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^9 * y^-1 * x^8 * z^-1 * x^4 ] T52.108 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^6 ] T52.109 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-3 * x^7 * z^-5 * x * z^-2 ] T52.110 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-6 * y^4 * x^-1 * y * x^-1 * y^4 ] T52.111 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, y^-1 * x^3 * y^-1 * x * y^-1 * x * y^-1 * x * z^-1 * x^9 * y^-1 * x * y^-1 * x ] T52.112 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7 * z, x^7 * z^-5 ] T52.113 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x^6 * y^2 * z^-6 ] T52.114 : Triangle type {22,55,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T52.115 : Triangle type {27,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^27 ] T52.116 : Triangle type {27,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x * y^-4 * x^3 * y^-3, y^-1 * z * y^-1 * z * y^-4 * z^4 ] T52.117 : Triangle type {27,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x * y^-4 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 * x ] T52.118 : Triangle type {27,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^7 * y^-5 * z^4 ] T52.119 : Triangle type {27,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^8 * z^-4 * x^2 ] T52.120 : Triangle type {28,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-3 * x^2 * y^-3 ] T52.121 : Triangle type {28,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, z^-1 * y^3 * z^-1 * y ] T52.122 : Triangle type {28,28,56} Group order 112 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x * z^-1 * x * z^-3 ] T52.123 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^23 * y^-1 * x^9 * y^-1 * x * y^-1 * x ] T52.124 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * x^-1 * z^4, x^2 * y^-1 * x * y^-4 * x^5 * y^-1 ] T52.125 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * x^-1 * z^4, x^3 * y^-3 * x^7 ] T52.126 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-2 * x^2 * z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-9 ] T52.127 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T52.128 : Triangle type {36,54,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-4 * x^3 * y^-3 ] T52.129 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-5 * y^2 * x^-3 * y * x^-10 * y * x^-1 * y * x^-1 * y * x^-2 ] T52.130 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^6 * y^-3 * x^7 * y^-1 * x^2 ] T52.131 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^4 * y^-3 * x^6 * z^-1 * x ] T52.132 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^5 * y^-1 ] T52.133 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^-2 * x * y^-4 * x^2 * y^-4 ] T52.134 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^-1 * z^4 * x^-4 * z^2 ] T52.135 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-6 * x * y^-4 ] T52.136 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T52.137 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z * x^-1 * z^5 * x^-6 * z^2 ] T52.138 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * z^-2 * y^2 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T52.139 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-8, x^-1 * z^4 * x^-6 ] T52.140 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-11 * y^2 * z^-9 ] T52.141 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T52.142 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^4 * y^-1 * z * y^-4 * x^-2 * z^4 ] T52.143 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7 * z, x^2 * y^-2 * x^4 * z^-4 * x ] T52.144 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^11 * x^-2 * z^5 * x^-1 * z * x^-1 * z ] T52.145 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-16 * x * y^-4 * x * y^-3 * z * y^-2 ] T52.146 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x * y^-4 * x^5 * y^-1 ] T52.147 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T52.148 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^3 * y^-1 * z * y^-1 * z^5 * x^-2 * z^5 * y^-1 * z ] T52.149 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-6 * x^2 * y^-4 ] T52.150 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T52.151 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z^2, x^2 * y^-2 * x^8 ] T52.152 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z ] T52.153 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-30 * x^2 * z^-4 ] T52.154 : Triangle type {53,106,106} Group order 106 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-53, y * z^-1 ] T52.155 : Triangle type {54,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-21 * x^2 * y^-5 ] T52.156 : Triangle type {54,54,54} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-1 * x^6 * z^-5 ] T52.157 : Triangle type {105,105,105} Group order 105 Reflexible action Defining relators: [ x^-2 * y^-1, y^-47 * x * y^-5, x * z^-1 ] T52.158 : Triangle type {105,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z^3, x^4 * y^-4 * x^4 * z^-2 * x ] T52.159 : Triangle type {105,105,105} Group order 105 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^4 * y^-4 * x^-1 * z^4 ] Genus 53 T53.1 : Triangle type {2,4,8} Group order 832 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * z^-1 * y ] T53.2 : Triangle type {2,4,8} Group order 832 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y ] T53.3 : Triangle type {2,4,12} Group order 624 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, y * x * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T53.4 : Triangle type {2,4,20} Group order 520 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * x * z * y * z^-1 * x * z * y^-1 * z^-2 * x ] T53.5 : Triangle type {2,4,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-14 * x * z^8 * y * x * z * y^-1 * z^-5 ] T53.6 : Triangle type {2,4,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-41 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T53.7 : Triangle type {2,4,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-14 * x * z^4 * y * z^-1 * x * z * y * x * y^-1 * z^-5 ] T53.8 : Triangle type {2,4,108} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-108 ] T53.9 : Triangle type {2,4,212} Group order 424 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-12 * x * y^-1 * z^-93 ] T53.10 : Triangle type {2,6,6} Group order 624 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y^-1 * z^2 * y^-1 * z * y^-1 * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T53.11 : Triangle type {2,6,15} Group order 390 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * z^-1 * y^2 * z^-1 * y^2 * x * y^-2 * z^2 ] T53.12 : Triangle type {2,6,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-1 * x * z^3 * y * z^-3 * x * y^-1 * z^-7 ] T53.13 : Triangle type {2,6,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T53.14 : Triangle type {2,6,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^4 * y^2 * x * z^3, z * y * z^-2 * x * z * y^-1 * z^3 * y^-1 * z^-1 * x ] T53.15 : Triangle type {2,6,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z^2 * y * z^-1 * x * z * y^3 * x * z * y^-1 * z^-4 ] T53.16 : Triangle type {2,6,159} Group order 318 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^41 * y * z^-1 * x * y * z^-7 * x * z^2 ] T53.17 : Triangle type {2,8,8} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y * z^-2 ] T53.18 : Triangle type {2,8,8} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z ] T53.19 : Triangle type {2,8,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-1 * x * z^3 * y * z^-3 * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-3 ] T53.20 : Triangle type {2,8,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^10 * y * z^-1 * x * z * y^-1 * z^-3 * x * y^-1 * z^-1 * x * z ] T53.21 : Triangle type {2,8,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^17 * y * x * z^3 * y * x * z * y^-1 * z^-6 * x * z^6 ] T53.22 : Triangle type {2,8,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^17 * y * z^-1 * x * z^6 * y * z^-7 * x * z^3 ] T53.23 : Triangle type {2,12,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1, y^12 ] T53.24 : Triangle type {2,12,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * z * y * x * y^-1 * z^-2 * x * z^2, y^12 ] T53.25 : Triangle type {2,12,12} Group order 312 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * z * y^-3 * z^-4, y^12 ] T53.26 : Triangle type {2,12,44} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-3 * x * z * y * x * z * y * x * y * z^-9 * x * y^-1 * z^-4 ] T53.27 : Triangle type {2,16,32} Group order 256 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z * y * z^-2 * x * y^-1 * z^-1 * x * z^2 ] T53.28 : Triangle type {2,16,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-1 * x * z^2 * y * x * z * y * x * z^4 * y^-1 * z^-5 ] T53.29 : Triangle type {2,16,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * z^-2 * x * z^3 * y^-1 * z^-1 * x ] T53.30 : Triangle type {2,16,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z^7 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x ] T53.31 : Triangle type {2,16,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-1 * x * z^8 * y * x * z * y^-1 * z^-4 ] T53.32 : Triangle type {2,20,20} Group order 260 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y ] T53.33 : Triangle type {2,20,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-8 * z^3 * y^-5 * z^3 * y^-1 ] T53.34 : Triangle type {2,24,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-1 * z * y^10 * x, x * z * y * x * z * y * x * z^2 * y^-1 * z^-3 ] T53.35 : Triangle type {2,24,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-1 * z * y^10 * x, x * z * y * x * z * y * x * y^-1 * z^-5 ] T53.36 : Triangle type {2,30,30} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-30 ] T53.37 : Triangle type {2,56,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-27 * y^28 * z^-1 ] T53.38 : Triangle type {2,56,56} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-11 * z^3 * y^-9 * z^2 * y^-1 ] T53.39 : Triangle type {2,107,214} Group order 214 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^99 * z^-8 ] T53.40 : Triangle type {2,108,108} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^8 * y^-99 ] T53.41 : Triangle type {2,212,212} Group order 212 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^7 * y^-98 ] T53.42 : Triangle type {3,6,6} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * z * y * x^-1 * y^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T53.43 : Triangle type {3,6,6} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 * y * x * y^3 * z^-1 * y * z^-1 ] T53.44 : Triangle type {3,15,15} Group order 195 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 ] T53.45 : Triangle type {3,16,16} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, y^-1 * z * y^2 * x * z * y * x^-1 ] T53.46 : Triangle type {3,16,16} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-1 * x * z * y, z^-5 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^2 * z^-2 ] T53.47 : Triangle type {3,16,16} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y * z^-1 * y * z^-2 * y^7 * z^-3 * y ] T53.48 : Triangle type {3,16,16} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, (y * z^-2 * y)^2 ] T53.49 : Triangle type {3,42,42} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y^5 * z^-1 * y * z^-5 ] T53.50 : Triangle type {3,159,159} Group order 159 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-42 * z * y^-1 * z * y^-6 * z^2 ] T53.51 : Triangle type {4,4,4} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z ] T53.52 : Triangle type {4,4,4} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * y * x * z * y^-1 * z * y^-1 * z * y^-2 ] T53.53 : Triangle type {4,4,6} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y * x^-1 * y * x^-2 * y^-1 * x * y^-1 * z^-1 * y ] T53.54 : Triangle type {4,4,10} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * y * x * y^-1 * x * z * y * x ] T53.55 : Triangle type {4,4,15} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1 ] T53.56 : Triangle type {4,4,15} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y * x * z^-1 * x^-1 * z * y^-1 * z^-1 ] T53.57 : Triangle type {4,4,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-4 * x * z^4 * y^-1 * x * y^-1 * z^-5 ] T53.58 : Triangle type {4,4,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^8 * y * z^-1 * x * z^2 * y * x^-1 * y * x^-1 * z ] T53.59 : Triangle type {4,4,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^22 * y^-1 * x * y^-1 * z^-4 * x ] T53.60 : Triangle type {4,4,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-5 * x^-1 * y * x * y^-1 * x * y^-1 * z^-3 * x^-1 * z^2 * y ] T53.61 : Triangle type {4,4,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-21 * x * z * y^-1 * x * z * y^-1 * z^-3 ] T53.62 : Triangle type {4,4,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-46 * x * y * z^-7 ] T53.63 : Triangle type {4,4,106} Group order 212 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^39 * y^-1 * x * z^13 ] T53.64 : Triangle type {4,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-1 * y ] T53.65 : Triangle type {4,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, (y * z^-2)^2 ] T53.66 : Triangle type {4,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^6, (x * z^-3)^2 ] T53.67 : Triangle type {4,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * z^4 ] T53.68 : Triangle type {4,8,8} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y^-1 * z * y^-2 * x * y^-2 * z^-1 * y * z^-1 ] T53.69 : Triangle type {4,8,8} Group order 208 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 ] T53.70 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-2)^2, y^8, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T53.71 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-2)^2, y^8, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z^2 * y ] T53.72 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T53.73 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z^2 * y ] T53.74 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1 ] T53.75 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T53.76 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^2 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y * z^-2 ] T53.77 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y * z^-2 ] T53.78 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y * z^-2 * x^-1 * z^3, y^8, x^-1 * z * y^2 * x * z * y^2 ] T53.79 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, y^8, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T53.80 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T53.81 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^2 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1 ] T53.82 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^5 * y^-1 * z^-2 * x^-1 * y * x * z^3 ] T53.83 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^6 * y * z^-1 * x^-1 * y * x * z^3 ] T53.84 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T53.85 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T53.86 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T53.87 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * x * z^2 * y ] T53.88 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^2 * x * y^-1 * x * y^-1 * z^2, y * x * y^-2 * x * z * y^-1 * z, y * x * z * y^-1 * x * z^3 ] T53.89 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, x^-1 * y * x^-2 * y^-2 * z, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z * y * z^-1, z * y * z^-1 * x^2 * z^2 * y^-1 ] T53.90 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^8, y * x^-1 * z * y * x * z^3 ] T53.91 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-1 * x^-1 * z^3 ] T53.92 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y ] T53.93 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T53.94 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * y * x^2 * z * y * x, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T53.95 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-2 * z^2 * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T53.96 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, x^-1 * z^6 * y * x^-1 * y * z^-4 ] T53.97 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-4 * x^-1 * y^-1 * x^-1 * z^6 ] T53.98 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * z^3 * y * z^-1 ] T53.99 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^4 * y * z^-1 * x^-1 * y^-1 * x^-1 * y^-1 * x * z^4 ] T53.100 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, z^-1 * x^-1 * z * y * x * y^-1 * z^-2 ] T53.101 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T53.102 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T53.103 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T53.104 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T53.105 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^3, y^8 ] T53.106 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * y * z^-4 * x * z^5 ] T53.107 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y * x * z^5 * y * x^-1 * z^5 ] T53.108 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, y * x * z^4 * y^-1 * z^-1 * x^-1 * z^5 ] T53.109 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^2 * y^-1 * z^-4 * x^-1 * z^5 ] T53.110 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * z^2 * y^-1 * z^-2 ] T53.111 : Triangle type {4,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^-6 * x * z^4 * y * z^-1 ] T53.112 : Triangle type {4,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y * z^-2 * y * z^-1 * y^13 ] T53.113 : Triangle type {4,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^20 ] T53.114 : Triangle type {4,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^6 * z^-1 * y^2 * z^-1 ] T53.115 : Triangle type {4,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^22 * z^-1 * y^5 * z^-1 * y * z^-5 ] T53.116 : Triangle type {4,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-13 * z * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T53.117 : Triangle type {6,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * y^-1 * x^2 * z^2, z * y^-1 * z^-1 * x^-1 * z * y * x ] T53.118 : Triangle type {6,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, (x * z * y)^2, z * y * x^-2 * y^-1 * x * y^-1 ] T53.119 : Triangle type {6,6,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^8 ] T53.120 : Triangle type {6,6,21} Group order 168 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-3 ] T53.121 : Triangle type {6,12,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^6, z * y * x^2 * z^2, y * x^-1 * y^-1 * x * z^-1 * y, z * x^-1 * y^-1 * x * y^-1 * z ] T53.122 : Triangle type {6,12,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, y * z^-2 * y^2 * z^-1 * y * z^-1 ] T53.123 : Triangle type {6,12,12} Group order 156 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x * z * y * x^-1 * y * x * z^-1 ] T53.124 : Triangle type {6,12,12} Group order 156 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, z * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T53.125 : Triangle type {6,12,12} Group order 156 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * z, x^6, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T53.126 : Triangle type {6,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3 ] T53.127 : Triangle type {6,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^16 * z^-1 * y * z^-1 * y * z^-1 * y ] T53.128 : Triangle type {8,8,10} Group order 160 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, y^-1 * z^-2 * x^-1 * z^3, x^8 ] T53.129 : Triangle type {8,8,10} Group order 160 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^3 ] T53.130 : Triangle type {8,8,10} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, (y * x * z^4)^2 ] T53.131 : Triangle type {8,8,10} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^-1 * z^2 * y^-1 * z^-1 * x * z * y * z^-4 ] T53.132 : Triangle type {8,8,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-4 * x * z * y^-1 * x * z * y^-1 * z^-2 * x * z * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T53.133 : Triangle type {8,8,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-12 * x * y^-1 * x * y^-1 * z^-4 ] T53.134 : Triangle type {8,32,32} Group order 128 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y^3 * z^-1 * y * z^-1 ] T53.135 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T53.136 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z^-1 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y ] T53.137 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^6 * z^-2 ] T53.138 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^5 * z^-1 * y * z^-1 ] T53.139 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^5 * z^-1 * y * z^-1 ] T53.140 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^5 * z^-1 * y * z^-1 ] T53.141 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (y * z^-1 * y^2)^2 ] T53.142 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^4 * z^-1 * y * z^-1 * y * z^-3 * y^2 * z^-3 ] T53.143 : Triangle type {8,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T53.144 : Triangle type {10,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z^4 * y^-6 ] T53.145 : Triangle type {10,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z^4 * y^-4 * z^2 ] T53.146 : Triangle type {12,12,22} Group order 132 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * z * y * z^-4 * x^-1 * y * x^-1 * y * z^-3 ] T53.147 : Triangle type {12,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-2 * x^-1 * z^4, y^-8 * x^4 * y^-2 ] T53.148 : Triangle type {12,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 ] T53.149 : Triangle type {12,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * z * y^-1 * z^2 ] T53.150 : Triangle type {15,24,40} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^2 * y^-1 * x * z^-2 * x^8 * y^-1 * x^2 ] T53.151 : Triangle type {15,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z^-1 * y, (x * z * y)^2, y^2 * x^-3 * y^4 ] T53.152 : Triangle type {15,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, (x^-6 * z * x^-1)^2 ] T53.153 : Triangle type {16,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x, z^-1 * y * x^2 * z * y^-1, z^-1 * y^4 * z^-3 ] T53.154 : Triangle type {16,16,16} Group order 128 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-1 * z * y^-1 * x * z * x^-1 ] T53.155 : Triangle type {16,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-1 * y * z^-1 * y * z^-1 * y * x^3 * z^-1 * y * z^-1 ] T53.156 : Triangle type {16,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^-7 * y^-1 * z^-1 ] T53.157 : Triangle type {16,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2, x^-6 * y^-1 * x * z^-1 ] T53.158 : Triangle type {16,16,16} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-2 * y * x^-4 * z * x^-1, x^-6 * y^-1 * x * z^-1 ] T53.159 : Triangle type {20,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^6 * y^-2 ] T53.160 : Triangle type {20,20,30} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z^4 * x^-3 * z^4 ] T53.161 : Triangle type {20,24,24} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^-1 * x^2 * z * y^-1 * z ] T53.162 : Triangle type {20,24,24} Group order 120 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z ] T53.163 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^6 * z^-2 ] T53.164 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^5 * y^-3 * x^-1 * z^4 ] T53.165 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-3 * z * y^-3 ] T53.166 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-3 * x * y^-1 * x * y^-4 ] T53.167 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-28 ] T53.168 : Triangle type {28,56,56} Group order 112 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-3 * y * x^-7 * z * x^-3 ] T53.169 : Triangle type {54,108,108} Group order 108 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-54, y * z^-1 ] T53.170 : Triangle type {54,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * z^-2 * x^11 ] T53.171 : Triangle type {54,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^6 * x^-7 * z^4 ] T53.172 : Triangle type {54,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-6 * x * y^-4 ] T53.173 : Triangle type {54,108,108} Group order 108 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^4 * x^-2 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T53.174 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x^-2 * y^-1, y^-48 * x * y^-5, x * z^-1 ] T53.175 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-29 * x * y^-6 ] T53.176 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^6 * y^-4 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 * x * y^-1 * x ] T53.177 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 * x ] T53.178 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^3 * x^-5 * y^4 * x^-1 * y * x^-1 * y^4 ] T53.179 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T53.180 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-4 * x^2 * y^-4 ] T53.181 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-7 * x * y^-4 ] T53.182 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, z^5 * x^-1 * z^4 ] T53.183 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^6 * x^-1 * z^4 ] T53.184 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T53.185 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^-1 * z^5 * x^-7 ] T53.186 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x^-2 * z^5 ] T53.187 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-4 * z^4, x * y^-1 * x * y^-4 * x^5 * y^-1 ] T53.188 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-10 * y^4 * z^-9 ] T53.189 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-1 * z * y^-4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^2 * y^-4 ] T53.190 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * y^-1 * x^7 * y^-2 * x^3 ] T53.191 : Triangle type {107,107,107} Group order 107 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-2 * z * y^-1 * z * y^-8 ] Genus 54 T54.1 : Triangle type {2,4,57} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-41 * x * z^8 * y^-1 * z^-7 ] T54.2 : Triangle type {2,4,110} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-110 ] T54.3 : Triangle type {2,4,216} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-13 * x * y^-1 * z^-94 ] T54.4 : Triangle type {2,6,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^46 * y * z^-5 * x * z^4 ] T54.5 : Triangle type {2,8,38} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-10 * x * z^17 * y * z^-1 * x * y^-1 * z^-8 ] T54.6 : Triangle type {2,10,135} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-4 * x * z * y * z^-3 * x * y * z^-17 ] T54.7 : Triangle type {2,12,66} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-1 * x * z^10 * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T54.8 : Triangle type {2,14,20} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-1 * z^-1 * x * y^-1 * z * y * x * z * y * x * y^-6 * z^-1 * x, z^-2 * x * z * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-10 ] T54.9 : Triangle type {2,14,126} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^3 * y^-5 * z^3, z^-1 * x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-3 ] T54.10 : Triangle type {2,20,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^10 * y^-1 * z^-1 * x ] T54.11 : Triangle type {2,24,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z * y * z^-2 * x * y^-1 * z^-5 ] T54.12 : Triangle type {2,26,117} Group order 234 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y^-4 * z^4 ] T54.13 : Triangle type {2,30,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y * x * z * y^2 * z^-1 * y * z^-1 ] T54.14 : Triangle type {2,30,40} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^7 * z^-1 * y * z^-1 ] T54.15 : Triangle type {2,38,114} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-8 * y^11 * z^-3 * y^13 * z^-1 * y ] T54.16 : Triangle type {2,57,57} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-43 * y^11 * z^-1 ] T54.17 : Triangle type {2,74,111} Group order 222 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-7 * y^11 * z^-2 * y^14 * z^-2 ] T54.18 : Triangle type {2,109,218} Group order 218 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^100 * z^-8 * y ] T54.19 : Triangle type {2,110,110} Group order 220 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-99 * z ] T54.20 : Triangle type {2,216,216} Group order 216 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^8 * y^-98 * z ] T54.21 : Triangle type {3,3,109} Group order 327 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-5 * x * z^5 * y * z^-1 ] T54.22 : Triangle type {3,55,165} Group order 165 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-44 * z * y^-1 * z * y^-7 * z ] T54.23 : Triangle type {3,56,56} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^43 * y^-3 * z * y^-7 * z ] T54.24 : Triangle type {3,162,162} Group order 162 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-43 * z * y^-1 * z * y^-6 * z^2 ] T54.25 : Triangle type {4,4,55} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * x * z^4 * y * x^-1 * z^5 ] T54.26 : Triangle type {4,4,55} Group order 220 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-47 * x * y * z^-7 ] T54.27 : Triangle type {4,4,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-46 * x * y^-1 * z^-7 ] T54.28 : Triangle type {4,6,32} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z * y * x * z^8 * y * x^-1 * z^5 ] T54.29 : Triangle type {4,8,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z^4 * y^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z^6 ] T54.30 : Triangle type {4,12,28} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-4 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * x * z * y * z^-3 ] T54.31 : Triangle type {4,14,21} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3 ] T54.32 : Triangle type {4,37,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^11 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T54.33 : Triangle type {4,38,38} Group order 152 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-10 * z^2 * y^-1 * z * y^-3 * z^3 * y^-5 * z * y^-1 * z * y^-10 ] T54.34 : Triangle type {4,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z * y^-3 * z * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T54.35 : Triangle type {5,28,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z^3 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T54.36 : Triangle type {5,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T54.37 : Triangle type {5,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T54.38 : Triangle type {6,6,28} Group order 168 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^2 * z * y^-1 * z^-1 ] T54.39 : Triangle type {6,6,28} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y * x^-1 * y^-1 * x * z^-2, x^-1 * z * y^-1 * x * z * y ] T54.40 : Triangle type {6,6,28} Group order 168 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, x^6, (x * y^-1 * x)^2 ] T54.41 : Triangle type {6,6,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-15 * x * y * z^-12 ] T54.42 : Triangle type {6,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-1 * y * z^-1 * y * z^-1 * y^12 ] T54.43 : Triangle type {6,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 ] T54.44 : Triangle type {7,19,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-3 * z^4 * x^-1 * y^-4 * z * y^-1 * z * y^-5 ] T54.45 : Triangle type {7,20,20} Group order 140 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-1 * z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-4 * z * y^-5 * z * y^-1 * z ] T54.46 : Triangle type {7,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T54.47 : Triangle type {7,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^6 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T54.48 : Triangle type {7,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-3 ] T54.49 : Triangle type {8,8,19} Group order 152 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^5 * y * x^-1 * y * x^-1 * y^-1 * x * z^4 * y^-1 * z^-1 * x * z^5 ] T54.50 : Triangle type {10,13,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^13 ] T54.51 : Triangle type {10,14,14} Group order 140 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^4 * z^-1 * y^8 * z^-1 ] T54.52 : Triangle type {10,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z^4 * y^-2 * x^-1 * z^4 ] T54.53 : Triangle type {10,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^6 * y^-2 * x^-1 * z^4 ] T54.54 : Triangle type {12,12,33} Group order 132 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-2 * x^-1 * z^3 * y * x^-1 * y * z^-4 ] T54.55 : Triangle type {12,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-2 * x^-1 * z^4, x^2 * y^-6 * x * y^-4 ] T54.56 : Triangle type {12,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-6, x^3 * y^-5 * x * z^-5 * x^3 ] T54.57 : Triangle type {12,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-3 * x * y^-2 * z * y^-1 ] T54.58 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^3 * y^-4 * x^2 * z^-4 * x^4 ] T54.59 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^-1 * y * x^-5 * y^8 ] T54.60 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-4, x^-1 * z^5 * x^-2 * z^4 ] T54.61 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, y^2 * x^-4 * y^6 * x^-1 * y ] T54.62 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^3 * y^-4 * x^2 * z^-4 * x^4 ] T54.63 : Triangle type {13,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-2 * z^4, x * y^-5 * x * y^-4 ] T54.64 : Triangle type {14,14,63} Group order 126 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^4 * y * x * z^4 ] T54.65 : Triangle type {14,14,63} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, y * x * z^3 * y^-1 * x^-1 * z^4 ] T54.66 : Triangle type {14,14,63} Group order 126 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, x^-1 * z^4 * y * z^-4 ] T54.67 : Triangle type {15,24,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y * x^-5 * y^7 ] T54.68 : Triangle type {15,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, z^-3 * y^2 * z^-3 ] T54.69 : Triangle type {15,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T54.70 : Triangle type {18,18,21} Group order 126 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * x * z^2, y^2 * x^-2 * y * x^-1 * z ] T54.71 : Triangle type {18,18,21} Group order 126 Chiral action Defining relators: [ x * y * z, z^-1 * y * x * z^-1, (x * y^-2)^2 ] T54.72 : Triangle type {18,18,21} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-1 * x * z^3 ] T54.73 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-5 * z^2, x^-1 * z^5 * x^-5 * z ] T54.74 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-8 * x * y^-4 ] T54.75 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-1 * x * y^-1 * x * y^-6 * x * y^-4 ] T54.76 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-4 * z^2, y^-2 * z^3 * y^-7 ] T54.77 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-4 * y^6 * x^-1 * y^3 ] T54.78 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^6 * y^-2 * x^-1 * z^4 ] T54.79 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-6 * y * x^-10 * z * x^-2 ] T54.80 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y^2 * x^-1 * y * x^-11 * y * x^-1 * y * x^-1 * y ] T54.81 : Triangle type {19,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * z^-2 * x^6 * y^-2 * x^5 ] T54.82 : Triangle type {20,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y * z^-1 * x^-1 * z^3 ] T54.83 : Triangle type {20,20,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y * x^-1 * z^3 ] T54.84 : Triangle type {20,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, (z^-1 * x)^3 ] T54.85 : Triangle type {20,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, y * z^-1 * y * x^-1 * z * y ] T54.86 : Triangle type {20,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, x^-1 * y * x^-7 * z * x^-1 ] T54.87 : Triangle type {20,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x * y^-1 * x * y^-3, z^-2 * x * z^-1 * x * z^-3 ] T54.88 : Triangle type {24,24,30} Group order 120 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * y^-1 * z^-1, z^-1 * x * y^-1 * x * z^-1 * x, y^-3 * x * z^2 ] T54.89 : Triangle type {24,24,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * z^3, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T54.90 : Triangle type {28,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^10 * z^-1 * x * z^-1 * x^10 * z^-1 * x * z^-1 * x^3 ] T54.91 : Triangle type {28,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^3 * y^-1 * x^5 * z^-5 * x^2 ] T54.92 : Triangle type {28,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-1 * x^2 * z^-1 * x * z^-1 * x * z^-5 * x^2 * z^-5 * x * z^-1 * x * z^-2 ] T54.93 : Triangle type {28,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^-1 * z^5 * x^-5 * y * x^-2 ] T54.94 : Triangle type {28,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-8 * x * y^-4 ] T54.95 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^10 * y^-4 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 * x * y^-1 * x ] T54.96 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T54.97 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^4, x^2 * y^-3 * x^7 ] T54.98 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^6 * y^-3 * x * y^-4 * z^2 ] T54.99 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-8 * x^2 * y * z^-9 ] T54.100 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 ] T54.101 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^7 * x^-5 * z^2 ] T54.102 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^7, y^-1 * z * y^-1 * z * y^-5 * z^3 ] T54.103 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^4 * y^-4 * x^-1 * z^4 ] T54.104 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-2 * z * y^-1 * z * y^-1 * z * y^-8 ] T54.105 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^3 * y^-3 * x^7 ] T54.106 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^37 ] T54.107 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^-16 * x * y^-5 * x ] T54.108 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, z^5 * x^-2 * z^4 ] T54.109 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^4 * y^-1 * z^4 * x^-3 * z^6 ] T54.110 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-4 * y * x^-7 * y^2 * x^-6 ] T54.111 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^-1 * z^4, x * y^-1 * x * y^-1 * x * y^-4 * x^6 ] T54.112 : Triangle type {37,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-8 * z, x^-1 * z^5 * x^-6 * z ] T54.113 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^5 * x^-1 * y * x^-1 * y * z^-1 * y ] T54.114 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, x * y^-1 * x^3 * y^-1 * x * y^-1 ] T54.115 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * y * x^-1 * z, z^-3 * x^2 * z^-3 ] T54.116 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, (x^-1 * z^4)^2 ] T54.117 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, y^5 * z^-1 * y * z^-1 ] T54.118 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3 ] T54.119 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^-5 * y * x^-1 * z * y ] T54.120 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-4 * y^2 * x^-8 ] T54.121 : Triangle type {38,38,57} Group order 114 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-6 * x * z^-1 * x * z^-1 * x^2 * z^-3 * x^3 * z^-1 * y * z^-3 ] T54.122 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-25 * z * y^-2 ] T54.123 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 ] T54.124 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-2 * x * z^-4 * y * x^3 * z^-7 ] T54.125 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^4 * y^-3 * x^3 * z^-5 * x^2 ] T54.126 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-30 * x * y^-6 ] T54.127 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^7 * y^-1 * x^-6 * z^2 ] T54.128 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z * x^-1 * z * x^-1 * y * x^-10 * z * x^-3 ] T54.129 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-3 * z * y^-1 * z * y^-4 * x * y^-4 ] T54.130 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^-1 * z^5 * x^-6 * z ] T54.131 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T54.132 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^7 * z^-2 * x * z^-1 * x * z^-1 * x^10 * z^-1 * x * z^-1 * x^3 ] T54.133 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-8 * z ] T54.134 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x^2 * y^-1 * x * y^-4 * x^5 * y^-1 ] T54.135 : Triangle type {55,110,110} Group order 110 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-55, y * z^-1 ] T54.136 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x^-2 * y^-1, y^-49 * x * y^-5, x * z^-1 ] T54.137 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-29 * x^2 * y^-6 ] T54.138 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^8 * y^-4 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 * x * y^-1 * x ] T54.139 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-5 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 * x ] T54.140 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T54.141 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T54.142 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-3 * x * y^-4 * x^2 * y^-4 ] T54.143 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^6 ] T54.144 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x * y^-4, z^5 * x^-1 * z^4 ] T54.145 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^5 * x^-9 * z^3 ] T54.146 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-5 * z^3, x^-1 * z^4 * x^-5 * y * x^-1 ] T54.147 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-2 * x * z^-4 * y * x * z^-8 ] T54.148 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-2 * x * y^-4 * x^2 * y^-4 ] T54.149 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, x^-1 * z^4 * x^-5 * z ] T54.150 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^4, x^3 * y^-2 * x^4 * z^-4 * x^2 ] T54.151 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^3 * y^-1 * z * y^-4 * x^-1 * z^4 ] T54.152 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-5 ] T54.153 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^2 * z^-4 * y^4 * z^-1 * y^6 ] T54.154 : Triangle type {109,109,109} Group order 109 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^5 * y^-1, y^-1 * z * y^-1 * z * y^-5 * z^3 ] Genus 55 T55.1 : Triangle type {2,3,12} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y * z^-1 * x * z^2 * y * z^-1 * x * z * y * x * z^2 * y * z^-1 * x * z * y * x * z * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T55.2 : Triangle type {2,3,24} Group order 864 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-23 * x ] T55.3 : Triangle type {2,3,60} Group order 720 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^4 * y^-1 * z^-5 ] T55.4 : Triangle type {2,4,6} Group order 1296 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * y * z^-1 * x * z * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y * z^-2 * y ] T55.5 : Triangle type {2,4,6} Group order 1296 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, z^-2 * y * x * z * y^-1 * z * y * z^-1 * y * x * y^-1 * z^-1 * y * z^-2 * y * z^-2 * y ] T55.6 : Triangle type {2,4,6} Group order 1296 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-2 * y * z^-1 * x * z^2 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-3 ] T55.7 : Triangle type {2,4,8} Group order 864 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, (y * z^-1)^6 ] T55.8 : Triangle type {2,4,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^5, (y * z^-4)^2 ] T55.9 : Triangle type {2,4,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z^10, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^3 ] T55.10 : Triangle type {2,4,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z * y^-1 * z)^3, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T55.11 : Triangle type {2,4,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-2 * z^-4 * y ] T55.12 : Triangle type {2,4,16} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z * y^-2 * z^-4 * y, z^3 * y * z^-3 * x * z * y^-1 * x * z^4 * y^-1 * z^-2 * x ] T55.13 : Triangle type {2,4,16} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-1 * x * z^2 ] T55.14 : Triangle type {2,4,16} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y * z^-1)^6, z^-8 * x * y * z^-7 ] T55.15 : Triangle type {2,4,16} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T55.16 : Triangle type {2,4,28} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y^-1 * z)^6, x * z^5 * y * x * y^-1 * z^-5 * x * y^-1 * z^-1 ] T55.17 : Triangle type {2,4,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-112 ] T55.18 : Triangle type {2,4,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-41 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T55.19 : Triangle type {2,4,220} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-14 * x * y^-1 * z^-95 ] T55.20 : Triangle type {2,5,6} Group order 810 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z * y^2 * x * y^-2 * z^-1 * x * y^-2 * z^-1 * y ] T55.21 : Triangle type {2,6,6} Group order 648 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-2 * z^-1 * y * z^-1, x * z * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * x * z * y^-1 * z^-1 * y ] T55.22 : Triangle type {2,6,6} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-2 * x ] T55.23 : Triangle type {2,6,6} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, z^2 * y^2 * x * z^2 * y^2 * x * z * y^-1 * z^-1 * y * x ] T55.24 : Triangle type {2,6,9} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z * y^-1 * z^-1 * x ] T55.25 : Triangle type {2,6,9} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * x ] T55.26 : Triangle type {2,6,9} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * y * z^-4 ] T55.27 : Triangle type {2,6,9} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y^-2 * z)^3, x * z^2 * y^-2 * z^-3 * y ] T55.28 : Triangle type {2,6,9} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * y * z^-4, y * x * z * y^-3 * z^-1 * x * y^-2 * z^-1 ] T55.29 : Triangle type {2,6,9} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, y^-1 * z^2 * y^-2 * z^2 * y^-1 * z, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * x ] T55.30 : Triangle type {2,6,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^2 * y^-1 * z * y^-2 * z^-2 * x * z^2 ] T55.31 : Triangle type {2,6,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, z * y^-1 * z^3 * y * z^-1 * x * z * y * z^-1 * y * z^-2 * x * z * y^-1 * z^-1 * x ] T55.32 : Triangle type {2,6,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^6 * y^-1 * x * z^5 ] T55.33 : Triangle type {2,6,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^12 ] T55.34 : Triangle type {2,6,21} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z^6 * y * x * z * y^-1 * z^-6 * x * z * y * z^-4 ] T55.35 : Triangle type {2,6,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^4 * y^-1 * z^-5, x * z * y * z^-1 * x * z * y * z^-2 * y * z^-2 ] T55.36 : Triangle type {2,6,57} Group order 342 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^26 * y * x * z^17 * y * z^-1 * x * y^-1 * z^-9 * x * z ] T55.37 : Triangle type {2,6,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-27 * x * z^15 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-2 ] T55.38 : Triangle type {2,7,7} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, z^-3 * x * y * z^-3, (y^-2 * z)^3, (y * z^-2 * y * z^-1)^2 ] T55.39 : Triangle type {2,8,8} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T55.40 : Triangle type {2,12,12} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-4 * z^-1 * y^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T55.41 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T55.42 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T55.43 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^12, (y * z^-1 * y^4)^2 ] T55.44 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^12 ] T55.45 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, x * z^8 * y^-1 * z^-7 * x * z^2 * y^-1 * z^-5 ] T55.46 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^12, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T55.47 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-3)^2 ] T55.48 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3)^2, z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T55.49 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-6 * x * z^5 * y * z^-1 * x * y^-1 * z^-10 ] T55.50 : Triangle type {2,12,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, z^6 * y * z^-5 * x ] T55.51 : Triangle type {2,12,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, y * x * z^10 * y * z^-9 * x * z ] T55.52 : Triangle type {2,15,30} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-3 * z^2 * y^-6 * z^4 ] T55.53 : Triangle type {2,16,16} Group order 288 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z^-1 * y * z^-2, y^2 * z^-1 * y^9 * z^-3 * y ] T55.54 : Triangle type {2,16,16} Group order 288 Chiral action Defining relators: [ x^2, x * y * z, z^-2 * y^3 * z^-1 * y * z^-1 ] T55.55 : Triangle type {2,16,16} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^2 * z^-3 * y^8 * z^-1 * y^2 ] T55.56 : Triangle type {2,16,16} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^-1 ] T55.57 : Triangle type {2,24,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-12 * z^3 * y^-5 * z^3 * y^-1 ] T55.58 : Triangle type {2,24,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y^-2 * z^5 ] T55.59 : Triangle type {2,28,28} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z^2 * y^-1 * z^2 * y^-6 * z * y^-1 ] T55.60 : Triangle type {2,30,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y * z^-1 * y^9 * z^-1 * y * z^-2 ] T55.61 : Triangle type {2,39,78} Group order 234 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-11 * y^9 * z^-1 * y^2 * z^-12 * y^3 ] T55.62 : Triangle type {2,46,115} Group order 230 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-11 * z^3 * y^-6 * z^2 * y^-1 ] T55.63 : Triangle type {2,111,222} Group order 222 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^101 * z^-10 ] T55.64 : Triangle type {2,112,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-26 * y^29 ] T55.65 : Triangle type {2,112,112} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^10 * y^-101 ] T55.66 : Triangle type {2,220,220} Group order 220 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-100 ] T55.67 : Triangle type {3,3,6} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T55.68 : Triangle type {3,3,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T55.69 : Triangle type {3,3,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z * y * x * z * x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^-1 * x^-1 * y * x * z ] T55.70 : Triangle type {3,3,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^6 * y^-1 * z^-1 * x^-1 * z^4 * y * x ] T55.71 : Triangle type {3,3,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * y * x^-1 * z * y^-1 * x * y^-1, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T55.72 : Triangle type {3,3,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-2 * x * z^2 ] T55.73 : Triangle type {3,3,39} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x^-1 * z^2 * y^-1 * z^-7 ] T55.74 : Triangle type {3,3,111} Group order 333 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^4 * y^-1 * z^-2 * x^2 * z^4 * y * x ] T55.75 : Triangle type {3,4,4} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * z * x^-1 * z * y * x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T55.76 : Triangle type {3,4,4} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, z * y * x^-1 * y * x^-1 * y * x * z^-1 * x^-1 * y^-1 * z^-1 * y * x ] T55.77 : Triangle type {3,4,4} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 * x * z^-1 ] T55.78 : Triangle type {3,4,6} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * x * z * y * x^-1 * z * y^-1 * z^-1, y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T55.79 : Triangle type {3,4,6} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x * z ] T55.80 : Triangle type {3,4,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * x * z ] T55.81 : Triangle type {3,4,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T55.82 : Triangle type {3,4,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T55.83 : Triangle type {3,4,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-2 * y * x^-1 * z * y^2, y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T55.84 : Triangle type {3,4,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T55.85 : Triangle type {3,4,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * y^-1, y * x^-1 * z * y^-1 * x * z * y * z^-1 ] T55.86 : Triangle type {3,4,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^-1 * z^-1 * x^-1 * y * x^-1 * y * z^-2 * x^-1 ] T55.87 : Triangle type {3,4,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y^-1 * z * y * x^-1 * y^-1 * z^2, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T55.88 : Triangle type {3,4,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T55.89 : Triangle type {3,4,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * x * z^-1 * x * z^2 * y^-1 * z^-1 ] T55.90 : Triangle type {3,4,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1 ] T55.91 : Triangle type {3,4,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-4 * x^-1 * z^3 * y ] T55.92 : Triangle type {3,4,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-4 * x^-1 * z^3 * y^-1 ] T55.93 : Triangle type {3,5,5} Group order 405 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x * y^-1 * z^-1, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T55.94 : Triangle type {3,5,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^6, y * z^-2 * x^-1 * y * z^-2, x^-1 * y * x^-1 * y * x^-1 * z * y * z^-1 * y ] T55.95 : Triangle type {3,6,8} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T55.96 : Triangle type {3,6,26} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * y^-2 * z^-1 ] T55.97 : Triangle type {3,6,74} Group order 222 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * y * x^-1 * z^3 * y ] T55.98 : Triangle type {3,8,24} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-1 * z^2, y^8 ] T55.99 : Triangle type {3,8,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y^8, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T55.100 : Triangle type {3,8,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^8 ] T55.101 : Triangle type {3,8,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, y^8, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y ] T55.102 : Triangle type {3,8,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-3 * y^2 * z^-3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T55.103 : Triangle type {3,9,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x * z * y * x * z^2 * y ] T55.104 : Triangle type {3,9,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x * y^-1 * z^-1, z^2 * x^-1 * y^-1 * x * z * y^-2, z^-3 * y * x^-1 * z^2 * y ] T55.105 : Triangle type {3,9,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, x^-1 * z^2 * y^2 * z^-3 ] T55.106 : Triangle type {3,9,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * y^2 * x^-1 * z * y^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T55.107 : Triangle type {3,9,9} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x * z * y * x * y^-1 * x * z * y^-1 * z * y ] T55.108 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, y^-9 ] T55.109 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-3 * x^-1 * z^2 * y^-1, y^-9 ] T55.110 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-9 ] T55.111 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1 ] T55.112 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x * z * y^-1, z^-1 * y^2 * x^-1 * y^-3 ] T55.113 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T55.114 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^-1 * y * x^-1 * y * z^-1 * x^-1 ] T55.115 : Triangle type {3,9,9} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * y^2 * x^-1 * z * y^2, (z^-1 * x^-1 * y^-1)^3 ] T55.116 : Triangle type {3,9,18} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-3, x * z * y * x^-1 * y * z^-1 * y ] T55.117 : Triangle type {3,9,18} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-9 ] T55.118 : Triangle type {3,12,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y^4 * x^-1 * z * y * z^-2 ] T55.119 : Triangle type {3,12,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-6 * x^-1 * y^-2 * z * y * z^-2 ] T55.120 : Triangle type {3,12,12} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y * x^-1 * z^2 * y * x^-1 * y * x * y^-2 * z^-1 * x^-1 ] T55.121 : Triangle type {3,20,60} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-2 * y^8 * z^-2 * y^4 ] T55.122 : Triangle type {3,21,21} Group order 189 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-4 * y * z^-2 * y^2 * z^-1 * y^6 * z^-1 * y * z^-1 * y^2 ] T55.123 : Triangle type {3,56,168} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-45 * z * y^-1 * z * y^-7 * z ] T55.124 : Triangle type {3,57,57} Group order 171 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-46 * z * y^-1 * z * y^-7 * z ] T55.125 : Triangle type {3,165,165} Group order 165 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-44 * z * y^-1 * z * y^-8 ] T55.126 : Triangle type {4,4,4} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, z^-2 * y * x^-2 * z * y^-1 * x * y^-1 ] T55.127 : Triangle type {4,4,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-2)^2, (x * y^-1)^4, y * x * z^-1 * y * x * z * y^-1 * z^-1 ] T55.128 : Triangle type {4,4,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, (z^-1 * x)^3 ] T55.129 : Triangle type {4,4,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2 ] T55.130 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * z * y^-1 ] T55.131 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * z * x^-1 * z, z^8 ] T55.132 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^2 ] T55.133 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, z^-1 * x^-1 * y * x^2 * z * y * x, z^8 ] T55.134 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, x^-1 * z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 * z ] T55.135 : Triangle type {4,4,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, x^-1 * z * y * z^-1 * x^-1 * z^2 * x^-1 * z ] T55.136 : Triangle type {4,4,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * y^-1 * z^-2 * y * z^-1 * x * z * y^-1 * z * y^-1 * z ] T55.137 : Triangle type {4,4,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z^2 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z ] T55.138 : Triangle type {4,4,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x ] T55.139 : Triangle type {4,4,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 ] T55.140 : Triangle type {4,4,14} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x, x * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T55.141 : Triangle type {4,4,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-56 ] T55.142 : Triangle type {4,4,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^17 * y * x^-1 * z^4 * y^-1 * x * y^-1 * z^-4 * x^-1 ] T55.143 : Triangle type {4,4,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^17 * y * x^-1 * z^4 * y^-1 * x * y^-1 * z^-4 * x ] T55.144 : Triangle type {4,4,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-21 * x * z * y^-1 * x * z * y * z^-3 ] T55.145 : Triangle type {4,4,110} Group order 220 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-47 * x * y^-1 * z^-7 ] T55.146 : Triangle type {4,5,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y^2 * x * z * y^2 ] T55.147 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T55.148 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T55.149 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y, y^6, z^-1 * y^2 * x^-1 * y^3 ] T55.150 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T55.151 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T55.152 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, (y * z^-2)^2, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T55.153 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y * z^-2 ] T55.154 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-3 * x^-1 * y * z^-2, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T55.155 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, y^2 * z^-1 * y * x^-1 * z * y^2 * z^-1 ] T55.156 : Triangle type {4,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T55.157 : Triangle type {4,6,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, (z^2 * y * x^-1 * z^5)^2 ] T55.158 : Triangle type {4,6,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-4 * x^-1 * z * y * z^-2 ] T55.159 : Triangle type {4,8,8} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * y^-2 * x * y^-1 * z^-1, x^-1 * z * y^-1 * x * y^-1 * z ] T55.160 : Triangle type {4,8,8} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * z * y^-1, y^-1 * z * y^-1 * x * z * x^-1 ] T55.161 : Triangle type {4,8,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-5 * x^-1 * z^6 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-5 ] T55.162 : Triangle type {4,8,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-5 * x^-1 * z^6 * y^-1 * x^-1 * z^4 * y * z^-5 ] T55.163 : Triangle type {4,10,20} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * x^-1 * z * x^-1 * z * y^-1 * z ] T55.164 : Triangle type {4,12,15} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x^-1 * z * y, y^-1 * z^-1 * y * x * z * x^-1 ] T55.165 : Triangle type {4,12,15} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x * y^-1 * x * z * y^-1 * z^-8 ] T55.166 : Triangle type {4,12,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x * z^4 * y * z^-5 ] T55.167 : Triangle type {4,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, y * x^-1 * z^2 * y^-1 * z^-4 * x^-1 * z^2 ] T55.168 : Triangle type {4,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, y * x^-1 * z^2 * y^-1 * z^-4 * x * z^2 ] T55.169 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-5 * y^2 * z^-4 * y^7 ] T55.170 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^3 * z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-1 * y^7 ] T55.171 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * z * y * z^-2, z^-1 * y * z^-1 * y^3 * z^-4 ] T55.172 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * z * y * z^-2, y^7 * z^-1 * y * z^-1 ] T55.173 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * z * y * z^-2, y^6 * z^-4 ] T55.174 : Triangle type {4,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y * z^-1 * y)^2 ] T55.175 : Triangle type {4,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^13 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T55.176 : Triangle type {4,74,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^14 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T55.177 : Triangle type {6,6,6} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * z * y^-1 * x * y^-1 * z, z^6, y^2 * x^3 * z * y * x^-1, y^-3 * x^2 * y^-1 * x * z ] T55.178 : Triangle type {6,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, z^-1 * y * x^-2 * y^-2 * x, z * y * x^-2 * y * x * z ] T55.179 : Triangle type {6,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-1 * y^-1 * x * z * y, y^6 ] T55.180 : Triangle type {6,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T55.181 : Triangle type {6,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, x * z^-1 * x^2 * y^-2, y * z^-1 * x^2 * z^-2 ] T55.182 : Triangle type {6,6,6} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z^-1 * x * z * y^-1 * z * y * x * z * y^-1 * z^-1 * x^-1 * y^-1 ] T55.183 : Triangle type {6,7,21} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-1 * z^2, y^-7 ] T55.184 : Triangle type {6,9,18} Group order 162 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, (y * z^-1 * y)^2, z^-2 * y * x * y^-1 * z^-1 ] T55.185 : Triangle type {6,9,18} Group order 162 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y * x * z * y ] T55.186 : Triangle type {6,9,18} Group order 162 Chiral action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-1 * x^-2 * y^-1 * z^-1 * y ] T55.187 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-3 * x * y^-4 ] T55.188 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, z^-1 * y * x^-2 * y^-1 * z^-1 * y ] T55.189 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z * x^-1 * y^-1 * x * y^-1 * x ] T55.190 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x * z * y^-1 ] T55.191 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z * y^-1 * z^-1 * x * z * y^-1 ] T55.192 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^2 * y^-3 * z^4 ] T55.193 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1 ] T55.194 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y * z^-1 * y * z^-2, y^-9 ] T55.195 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, (y * z^-1 * y)^2, y^-9 ] T55.196 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, (y * x^-1 * z)^3 ] T55.197 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * y * z^-2, (y * x^-1 * z)^3 ] T55.198 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, y^-1 * z^2 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T55.199 : Triangle type {6,9,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^2 * z^-3, (y * x^-1 * z)^3 ] T55.200 : Triangle type {6,16,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T55.201 : Triangle type {6,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, (y * z^-1 * y)^2, z^2 * y * x^-1 * z * y^-1 ] T55.202 : Triangle type {6,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^2 * y * x * z * y^-1 ] T55.203 : Triangle type {6,23,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T55.204 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z^2 * y^-1 * z * y^-2 * z^3 * y^-1 ] T55.205 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^4 * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T55.206 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-1 * y^2 * z^-3 ] T55.207 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, z^-2 * y * z^-1 * y * z^-3 ] T55.208 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^4 * y^-1 * z * y^-1 * z * y^-4 * z * y^-9 * z * y^-1 ] T55.209 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^-1 * y^4 * z^-3 ] T55.210 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^6 ] T55.211 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y^-8 * z * y^-1 ] T55.212 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y * x^-1 * y^-3 ] T55.213 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^3 * x^-1 * y^-1 * z^-1 * y ] T55.214 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, (y * z^-1 * y)^2, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x ] T55.215 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T55.216 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, z^-2 * y * x^-1 * y^2 * z^-1 ] T55.217 : Triangle type {6,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z * y^2 * x^-1 * z * y^-1 * z, z^-1 * y^4 * z^-3 ] T55.218 : Triangle type {6,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^12 ] T55.219 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^8 ] T55.220 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^4 * x * z^-1 * x * z^-1 ] T55.221 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3, x^8 ] T55.222 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x^8, y^4 * x * z^-1 * x * z^-1 ] T55.223 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^8, z^-3 * x^2 * z^-3 ] T55.224 : Triangle type {8,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, x^8, y^4 * x * z^-1 * x * z^-1 ] T55.225 : Triangle type {8,16,16} Group order 144 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * y^-1 * z^-1, z^-2 * x^2 * z * y, y * x^-3 * y^2 * z^-1 ] T55.226 : Triangle type {8,16,16} Group order 144 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * y^-2, z * x^-1 * y^-1 * x * z * y^-1 ] T55.227 : Triangle type {8,16,16} Group order 144 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^2 * x^2 * z * y, x^8 ] T55.228 : Triangle type {8,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, x^8 ] T55.229 : Triangle type {8,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, y * z^-1 * x * y^-1 * x * y^-1 * z^-2 ] T55.230 : Triangle type {8,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y * z^-1 * y * x^-1 * y^-1 * z * y ] T55.231 : Triangle type {8,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^4 * z^-1 * y * z^-1 * y * z^-3 * y^3 * z^-1 * y ] T55.232 : Triangle type {8,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-3 ] T55.233 : Triangle type {9,12,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y * x * z^2, y * x^-3 * y^3 ] T55.234 : Triangle type {9,12,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^-1 * y * x^-2 * z * y * z^-1 ] T55.235 : Triangle type {9,15,45} Group order 135 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-2 * z * y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z * y^-2 ] T55.236 : Triangle type {9,15,45} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-4 * y * z^-1 * y^5 * z^-4 ] T55.237 : Triangle type {9,42,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T55.238 : Triangle type {9,42,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y * z^-1 * y^5 * z^-4 ] T55.239 : Triangle type {11,12,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^12, x^-11 ] T55.240 : Triangle type {11,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^2 * y^-3 * x * y^-4, z^7 * x^-1 * z^4 ] T55.241 : Triangle type {11,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4 * z^2, x^-11 ] T55.242 : Triangle type {11,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-6, x^-11 ] T55.243 : Triangle type {11,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-2 * x * y^-4, x^-11 ] T55.244 : Triangle type {11,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-2 * x^-1 * z^4, x^-11 ] T55.245 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z^-1 * y * x^-1 * y^-2, (z^-1 * x)^3 ] T55.246 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-2, z * x^-1 * y^-1 * x * y^-1 * x ] T55.247 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * x * y * z^-4, y^12 ] T55.248 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x * z^-3 * x * z^-1 * x^3 * z^-1 * x * z^-1 ] T55.249 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2 ] T55.250 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * x * z * y, (y * z^-1 * y)^2 ] T55.251 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * x^-3 * y * z^-1 * y * z^-1 ] T55.252 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-1 * z * y^-6 * z * y^-1 * z^2 ] T55.253 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^3 * z^-1 * y^6 * z^-1 * y, x^12 ] T55.254 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^4 * z^-3, y^-2 * x^3 * y^-2 * x ] T55.255 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y^-3 * z^-1 * y^7 ] T55.256 : Triangle type {12,12,12} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * z^-1 * x^-1 * z^3, y^-1 * x^4 * y^-3 ] T55.257 : Triangle type {12,12,66} Group order 132 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z * y^-1 * z^-1 * x^-1 * z^3 * y * x^-1 * y * x * z^3 ] T55.258 : Triangle type {12,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-4 * z^2, x^3 * y^-5 * x * z^-5 * x^3 ] T55.259 : Triangle type {12,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-1 * z^4, y^-6 * x * y^-4 ] T55.260 : Triangle type {14,18,63} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, y^-1 * x^6 * y^-5 * x * y^-3 ] T55.261 : Triangle type {14,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3, y^-3 * x^2 * y^-3 ] T55.262 : Triangle type {14,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1 ] T55.263 : Triangle type {14,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z, y^3 * x^-1 * y * x^-4 * y^2 * x^-1 ] T55.264 : Triangle type {14,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^-1 * y^2 * x^-1 * y^3 * x^-1 * y * x^-7 ] T55.265 : Triangle type {14,21,42} Group order 126 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-2 * x^4 * z^-4 ] T55.266 : Triangle type {15,15,15} Group order 135 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * x^-3 * y^4 ] T55.267 : Triangle type {15,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-2 * y * x^-5 * y^6 * x^-1 * y * x^-1 ] T55.268 : Triangle type {15,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-3 * z^3, x * y^-5 * x^2 * y^-3 ] T55.269 : Triangle type {15,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-1 * x * y^-6 * x^5 * y^-1 ] T55.270 : Triangle type {20,24,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 ] T55.271 : Triangle type {20,24,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-1 * z^4 * y^-2 * x^-1 * z^4, x * y^-5 * x^4 * y^-1 ] T55.272 : Triangle type {20,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-5 * z, y^-2 * z^4 * y^-6 ] T55.273 : Triangle type {20,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x * y^-1 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x ] T55.274 : Triangle type {20,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-5 * z^2 * y^-3 * x^5 * y^-1 * x * y^-1 ] T55.275 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, x^2 * y^-6 * x * y^-4 ] T55.276 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, x^-2 * z * x^-1 * z^5 * x^-2 * z^4 ] T55.277 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z^2 ] T55.278 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-3 * x * y^-4, x^-1 * z^5 * x^-6 ] T55.279 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-11 * y^2 * x^-6 * z^2 * x^-4 ] T55.280 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-2 * x^5 * z^-5 * x * z^-1 * x * z^-2 ] T55.281 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-1 * z^4, x * y^-5 * x^5 ] T55.282 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-2 * z^4, x^-6 * y^5 * x^-2 ] T55.283 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y ] T55.284 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, z^6 * x^-1 * z * x^-1 * z * x^-12 * z * x^-1 * z ] T55.285 : Triangle type {23,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-4 * z^2, x^-2 * z * x^-5 * z^4 * x^-2 ] T55.286 : Triangle type {24,24,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-3 * x * z^-1 * x^2 * z^-3 * y * z^-1 * y * z^-1 ] T55.287 : Triangle type {24,24,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-2 * z^3 ] T55.288 : Triangle type {24,30,40} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^2 * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T55.289 : Triangle type {30,30,30} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, z^-1 * x^3 * z^-2, (y * x^-1 * y)^3 ] T55.290 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-6 * x * y^-6 * x * y^-6 ] T55.291 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-3 * z^3 * x^-8 ] T55.292 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^12 * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x * y^-4 * x * y^-1 * x * y^-1 ] T55.293 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z * x^-1 * z * x^-1 * z^5 * x^-5 * z^2 ] T55.294 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^4 * y^-1 * z * y^-1 * z^3 * y^-3 * x^-1 * z^5 ] T55.295 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-4 * z^3 ] T55.296 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^3 * x^-1 * z^12 * x^-2 * z^6 ] T55.297 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * y * x^-10 * z * x^-2 ] T55.298 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^4, x * y^-6 * x^5 ] T55.299 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-8 * y^3 * x^-2 ] T55.300 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, x^2 * y^-6 * x^2 * y^-3 ] T55.301 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-2 * z * y^-1 * z * y^-1 * z^3 * y^-3 * x^3 * y^-3 ] T55.302 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x * y^-4, z^5 * y^-3 * x^-1 * z^4 ] T55.303 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-2 * z^3 * y^-3 * x * y^-4 ] T55.304 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-1 * z * x^-1 * z^5 * x^-6 ] T55.305 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^24 * y^-1 * x^9 * y^-1 * x * y^-1 * x^2 ] T55.306 : Triangle type {38,57,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-4 * z^3, x * y^-3 * x^7 ] T55.307 : Triangle type {39,39,39} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-9 * z * y^-5 * z^2 * y^-4 ] T55.308 : Triangle type {39,39,39} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-1 * y * x^-5 * y^8 ] T55.309 : Triangle type {39,39,39} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-2 * z^4, y^-2 * z^4 * y^-2 * x * y^-4 ] T55.310 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T55.311 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x * y^-4, x^2 * y^-2 * x^4 * z^-4 * x ] T55.312 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-11 * y^4 * z^-9 ] T55.313 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^6 * y^-2 * x * y^-4 * z^2 ] T55.314 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-1 * y * x^-1 * y * z^-1 * y^3 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T55.315 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-30 * x^2 * y^-6 ] T55.316 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-8, z^-2 * x^4 * z^-6 ] T55.317 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, z^-2 * x^4 * z^-6 ] T55.318 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-56, y * z^-1 ] T55.319 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-21 * y^2 * x^-6 ] T55.320 : Triangle type {56,112,112} Group order 112 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^4 * y^-2 * x^4 * y^-4 * x^3 ] T55.321 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x^-2 * y^-1, y^-50 * x * y^-5, x * z^-1 ] T55.322 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^4 * y^-1 * x * y^-1 * x * y^-1 * x * z^-1 * x^9 * y^-1 * x * y^-1 * x ] T55.323 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^4 * y^-1 * x * y^-4 * x^5 * z^-1 * x^2 ] T55.324 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-4 * x^-1 * z^4, x^4 * y^-4 * x^4 * z^-2 * x ] T55.325 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-1 * z * y^-4 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^3 * y^-3 ] T55.326 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y^-3 * z * y^-1 * z * y^-4 * x * y^-4 ] T55.327 : Triangle type {111,111,111} Group order 111 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-8, x * y^-1 * x^9 ] Genus 56 T56.1 : Triangle type {2,3,12} Group order 1320 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^2 * y * x * z^2 * y * x * z * y^2 * z^-1 * x * z * y^-1 * z^-1 * x ] T56.2 : Triangle type {2,3,12} Group order 1320 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * x * z^2 * y * x * z^2 * y * x * z * y * z^-1 * x * y^-1 * z^-2 * x, z * y * x * z^6 * y * x * z * y^2 * z^-4 * x * z ] T56.3 : Triangle type {2,4,6} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T56.4 : Triangle type {2,4,114} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-114 ] T56.5 : Triangle type {2,4,224} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-15 * x * y^-1 * z^-96 ] T56.6 : Triangle type {2,5,10} Group order 550 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T56.7 : Triangle type {2,5,10} Group order 550 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z^-3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T56.8 : Triangle type {2,6,6} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y^-2 * z)^3, (z * y^-1 * z)^3, (z^-1 * y)^5 ] T56.9 : Triangle type {2,6,58} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^39 * y * x * y^-1 * z^-5 * x * y^-1 * z^-3 * x * z^8 ] T56.10 : Triangle type {2,6,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-26 * x * z^17 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-2 ] T56.11 : Triangle type {2,8,10} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^10 ] T56.12 : Triangle type {2,8,21} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z^8 * y * z^-2 * x * y^-1 * z^-7 ] T56.13 : Triangle type {2,8,76} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-10 * x * z^17 * y * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T56.14 : Triangle type {2,10,15} Group order 330 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * x * y^-1 * z^-1 ] T56.15 : Triangle type {2,10,15} Group order 330 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * x * z * y^2 * z^-1 * y * z^-1 ] T56.16 : Triangle type {2,10,30} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^13 * y * x * z^5 * y * z^-1 * x * y^-1 * z^-3 * x * z^5 ] T56.17 : Triangle type {2,10,30} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-2 * x * z^21 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T56.18 : Triangle type {2,10,30} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^10, z^-1 * y^2 * z^-1 * y^2 * z^-4 ] T56.19 : Triangle type {2,10,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^2 * y * z^-2 * x * z * y * z^-3 * x * z * y^-1 * z^-5 * x * z^2 * y^-1 * z^-7 * x * z ] T56.20 : Triangle type {2,16,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^16, z^-3 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T56.21 : Triangle type {2,18,126} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * x * z^3 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-6 * z^3 * y^-5 * z^3 * y^-1 ] T56.22 : Triangle type {2,25,50} Group order 250 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y^-1 * z^11 * y^-4 * z * y^-8 ] T56.23 : Triangle type {2,30,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-3 * y^7 * z^-3 * y^17 ] T56.24 : Triangle type {2,34,119} Group order 238 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y * z^-4 * x * z^3 * y^-1 * z^-2, y^-5 * z^3 * y^-4 * z^4 * y^-1 ] T56.25 : Triangle type {2,40,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-2 * y^4 * z^-4 ] T56.26 : Triangle type {2,58,116} Group order 232 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-29 * y^12 * z^-1 * y^13 * z^-2 ] T56.27 : Triangle type {2,113,226} Group order 226 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^102 * z^-10 * y ] T56.28 : Triangle type {2,114,114} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-101 * z ] T56.29 : Triangle type {2,224,224} Group order 224 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^10 * y^-100 * z ] T56.30 : Triangle type {3,3,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x, x * y^-1 * z^-2 * x^-1 * y * x^2 * z * y * x * z^-2 ] T56.31 : Triangle type {3,3,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T56.32 : Triangle type {3,4,20} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^4 * y * x^-1 * z^5 ] T56.33 : Triangle type {3,5,10} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^-5, x^-1 * z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 * z ] T56.34 : Triangle type {3,8,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-2 * z ] T56.35 : Triangle type {3,8,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T56.36 : Triangle type {3,58,58} Group order 174 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^45 * y^-10 * z * y^-1 ] T56.37 : Triangle type {3,168,168} Group order 168 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-45 * z * y^-1 * z * y^-6 * z^2 ] T56.38 : Triangle type {4,4,57} Group order 228 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-57 ] T56.39 : Triangle type {4,4,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-42 * x^-1 * z^4 * y * z^-9 ] T56.40 : Triangle type {4,5,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T56.41 : Triangle type {4,5,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1 ] T56.42 : Triangle type {4,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, (z^-1 * y)^3 ] T56.43 : Triangle type {4,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T56.44 : Triangle type {4,6,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x * z^7 * y * x^-1 * z^5 ] T56.45 : Triangle type {4,10,10} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z * y^2 * x * z^-1 * x, y^-4 * z^2 * y^-1 * z^2 * y^-1 ] T56.46 : Triangle type {4,10,10} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, (y * z^-2)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T56.47 : Triangle type {4,10,10} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * y^4 * z^-1 * y * z^-2, z^10 ] T56.48 : Triangle type {4,10,10} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^5 * x^-1 * y^-4 * z^-1, z^10 ] T56.49 : Triangle type {4,12,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x * z^6 * y^-1 * z^-3 ] T56.50 : Triangle type {4,14,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-5 * z * y^-4 * z * y^-1 * z^2 ] T56.51 : Triangle type {4,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * y^-1 * z^-3, y^7 * z^-1 * y * z^-1 ] T56.52 : Triangle type {4,21,21} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^6 * z^-3 * y^2 * z^-1 * y^6 * z^-2 * y ] T56.53 : Triangle type {4,39,52} Group order 156 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-5 * y^4 * z^-3 ] T56.54 : Triangle type {4,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-8 * z^2 * y^-1 * z * y^-3 * z^3 * y^-5 * z * y^-1 * z * y^-9 * z ] T56.55 : Triangle type {5,5,5} Group order 275 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1 ] T56.56 : Triangle type {5,5,5} Group order 275 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, y^2 * x^-2 * z * x^-1 * z ] T56.57 : Triangle type {5,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^2 * y^-2, z^-2 * x^2 * z * y^-1, y^8 ] T56.58 : Triangle type {5,8,8} Group order 200 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y^-2 * x * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y^8 ] T56.59 : Triangle type {5,8,8} Group order 200 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T56.60 : Triangle type {5,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z^2 ] T56.61 : Triangle type {5,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x^-5, x * z^-1 * x^-1 * y^2 ] T56.62 : Triangle type {5,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-2 * y^2 ] T56.63 : Triangle type {5,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y^2 * x^-1 * z * y, z^-2 * y * x * y^-1 * z^-1 ] T56.64 : Triangle type {5,29,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^6 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T56.65 : Triangle type {5,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T56.66 : Triangle type {5,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z ] T56.67 : Triangle type {5,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2 ] T56.68 : Triangle type {5,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z^-2 * y^3 * z^-1 * y^11 * z^-1 * y^4 * z^-1 * y * z^-1 * y * z^-4 ] T56.69 : Triangle type {5,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^4 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T56.70 : Triangle type {5,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T56.71 : Triangle type {6,6,29} Group order 174 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^16 * y * z^-1 * x^-1 * z^4 * y * x * y^-1 * x * z^5 ] T56.72 : Triangle type {6,6,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-15 * x * z * y * z^-3 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T56.73 : Triangle type {6,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^-2 * y^3 ] T56.74 : Triangle type {6,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^3 * y * x^-1 * z^4 ] T56.75 : Triangle type {6,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^-4 * x^-1 * z * y * z^-2 ] T56.76 : Triangle type {6,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^3 * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T56.77 : Triangle type {8,8,38} Group order 152 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^5 * y * x^-1 * y * x^-1 * z^12 ] T56.78 : Triangle type {8,17,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T56.79 : Triangle type {8,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^-2 * z * y^-1 * z * y^-4 * z * y^-7 * z ] T56.80 : Triangle type {8,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T56.81 : Triangle type {8,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T56.82 : Triangle type {9,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^7 * z^-1 * y^6 * z^-1 * y ] T56.83 : Triangle type {9,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^4 * z^-1 * y^9 ] T56.84 : Triangle type {9,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T56.85 : Triangle type {10,10,15} Group order 150 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-4 * x^-1 * z^2 * y^-1 * x^-1 * z^5 * y * z^-2 ] T56.86 : Triangle type {10,10,15} Group order 150 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-3 * x^-1 * z * y * z^-1 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * z^-4 ] T56.87 : Triangle type {10,10,15} Group order 150 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^10 * y * x * z^4 ] T56.88 : Triangle type {10,10,15} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y * x * z^-2, x^10 ] T56.89 : Triangle type {10,10,70} Group order 140 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^6 * y * x^-1 * z^7 ] T56.90 : Triangle type {10,10,70} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-3 * x^-1 * y^-1 * z^-1 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * z^-4 ] T56.91 : Triangle type {10,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y^6 * z^-3 ] T56.92 : Triangle type {15,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^7 * z^-5 * x * z^-3 ] T56.93 : Triangle type {15,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^4 * y^-4 * x^2 * y^-4 * x^5 ] T56.94 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^-1 * z * x^-1 * z^5 * x^-5 * z ] T56.95 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-8 ] T56.96 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-2 * z * x^-1 * z^5 * x^-5 * z ] T56.97 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^3 * y^-2, x^-2 * z^5 * x^-4 * z^2 ] T56.98 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x * y^-1 * x * y^-6 * x^7 ] T56.99 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-8 * z^2 * x^-4 ] T56.100 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^-8 * y^6 * x^-1 * y * x^-2 ] T56.101 : Triangle type {17,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-4 * z^2, x * y^-6 * x^4 * y^-1 ] T56.102 : Triangle type {18,18,63} Group order 126 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^3 * y^-1 * x * z^3 ] T56.103 : Triangle type {18,18,63} Group order 126 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x^-1 * z^3 * y * z^-3, z^-4 * y * x * z^-4 ] T56.104 : Triangle type {20,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^-1 * y * x^-7 * z * x^-1 ] T56.105 : Triangle type {20,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, z^-3 * x^2 * z^-3 ] T56.106 : Triangle type {24,30,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^2 * y^-1 * x^6 * y^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x ] T56.107 : Triangle type {24,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-3 * z^3, x^-2 * z * x^-4 * y^6 * x^-2 ] T56.108 : Triangle type {24,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^3 * y^-1 * x^6 * y^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x ] T56.109 : Triangle type {25,25,25} Group order 125 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * z^-1 * x, z^-1 * x^-1 * y^-1 * x * z * y, z * y^-2 * x * y^-2 ] T56.110 : Triangle type {25,25,25} Group order 125 Chiral action Defining relators: [ x * y * z, x^4 * y^-1 * z^-1, z^-1 * x^-1 * y^-1 * x * z * y, z * y^-2 * x * y^-2 ] T56.111 : Triangle type {25,25,25} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^-7 * x^5 * z^-3 ] T56.112 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^3 * z^-3 * y^10 ] T56.113 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-1 * y * x^-1 * y * x^-1 * y * z^-1 * y^9 * x^-1 * y * x^-1 * y * x^-1 * y ] T56.114 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * y^-2 * x^4 * z^-5 * x * z^-1 * x^2 ] T56.115 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-11 * x * y^-1 * x * y^-1 * x ] T56.116 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^8 * x^-2 * z^4 ] T56.117 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^4 * z^-3 * x^6 * z^-1 * x^3 ] T56.118 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-8 * x * y^-4 ] T56.119 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-5 * z * y^-3 * x^3 * y^-2 * z^2 * y^-1 * x * y^-2 ] T56.120 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-6, y^-2 * z^4 * y^-6 ] T56.121 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-3 * z^3, x^-2 * z^4 * x^-6 ] T56.122 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^6 * y^-2 * x^-1 * z^4 ] T56.123 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^10 * x^-2 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-10 * z * x^-1 * z ] T56.124 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-2 * z^4, y^-3 * z^3 * y^-2 * x * y^-4 ] T56.125 : Triangle type {29,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^15 * y^-1 * x^8 * z^-1 * x^5 ] T56.126 : Triangle type {30,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, (y^4 * z^-1 * y^3)^2 ] T56.127 : Triangle type {30,30,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-5 * x^2 * z^-4 * y * z^-2 ] T56.128 : Triangle type {30,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^-3 * z * x^-4 * y * x^-2 ] T56.129 : Triangle type {30,40,40} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, z * x^-3 * z^3 ] T56.130 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-21 * x^2 * y^-3 * z * y^-3 ] T56.131 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * z * y^-3 * x^5 * y^-1 ] T56.132 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^3 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^7 ] T56.133 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^-2 * z^3 * y^-7 ] T56.134 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * x * y^-4, x^-1 * z^4 * x^-6 ] T56.135 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^7 * z^-5 * x * z^-1 * x ] T56.136 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-3 * x * y^-4 * z ] T56.137 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-7, x^-2 * z^5 * x^-3 * z^3 ] T56.138 : Triangle type {57,114,114} Group order 114 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-57, y * z^-1 ] T56.139 : Triangle type {58,58,58} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-10 * z * y^-11 * x^3 * y^-6 ] T56.140 : Triangle type {58,58,58} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-3 * x * y^-1 * x * y^-9 * z * y^-1 * x * y^-3 ] T56.141 : Triangle type {58,58,58} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-2 * x * y^-6 * x^5 * y^-2 ] T56.142 : Triangle type {58,58,58} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x * y^-6 * x * y^-4 ] T56.143 : Triangle type {58,58,58} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-5 * z, x^-1 * z * x^-1 * z^5 * x^-6 ] T56.144 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x^-2 * y^-1, y^-51 * x * y^-5, x * z^-1 ] T56.145 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^24 * x^-4 * y^11 ] T56.146 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-10 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x^2 * y^-4 * x * y^-1 ] T56.147 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-5 * x * y^-1 ] T56.148 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-6 * y^5 * x^-1 * y * x^-1 * y * x^-3 ] T56.149 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-5 * x^2 * y^-4 ] T56.150 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-5 * x^4 * y^-2 ] T56.151 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-5 * x^2 * y^-4 ] T56.152 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^6, z^5 * x^-1 * z^4 ] T56.153 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^7, y^-1 * z * y^-1 * z * y^-1 * z * y^-7 ] T56.154 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^7 * x^-1 * z^4 ] T56.155 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x^11 * z^-1 * y * z^-3 ] T56.156 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-4 * z^3, x^2 * y^-5 * x^6 ] T56.157 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^9 * z^-5 * x^2 ] T56.158 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-12 * x * z^-10 ] T56.159 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 * x^2 * y^-4 ] T56.160 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^4 * x^-2 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T56.161 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, x^6 * y^3 * z^-3 * x * z^-1 ] T56.162 : Triangle type {113,113,113} Group order 113 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-1 * z^2 * x^-10 ] Genus 57 T57.1 : Triangle type {2,3,12} Group order 1344 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y * x * z * y * x * z * y * x * z * y * x * z * y * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 ] T57.2 : Triangle type {2,3,18} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^-1 * z^3 * y^-1 * z^-1 * x, y * x * z^7 * y * x * z * y^-1 * x * z^5 ] T57.3 : Triangle type {2,4,6} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^-1 * z * y * x * z^2 * y * x * y^-1 * z * y^-1 * z^-2 * x * z ] T57.4 : Triangle type {2,4,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * z * y^2 * z^-4 * y, x * z^4 * y * x * z * y * z^-2 * x * z * y * x * z^3 * y^-1 * z^-3 ] T57.5 : Triangle type {2,4,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z^4 * y * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-6 ] T57.6 : Triangle type {2,4,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-15 * x * z^8 * y * z^-8 ] T57.7 : Triangle type {2,4,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, x * z^2 * y * z^-5 * x * z * y^-1 * z^-6 ] T57.8 : Triangle type {2,4,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, z^6 * y * z^-2 * x * y * z^-2 * x * z * y^-1 * z^-2 * x ] T57.9 : Triangle type {2,4,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-2 * z^-4 * y, z^-2 * x * z^6 * y^-1 * x * z^4 * y^-1 * z^-2 ] T57.10 : Triangle type {2,4,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-44 * x * z^8 * y^-1 * z^-7 ] T57.11 : Triangle type {2,4,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-14 * x * z^8 * y * x * z^4 * y^-1 * z^-2 ] T57.12 : Triangle type {2,4,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-45 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T57.13 : Triangle type {2,4,116} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-116 ] T57.14 : Triangle type {2,4,228} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-16 * x * y^-1 * z^-97 ] T57.15 : Triangle type {2,5,8} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-3)^2, y * z^-1 * y * x * z * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T57.16 : Triangle type {2,6,6} Group order 672 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-3 * z^-2 * y^2, x * z * y * x * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T57.17 : Triangle type {2,6,6} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, y * z^-1 * x * z * y^-2 * z * y^-1 * z^-2 * y, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y ] T57.18 : Triangle type {2,6,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, z^10, z^-2 * x * z * y^-2 * z^-3 * y * z^-1 ] T57.19 : Triangle type {2,6,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-4)^2, z^10, z * y^-1 * z * y^-3 * z^-1 * x * z^2 * y^-1 ] T57.20 : Triangle type {2,6,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, y * z^-1 * x * z * y^-2 * z^5 ] T57.21 : Triangle type {2,6,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z, y * z^-4 * x * y^-1 * z^-5 ] T57.22 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * y^2 * z^-1 * y^3 * z^-2 * y^3 ] T57.23 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z ] T57.24 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * z^2 * y^-1 * z^-5 ] T57.25 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T57.26 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z * y^-1 * x * z^3 * y^-1 * z^-2 ] T57.27 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z^2 * y^-2 * z^2 * y^-1 * z^-1 ] T57.28 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T57.29 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T57.30 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-1 * x * y^-3 * z^-4, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T57.31 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-1 * x * y^-3 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T57.32 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z^-2 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T57.33 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z * y * z^-1 * x * y^-1 * z^-2 * x, y * x * y^-3 * z^-1 * y * z^-2 ] T57.34 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1 * y * z^-1 * y)^2 ] T57.35 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, y * x * y^-3 * z^-1 * y * z^-2, z^-4 * x * z^5 * y^-1 * z^-2 ] T57.36 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, x * z^4 * y * z^-1 * x * z^3 * y^-1 * z^-2 ] T57.37 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z^-2 * x * y^-1, z^2 * y * x * z^3 * y^-1 * x * z^3 * y^-1 * z^-1 * x ] T57.38 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, z^-4 * x * z * y^-1 * x * z^3 * y^-1 * z^-2 ] T57.39 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x ] T57.40 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T57.41 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-12 ] T57.42 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-12 ] T57.43 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^-12 ] T57.44 : Triangle type {2,8,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, z^-6 * x * y * z^-5 ] T57.45 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^22 * y * x * z * y * z^-1 * x * y^-1 * z^-3 * x * z^10 ] T57.46 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^30 * y * z^-7 * x * z^2 ] T57.47 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^3 * y * x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x ] T57.48 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T57.49 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, x * z * y * x * z * y * x * z^3 * y * z^-1 * x * z * y * z^-9 ] T57.50 : Triangle type {2,8,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, x * z^2 * y * z^-1 * x * z^3 * y * z^-3 * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T57.51 : Triangle type {2,8,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-8 * x * z * y * x * z^17 * y * x * y^-1 * z^-9 ] T57.52 : Triangle type {2,8,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-11 * x * z^16 * y * x * y^-1 * z^-9 ] T57.53 : Triangle type {2,10,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-1 * x * z, y^10, z * y^2 * z^-1 * y^2 * z^-2 * x * z ] T57.54 : Triangle type {2,10,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^10, (y * z^-1 * y^3)^2, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T57.55 : Triangle type {2,12,12} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, y^12 ] T57.56 : Triangle type {2,14,21} Group order 294 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-1 * y^11 * z^-1, x * z^9 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T57.57 : Triangle type {2,14,133} Group order 266 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^3 * y^-5 * z^3, z^9 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T57.58 : Triangle type {2,18,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-3 * z * y^-11 * z * y^-2 ] T57.59 : Triangle type {2,18,18} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-1 * y, y^-3 * z * y^-1 * z * y^-9 * z * y^-1 * z ] T57.60 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^-1 * z * y^-1 * z^3 * y^-5 * z^3 * y^-1 * z ] T57.61 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-1 * y^11 * z^-3 * y^15 * z^-2 ] T57.62 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^5 * y * z^-4 * x * z^2 * y^-1 * z^-3, y^-4 * z^3 * y^-4 * z^5 ] T57.63 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^-1 * z * y^-1 * z^3 * y^-5 * z^3 * y^-1 * z ] T57.64 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^2 * y^-1 * z^3 * y^-5 * z^5 ] T57.65 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-15 * z^3 * y^-10 * z^2 ] T57.66 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^-2 * z * y^-2 * z^2 * y^-5 * z * y^-1 * z^2 ] T57.67 : Triangle type {2,32,32} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^2 * z^-3 * y * z^-1 * y^6 * z^-2 * y ] T57.68 : Triangle type {2,40,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-9 * y^11 * z^-3 * y^16 ] T57.69 : Triangle type {2,40,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-8 * z^3 * y^-6 * z^3 ] T57.70 : Triangle type {2,60,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-27 * z^3 ] T57.71 : Triangle type {2,60,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-46 * y^11 * z^-1 ] T57.72 : Triangle type {2,60,60} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-31 * y^12 * z^-1 * y^16 ] T57.73 : Triangle type {2,115,230} Group order 230 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^103 * z^-12 ] T57.74 : Triangle type {2,116,116} Group order 232 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^12 * y^-103 ] T57.75 : Triangle type {2,228,228} Group order 228 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-102 ] T57.76 : Triangle type {3,3,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, x^-1 * z * y * x * y^-1 * x * z * y * x * z ] T57.77 : Triangle type {3,3,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z * x^-1 * z * x^-1 * z * y * x^-1 * y * x * z * x^-1 * z * y * x * y^-1 * x * z * y * x * y^-1 * x ] T57.78 : Triangle type {3,3,9} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x, x^-1 * z^2 * x^-1 * y^-1 * x * z * y^-1 * x * z ] T57.79 : Triangle type {3,4,4} Group order 672 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (y * z^-1)^4, x * z * y * z^-1 * y * x^-1 * y^-1 * z^-1 * y * z^-1 ] T57.80 : Triangle type {3,4,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-2 * x * z * y^-1 * z ] T57.81 : Triangle type {3,4,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^8, y * z^-3 * x^-1 * y * z^-3 ] T57.82 : Triangle type {3,4,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x * z^2 * y^-1 * x * z^2 * y, y * z^-1 * y * z^-1 * x^-1 * y^2 * z^-2 ] T57.83 : Triangle type {3,4,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x^-1 * z * y^-1 * z^-1 * x^-1 * z * y * z^-1, z^8 ] T57.84 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^8, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T57.85 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * z^-1 * x^-1 * z^2 * y, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x ] T57.86 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * y^-2 * x * z * y^-1 * z, (x * z^2 * y)^2 ] T57.87 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z^2 * y)^2 ] T57.88 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T57.89 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y * z^-1 * x * y^-1 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^-2 ] T57.90 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^8, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T57.91 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^8, y * z^-3 * x^-1 * y * z^-3 ] T57.92 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z * x^-1 * z * y * x^-1 * y^-1 * x * z^2 ] T57.93 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * x^-1 * z * y^-1 * x * z^2 * y, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T57.94 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z * y^-1 * z^-3 * x^-1 * y^-1 * x * z^3 * y^-1 * x ] T57.95 : Triangle type {3,4,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^8, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T57.96 : Triangle type {3,4,12} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 * x^2 * z * y * x * z * y * z^-1 ] T57.97 : Triangle type {3,6,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y * z^-2, y^2 * x * y^-1 * x * y^-1 * z^-2 ] T57.98 : Triangle type {3,6,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * z * y^-1 ] T57.99 : Triangle type {3,6,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-2 * x^-1 * z * y^-1 * z ] T57.100 : Triangle type {3,6,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * y * z^-2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T57.101 : Triangle type {3,6,6} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-2 * z^2 ] T57.102 : Triangle type {3,6,6} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, z^6, x^-1 * z * y^-2 * x * y^-1 * z^2, (x * z * y^2)^2 ] T57.103 : Triangle type {3,10,10} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, z^-1 * y^3 * x^-1 * y^-1 * z^-1 * y^2 ] T57.104 : Triangle type {3,10,10} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z^2, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1, y^2 * x * y^-1 * x * y^-2 * z ] T57.105 : Triangle type {3,10,30} Group order 210 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1, y^10 ] T57.106 : Triangle type {3,16,48} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * y^2 * z^-3 ] T57.107 : Triangle type {3,16,48} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z * y^-2 * z^2 * x^-1 * z * y^-1 * z * y^-4 * z * y^-1 * z^2 ] T57.108 : Triangle type {3,24,24} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T57.109 : Triangle type {3,58,174} Group order 174 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-47 * z * y^-8 * z^2 ] T57.110 : Triangle type {3,171,171} Group order 171 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-46 * z * y^-1 * z * y^-6 * z^2 ] T57.111 : Triangle type {4,4,6} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x * z * y^-1, (z^-1 * y)^3 ] T57.112 : Triangle type {4,4,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, z^4 * y^-1 * x^-1 * z^4 ] T57.113 : Triangle type {4,4,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z^9 ] T57.114 : Triangle type {4,4,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T57.115 : Triangle type {4,4,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y, y^-1 * z * y * z^-1 * x^-1 * z^2 * y^-1 * z ] T57.116 : Triangle type {4,4,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1, (y * z^-3)^2 ] T57.117 : Triangle type {4,4,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * z^-1 * y * x^-1 * z^2 * y * z^-1, y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^2 ] T57.118 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z * y^-1 * z^-2 * x^-1 * z^4 ] T57.119 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^4 * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z^5 ] T57.120 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T57.121 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z * y * x * z * y * x * z^4 ] T57.122 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^2 * y * x^-2 * z^3 * x^-1, z^-3 * x^-1 * y^-1 * x * z * y * z^-2 ] T57.123 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x * z * y * z^-3 * x^-1 * y * x^-1 * z^7 * y ] T57.124 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T57.125 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z * y^-1 * x * z^2 * y ] T57.126 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T57.127 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y ] T57.128 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-6 * x * z^8 * y * z^-1 ] T57.129 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^-1 * z^-2 * x^-1 * y * x^-1 * z^4 ] T57.130 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, y^-1 * z * y * z^-1 * x^-1 * y^-1 * z^3, z * y * z^-2 * x^-1 * z^4 ] T57.131 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x * z^5 * y^-1 * z^-1 * x * z * y * z^-4 ] T57.132 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-4 * x^-1 * z * y * z^-2 ] T57.133 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-2 * x^-1 * z^4 ] T57.134 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^2 * y * x^-2 * z^3 * x^-1, z^3 * y * x^-1 * z^4 ] T57.135 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^2 * y * x^-2 * z^3 * x^-1, z^-3 * x^-1 * y^-1 * x * z * y^-1 * z^-2 ] T57.136 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x * z * y * z^-3 * x^-1 * y * x^-1 * z^7 * y ] T57.137 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^3 * y * x^-1 * z^4 ] T57.138 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1, z^3 * y * x^-1 * z^4 ] T57.139 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, (x * z^-3)^2, z^3 * y * x^-1 * z^4 ] T57.140 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2, (x * z^-3)^2 ] T57.141 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, (x * z^-3)^2 ] T57.142 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T57.143 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T57.144 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, z^3 * y * x^-1 * z^4 ] T57.145 : Triangle type {4,4,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^3 * y * x^-1 * z^4 ] T57.146 : Triangle type {4,4,30} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1, z * y^-1 * z^-1 * x^2 * z^2 * y^-1 ] T57.147 : Triangle type {4,4,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-23 * x^-1 * y^-1 * x * z * y * z^-4 ] T57.148 : Triangle type {4,4,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^5 * y^-1 * z^-2 * x^-1 * y * z^-1 * x * z^2 * y * x^-1 * z^2 ] T57.149 : Triangle type {4,4,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z^4 * y * x^-1 * y * z^-1 * x^-1 * z^3 * y ] T57.150 : Triangle type {4,4,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-30 ] T57.151 : Triangle type {4,4,58} Group order 232 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * x^-1 * z^6 * y^-1 * z ] T57.152 : Triangle type {4,4,58} Group order 232 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-58 ] T57.153 : Triangle type {4,4,114} Group order 228 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-43 * x^-1 * z^4 * y * z^-9 ] T57.154 : Triangle type {4,5,5} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, y^2 * z^-1 * y * x^-1 * z * y^-1 * z^2 ] T57.155 : Triangle type {4,5,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, (y * z^-2)^2 ] T57.156 : Triangle type {4,5,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^-5, (x * z * y^-1)^2, (y * z^-2)^2 ] T57.157 : Triangle type {4,5,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^-5, (x * z * y)^2, x^-1 * y^2 * x^-1 * y * z^-2, y^-1 * z * y * x^-1 * y^-1 * z * x^-1 ] T57.158 : Triangle type {4,5,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^-1 * y * z^-2 ] T57.159 : Triangle type {4,5,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2 ] T57.160 : Triangle type {4,7,28} Group order 196 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-7 ] T57.161 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^5 * y^-1 * z^-2 * x^-1 * y * x^-1 * z^3 ] T57.162 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^6 * y * z^-1 * x^-1 * y * x^-1 * z^3 ] T57.163 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, (y * z^-1)^4 ] T57.164 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, (y * z^-1)^4 ] T57.165 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, (x * z * x^-1 * y^-1)^2 ] T57.166 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, (x * z * x^-1 * y^-1)^2, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T57.167 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T57.168 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, y * x * z^-1 * x^-1 * z * x^-1 * z ] T57.169 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, x^-1 * y * x^-2 * y^-2 * z, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-3 * x^-1 * z^2 * y^-1 ] T57.170 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z * y * z^-1 * x^-1 * z^3 ] T57.171 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T57.172 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, x^-1 * y * x^-2 * y^-2 * z, y^-1 * z * y * x^-1 * y^-1 * z^2, z * y * z^-1 * x^-1 * z^3 ] T57.173 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-3 * x^-1 * z * y * z^-1 ] T57.174 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z * y * x^-1 * y^-1 * x * z^3 ] T57.175 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T57.176 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-3 * x^-1 * z * y * z^-1 ] T57.177 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, (y * x^-1 * z^5)^2 ] T57.178 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, (y * x^-1 * z^5)^2 ] T57.179 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^4 * y * z^-1 * x * z^6 ] T57.180 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y * z^-5 * x^-1 * y^-1 * x * z^4 ] T57.181 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, y * x^-1 * y^-1 * z^-5 * x * z^5 ] T57.182 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, (y * x^-1 * z^5)^2 ] T57.183 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^2 * y * z^-1 * x^-1 * y^-1 * z^-2 * x^-1 * z * y * z^-1 * x * z^2 ] T57.184 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^-1 * x * z^2 * y * z^-4 * x * z^2 * y * z^-1 ] T57.185 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, (y * x^-1 * z^5)^2 ] T57.186 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, y * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z^5 ] T57.187 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * y^-1 * z^-4 ] T57.188 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * z^2 * y^-1 * z^-2 ] T57.189 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, x^-1 * z^6 * y * x^-1 * z * y^-1 * z^-3 ] T57.190 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * y^-1 * z^-4 ] T57.191 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, y * x^-1 * y^-1 * z^-5 * x * y * z^-1 * x * z^3 ] T57.192 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^7 * y^-1 * z^-5 * x^-1 * z^4 * y^-1 * z^-3 * x^-1 * z^3 ] T57.193 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x^-1 * z^6 * y * x^-1 * z^3 * y^-1 * z^-1 ] T57.194 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * z^3 * y * z^-1 ] T57.195 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^7 * y^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-7 * x ] T57.196 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * y * z^-4 * x * y * z^-1 * x * z^3 ] T57.197 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x^-1 * z^6 * y * x^-1 * y * z^-4 ] T57.198 : Triangle type {4,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-1 * x^-1 * z^5 * y * x^-1 * y^-1 * z^-4 ] T57.199 : Triangle type {4,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z * y, z^2 * y * x * z^-1 * x, (z^-1 * y)^3 ] T57.200 : Triangle type {4,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * z * y^-1, x^-1 * z * y * x^-1 * y * x * z, z^2 * x^-1 * y^-1 * x * z * y^-1 * z ] T57.201 : Triangle type {4,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * z * y^-1, y * x * y^-1 * x * z * y, y^-2 * z * y^-1 * z^3 * x^-1 * y^-2 * z * y^-1 * z ] T57.202 : Triangle type {4,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y^3 * x^-1 * y * z^-2 ] T57.203 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^3 * z^-2 ] T57.204 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, (z^-1 * y)^3 ] T57.205 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z^3 * y^-1 * z^2 * y^-3 * z * y^-1 ] T57.206 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T57.207 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y^-1 * z^2 ] T57.208 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-5 * z * y^-1 * z * y^-1 ] T57.209 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3 ] T57.210 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-2 * y * x^-1 * y * z^-1 * y ] T57.211 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-2 * y * x^-1 * y * z^-1 * y ] T57.212 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3 ] T57.213 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^4 * y^-2 * z * y^-2 * z^3 ] T57.214 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y * z^-2 ] T57.215 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^-1 * z^2 * y^-7 * z^2 ] T57.216 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, (y * z^-2)^2 ] T57.217 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * y^-2 * z, y^-1 * z * y^-3 * z * y^-4 * z^2 ] T57.218 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (y * z^-2)^2, y^-2 * z * x^-1 * y^-3 ] T57.219 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y * x^-1 * y * x^-1 * z * x^-1 * z ] T57.220 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-1 * y^-1 * x * z * y, (y * z^-1 * y)^2 ] T57.221 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y^3 * x^-1 * y^-2 * z ] T57.222 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, (z^2 * y^-2)^3 ] T57.223 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (z^-1 * y)^3, z^-3 * x^-1 * y * z^-2 ] T57.224 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, z^-3 * x^-1 * y * z^-2 ] T57.225 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y * z^-1 * y * x^-1 * y^2 * z^-1, z^-3 * x^-1 * y * z^-2 ] T57.226 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * y^2 * z^-1, z^-3 * x^-1 * y * z^-2 ] T57.227 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, (y^-1 * z^2)^4 ] T57.228 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y^-3 * z^2 * y^-1)^2 ] T57.229 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^-1 * z^2 * y^-1 * z^3 * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T57.230 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (y^-2 * z)^4 ] T57.231 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, (y^-2 * z^2 * y^-2)^2 ] T57.232 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z * x^-1 * y^-1 * x * y^-2 * z ] T57.233 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * y * z^-2 ] T57.234 : Triangle type {4,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1 ] T57.235 : Triangle type {4,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z * y^-1 * z^2 * y^-5 * z ] T57.236 : Triangle type {4,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * z * y^-1 * z ] T57.237 : Triangle type {4,39,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^16 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-2 ] T57.238 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^8 * z^-1 * y * z^-1 * y^5 * z^-1 ] T57.239 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^9 * z^-1 * y^3 * z^-1 * y^6 ] T57.240 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-12 * z * y^-1 * z^4 * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T57.241 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^12 * z^-3 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y^5 * z^-3 * y^2 * z^-1 ] T57.242 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-1 * y^14 ] T57.243 : Triangle type {4,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y^17 ] T57.244 : Triangle type {4,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z^3 * y^-1 * z * y^-2 * z * y^-1 * z^2 ] T57.245 : Triangle type {4,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^14 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T57.246 : Triangle type {4,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^17 * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T57.247 : Triangle type {5,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, y^6, z^6, x^-1 * y * x^-2 * y^-1 * z^-2, y^-1 * z^-1 * x^-2 * z * x^-1 * y^-1 ] T57.248 : Triangle type {5,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T57.249 : Triangle type {6,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z^2 * y * x^-1 * z^2 * x^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T57.250 : Triangle type {6,6,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x * z * x^-2 * z^2 * y ] T57.251 : Triangle type {6,8,8} Group order 192 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, z^-1 * x^-1 * y^-1 * x * z^-2 ] T57.252 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, (x^-1 * z * y)^2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T57.253 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, (z^-1 * y)^3, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x ] T57.254 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T57.255 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T57.256 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x^-1 * z * y)^2 ] T57.257 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T57.258 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * y^2 * x^-1 * z * x^-1, x^-1 * y * x^-2 * y^2 * z^-1 ] T57.259 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * y^2 * x^-1 * z * x^-1, y * x^-3 * z * x^-2, y^8 ] T57.260 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x^-1 * y^-1 * x * z * y, y^8 ] T57.261 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z^-1 * y, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z ] T57.262 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y * z^-1, x^6, y * x * y^-2 * x * y^-2 * z ] T57.263 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z * y^2 * x^-1 * z * y^-1 * z, y^8 ] T57.264 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (z^-1 * y)^3, y^8 ] T57.265 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, (z^-1 * y)^3, y^8 ] T57.266 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y^2 * x^-1 * z * y^-1 * z, y^8 ] T57.267 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (y * z^-2)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T57.268 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, (y * z^-1 * y)^2, y * x^-3 * z * x^-2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T57.269 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, z^-2 * y * x^-1 * y^2 * z^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T57.270 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (z^-1 * y)^3, y^2 * x^-1 * y^-1 * x * z * y^2 ] T57.271 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, y^3 * x^-1 * z^3 ] T57.272 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, y^8 ] T57.273 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T57.274 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, (y * z^-1 * y)^2, y^3 * x^-1 * z^3, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1 ] T57.275 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x * y^-2 * x * z * y^-1, y^3 * x^-1 * z^3 ] T57.276 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, y^8 ] T57.277 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T57.278 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x^-1 * z * y)^2 ] T57.279 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-2, x^6, x^-1 * y * x^-2 * z^3, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1 ] T57.280 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, (y * z^-2)^2, x^-1 * z * x^-2 * z * y * z^-1 ] T57.281 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z^8 ] T57.282 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^6, y^8, y^2 * z^-1 * y^2 * z^-3 ] T57.283 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^8 ] T57.284 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T57.285 : Triangle type {6,8,8} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T57.286 : Triangle type {6,8,24} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^2 * y * x^2 * z^3, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 ] T57.287 : Triangle type {6,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z * x^-1 * y^-1 * x * y^-1 * z ] T57.288 : Triangle type {6,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T57.289 : Triangle type {6,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, x * z^-1 * x^-2 * y * z^-2 ] T57.290 : Triangle type {6,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * x^-1 * z^3 ] T57.291 : Triangle type {6,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z^3 * y^-3 * z^2 * y^-1 * z^2 ] T57.292 : Triangle type {6,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z^2 * y^-1 * z * y^-4 * z * y^-1 ] T57.293 : Triangle type {6,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-13 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T57.294 : Triangle type {7,20,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 * y^8 * z^-1 ] T57.295 : Triangle type {7,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * z, (y^-1 * x)^3, x^-1 * z * y * x * y^-1 * z^-1 ] T57.296 : Triangle type {7,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * z * y^-1, z^-1 * y * x^2 * z^-1 * x ] T57.297 : Triangle type {7,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y * x, z^-1 * y^2 * x * z * y, x^-7 ] T57.298 : Triangle type {7,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, y * x^2 * z, z * x^-2 * y * x^-1, y^-1 * z * y^-6 * z * y^-1 * z * y^-4 * z^2 * y^-1 * z^2 * y^-1 ] T57.299 : Triangle type {7,21,21} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^9 ] T57.300 : Triangle type {7,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 * y ] T57.301 : Triangle type {7,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-6 ] T57.302 : Triangle type {7,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T57.303 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * y^-1 * z, x * y^-2 * x * z^-2, z * x^-3 * y^-3 ] T57.304 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^-1 * z * y^-1 * x * z^-1 * y, x^8 ] T57.305 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, y * x^-1 * y^-1 * x * z^-2, x^8 ] T57.306 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, y^-1 * z * y^-1 * x * z^-1 * x, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-3 * z * y * z^-1, z * x^-3 * y^-3 ] T57.307 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z * y^-1 * x^2 * z^3 ] T57.308 : Triangle type {8,8,20} Group order 160 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, y^-1 * z * y^-1 * x^2 * z^3 ] T57.309 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^13 * y * x * z^6 ] T57.310 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T57.311 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x * z^6 * y * z^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T57.312 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^3 * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T57.313 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^-1 * x * z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T57.314 : Triangle type {8,8,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^3 * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T57.315 : Triangle type {8,8,76} Group order 152 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-2 * x^-1 * z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * z * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T57.316 : Triangle type {8,8,76} Group order 152 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-2 * x * z^3 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T57.317 : Triangle type {9,12,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-2)^2, y * x^-3 * y^3 ] T57.318 : Triangle type {9,12,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^-1 * x^-1 * y^-1 * x * z * y, x^-9 ] T57.319 : Triangle type {9,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * y^-1 * z^-1, z^-1 * x * y^-1 * x * z^-1 * y, x * y^-2 * x * z * y^-1 ] T57.320 : Triangle type {9,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^-9 ] T57.321 : Triangle type {10,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y^2 * x * y^-2, z * y * x^-2 * y * x^-1 * z ] T57.322 : Triangle type {10,10,10} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * z * x^-1, z^-1 * y^2 * x * y^-2, (x * z * y)^2 ] T57.323 : Triangle type {16,32,32} Group order 128 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x^-1, z^-2 * x^2 * y^-2, z^-1 * y^4 * z^-3 ] T57.324 : Triangle type {16,32,32} Group order 128 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x^-1, z^-2 * x^2 * y^-2, z^-2 * y^3 * z^-2 * y ] T57.325 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^-3 * y * z^-1 * y ] T57.326 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x^2 * z^-3 * y * x^2 * z^-1 * x * z^-2 ] T57.327 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * y * x^-1 * z * x^-1 * z * x^-7 * z^2 * x^-1 * z * x^-1 ] T57.328 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1, x^-6 * z * x^-1 * y ] T57.329 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, y^-1 * x^5 * y^-1 * x * y^-2 ] T57.330 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z * x^-1 * y * x^-6 ] T57.331 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^6 * z^-4 ] T57.332 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-4 * z * x^-1 * z^2 * x^-6 * z * y * x^-1 * z * x^-1 ] T57.333 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * x^6 * y^-3 ] T57.334 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^6 * y^-4 ] T57.335 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, y^-2 * x^5 * y^-2 * x ] T57.336 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * x^5 * y^-2 * x * y^-1 ] T57.337 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-1 * x^2 * z^-3 * y * x^2 * z^-1 * x * z^-2 ] T57.338 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T57.339 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (x * y^-2)^2, z * x^-1 * z * x^-1 * y^-1 * z * x^-1 ] T57.340 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T57.341 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-4 * y * x^-1 * z^3 * x^-3 * y^4 * x^-1 * z * x^-1 * z * x^-1 ] T57.342 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^-7 * z * y ] T57.343 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, z^2 * x^-4 * z^6 ] T57.344 : Triangle type {16,32,32} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x^-7 * z * y ] T57.345 : Triangle type {18,21,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^8 * y^-5 * x * y^-1 * x * y^-1 * x^2 ] T57.346 : Triangle type {18,21,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-4 * y^2, z^-6 * x^5 * z^-1 ] T57.347 : Triangle type {20,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^8 * x^-2 * z^4 ] T57.348 : Triangle type {20,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-4 * z^2, x^-2 * z^5 * x^-5 * z ] T57.349 : Triangle type {20,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x * y^-6 * x^5 * y^-3 ] T57.350 : Triangle type {20,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * z^-1 * x^8 * y^-1 * x^5 ] T57.351 : Triangle type {24,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-8 * x^4 * y^-2 ] T57.352 : Triangle type {24,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-3 ] T57.353 : Triangle type {30,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-9 * x^4 * y^-1 * x * y^-1 * x * y^-2 * x^8 * y^-1 * x * y^-1 * x * y^-1 * x ] T57.354 : Triangle type {30,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-3 * z^3, y^-2 * z^4 * y^-2 * x * y^-4 ] T57.355 : Triangle type {30,40,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-5 * y^4 * z^-4 * y * z^-6 ] T57.356 : Triangle type {30,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * z * y^-1 * z^4 * y^-2 * x^3 * y^-4 ] T57.357 : Triangle type {30,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^16 * y^-1 * x^8 * z^-1 * x^5 ] T57.358 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^8 * z^-5 * x * z^-4 ] T57.359 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^6 * y^-2 * x^-1 * z^4 ] T57.360 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^11 * x^-1 * z^5 * x^-2 * z^4 * x^-1 * z ] T57.361 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-7, y^-2 * z^4 * y^-5 * z ] T57.362 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^8 * y^-2 * x * y^-1 * x * y^-1 * x * y^-6 * x * y^-4 * x * y^-1 * x * y^-1 * x ] T57.363 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-2 * z^4, x * y^-5 * x^4 * y^-1 ] T57.364 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^5 * x^-3 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y^3 ] T57.365 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 ] T57.366 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^24 * y^-1 * x^8 * z^-1 * x^6 ] T57.367 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-4 * z^4 * x^-5 * y * x^-1 ] T57.368 : Triangle type {39,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^9 * y^-2 * x^-1 * z^4 ] T57.369 : Triangle type {40,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^9 * y^-1 * z^-1 * x^3 * y^-1 ] T57.370 : Triangle type {40,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^5 * x^-2 * z^4 ] T57.371 : Triangle type {40,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^5 * y^-1 * z^-2 ] T57.372 : Triangle type {40,40,60} Group order 120 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^9 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T57.373 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^3 * z^-3 * y^3 * z^-4 * y^5 ] T57.374 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-29 * x^4 * y^-7 ] T57.375 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-2 * z * y^-1 * z^4 * y^-2 * z^4 ] T57.376 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^-6 * y^6 * x^-1 ] T57.377 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x^2 ] T57.378 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-4 * z^2, y^-6 * x * y^-4 ] T57.379 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x^-2 * z^4 ] T57.380 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-6, x^-1 * z * x^-1 * z^5 * x^-4 * z^2 ] T57.381 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-6, z * x^-1 * z^5 * x^-2 * z^4 ] T57.382 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-3 * x * y^-4, x^-2 * z^4 * x^-6 ] T57.383 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^12 * y^-1 * z^4 * y^-2 * x^-1 * z^5 ] T57.384 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x * z^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x ] T57.385 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z^2 ] T57.386 : Triangle type {58,116,116} Group order 116 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-58, y * z^-1 ] T57.387 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x^-2 * y^-1, y^-52 * x * y^-5, x * z^-1 ] T57.388 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-7 * x * y^-4 ] T57.389 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-2 * z * x^-1 * z^5 * x^-2 * z^4 ] T57.390 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-30 * x^2 * y^-7 ] T57.391 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-3 * z^2 * x^-7 * y * x^-1 ] T57.392 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-3 * z^3, x^-6 * y^7 ] T57.393 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * z, z * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T57.394 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^10 * y^-2 * x * y^-1 * x * y^-1 * x * y^-6 * x * y^-4 * x * y^-1 * x * y^-1 * x ] T57.395 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z, y^-4 * z * y^-1 * z^4 * y^-2 * x * y^-5 ] T57.396 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^3 * y^-1 * x^13 ] T57.397 : Triangle type {115,115,115} Group order 115 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-2 * z^4, x^2 * y^-5 * x^2 * z^-3 * x^2 ] Genus 58 T58.1 : Triangle type {2,3,12} Group order 1368 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, z * y * x * z^3 * y * x * z * y^2 * x * y^-1 * z^-1 * x * z^2, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z ] T58.2 : Triangle type {2,4,42} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y^-1 * z)^6, z^-2 * x * z * y * z^-8 * x * y^-1 * z^-1 ] T58.3 : Triangle type {2,4,118} Group order 472 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-118 ] T58.4 : Triangle type {2,4,232} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-17 * x * y^-1 * z^-98 ] T58.5 : Triangle type {2,6,6} Group order 684 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^2 * y * z^-1 * y * z^-1 * x * y^-1 * z^2 * y^-1 * z^-2 * x ] T58.6 : Triangle type {2,6,6} Group order 684 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, y * x * z * y^-1 * z^2 * y^-1 * z^3 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * x * z ] T58.7 : Triangle type {2,6,12} Group order 456 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z^2 * y * z^-1 * y * z^-2 * x * z^2 * y^-2 * z^-1 * x ] T58.8 : Triangle type {2,6,12} Group order 456 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, y^-1 * z * y^2 * z^-1 * y^2 * x * y^-2 * z * y^-1 * z^-1 * x ] T58.9 : Triangle type {2,6,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-30 * x * z^16 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-3 ] T58.10 : Triangle type {2,6,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-41 * x * z * y * x * z^5 * y * x * y^-1 * z^-10 ] T58.11 : Triangle type {2,6,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-8 * x * z^3 * y * z^-2 * x * y * x * y^-1 * z^-4 ] T58.12 : Triangle type {2,6,174} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^27 * y * x * z^17 * y * z^-1 * x * y * z^-7 * x * z^3 ] T58.13 : Triangle type {2,9,18} Group order 342 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, y^-9, y^-1 * z * y^-3 * z^3 * y^-1 ] T58.14 : Triangle type {2,9,18} Group order 342 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^-9, y^-2 * z * y^-2 * z * y^-1 * z^2 ] T58.15 : Triangle type {2,9,18} Group order 342 Chiral action Defining relators: [ x^2, x * y * z, y^-9, z^-1 * y * x * y^-2 * z * y^-1 * z^-1 * y ] T58.16 : Triangle type {2,9,18} Group order 342 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, z^2 * y * x * z * y * x * y * x * z * y^-1 * z^-2 * x ] T58.17 : Triangle type {2,10,145} Group order 290 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-3 * x * z^17 * y * z^-8 ] T58.18 : Triangle type {2,12,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^-1 * z^3 * y * x * y^-1 * z^-1 * x * z^2 * y^-1 ] T58.19 : Triangle type {2,12,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-8 * x * y^-1 * z^-6 * x * z * y^-1 * z^-7 ] T58.20 : Triangle type {2,12,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-6 * x * z^5 * y * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T58.21 : Triangle type {2,18,45} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * z^-1 * x * z^3 * y^-1 * z^-1 * x ] T58.22 : Triangle type {2,42,42} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^2 * z^-3 * y^4 * z^-1 * y^2 * z^-2 ] T58.23 : Triangle type {2,42,42} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-10 * y^11 * z^-3 * y^16 ] T58.24 : Triangle type {2,60,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-1 * y^8 * z^-3 * y^17 ] T58.25 : Triangle type {2,117,234} Group order 234 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^104 * z^-12 * y ] T58.26 : Triangle type {2,118,118} Group order 236 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-103 * z ] T58.27 : Triangle type {2,232,232} Group order 232 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^12 * y^-102 * z ] T58.28 : Triangle type {3,3,6} Group order 684 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z * y^-1 * x * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z * y * x^-1 * y^-1 * z^-1 * x ] T58.29 : Triangle type {3,6,6} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, z^-1 * y * x^-1 * y * x^-1 * y * x * z * y ] T58.30 : Triangle type {3,6,6} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^2 * x^-1 * y^3 * z^-1 * y * z^-1 ] T58.31 : Triangle type {3,6,6} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * y)^3, x * y^-1 * z * y^2 * x^-1 * y * x^-1 * y^-2 * z * y^2 ] T58.32 : Triangle type {3,6,6} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, z * y^-1 * z * y^2 * x * y^-2 * z * y^-1 * z ] T58.33 : Triangle type {3,6,6} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^2 * z * y * x * z * y * z^-1 ] T58.34 : Triangle type {3,6,21} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, x^-1 * z * y^2 * x^-1 * z * y^-1 * z^-1 ] T58.35 : Triangle type {3,6,78} Group order 234 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * y * x^-1 * z * y * z^-2 ] T58.36 : Triangle type {3,9,36} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y^2 * z^-2, x^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T58.37 : Triangle type {3,9,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-9 ] T58.38 : Triangle type {3,12,12} Group order 228 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 * y * z^-1 ] T58.39 : Triangle type {3,12,12} Group order 228 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, x^-1 * z * y^-1 * z * y^3 * z^-2 * y^2 ] T58.40 : Triangle type {3,15,65} Group order 195 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * x * y^-1 * z ] T58.41 : Triangle type {3,59,177} Group order 177 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-48 * z * y^-8 * z^2 ] T58.42 : Triangle type {3,60,60} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^47 * y^-10 * z * y^-1 ] T58.43 : Triangle type {3,60,60} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-6 * y^8 * z^-2 * y^2 * z^-2 ] T58.44 : Triangle type {3,60,60} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-49 * z * y^-8 * z^2 ] T58.45 : Triangle type {3,174,174} Group order 174 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-47 * z * y^-9 * z ] T58.46 : Triangle type {4,4,21} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * z * y * x^-1 * z^4 ] T58.47 : Triangle type {4,4,59} Group order 236 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-47 * x * y * z^-11 ] T58.48 : Triangle type {4,4,116} Group order 232 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-44 * x^-1 * z^4 * y * z^-9 ] T58.49 : Triangle type {4,6,12} Group order 228 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z * y * z^-1 * x * z^2 * y * x^-1 * y^-1 * z^-2 * x * z ] T58.50 : Triangle type {4,6,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, x^-1 * z^2 * y * x * z * y * z^-1 ] T58.51 : Triangle type {4,6,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^9 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x * z ] T58.52 : Triangle type {4,6,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z * y * x * z^4 * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z^8 ] T58.53 : Triangle type {4,12,30} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x * y^-1 * x * z^2 * y * z^-7 ] T58.54 : Triangle type {4,15,20} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-1 * x ] T58.55 : Triangle type {4,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^7 * z^-2 ] T58.56 : Triangle type {4,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^16 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y^3 ] T58.57 : Triangle type {5,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^10 * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T58.58 : Triangle type {5,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^5 * z^-4 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T58.59 : Triangle type {6,6,6} Group order 228 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, x * z * y * x^-2 * z * y^-1 * z * y ] T58.60 : Triangle type {6,6,6} Group order 228 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, y^2 * z^-2 * y * x * z * y * z^-1 * y * z^-1 ] T58.61 : Triangle type {6,6,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^4 * y * z^-1 * x * z^4 ] T58.62 : Triangle type {6,6,30} Group order 180 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z^4 * y * z^-1 * x * z^4 ] T58.63 : Triangle type {6,6,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T58.64 : Triangle type {6,6,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-17 * x * z * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T58.65 : Triangle type {6,6,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^16 * y^-1 * x * y * z^-5 * x^-1 * z^7 ] T58.66 : Triangle type {6,6,87} Group order 174 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-9 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-6 * x * z * y * z^-4 * x^-1 * z * y * z^-1 ] T58.67 : Triangle type {6,12,14} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z^-1 * y, x * z^-1 * y * x^-1 * y^-1 * z^-1, x^-1 * y * x^-2 * y * z^-1 * y ] T58.68 : Triangle type {6,12,14} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z * y, (x * y^-2)^2, z * y^2 * x * z^-1 * x ] T58.69 : Triangle type {6,12,14} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^-4 * x^-1 * z * y * x^-1 * z * y * z^-3 * x^-1 * y * z^-2 ] T58.70 : Triangle type {6,12,52} Group order 156 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z^2, z^-1 * x * y^-1 * x * z^-2 ] T58.71 : Triangle type {6,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^2 * x^-1 * y * z^-2 ] T58.72 : Triangle type {6,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^2 * z^-2 ] T58.73 : Triangle type {6,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-3 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T58.74 : Triangle type {6,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^4 * x^-1 * y * z^-1 * y * z^-1 ] T58.75 : Triangle type {6,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y^8 * z^-1 * y^4 * z^-1 * y * z^-1 * y * z^-4 ] T58.76 : Triangle type {8,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^9 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T58.77 : Triangle type {8,34,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T58.78 : Triangle type {9,9,9} Group order 171 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, (y^-1 * x)^3 ] T58.79 : Triangle type {9,9,9} Group order 171 Chiral action Defining relators: [ x * y * z, x * z^-1 * x^2 * z^-2, (y^-1 * x)^3, (z^-1 * y)^3, z^-1 * x^-3 * y^2 * z^-1 ] T58.80 : Triangle type {9,9,9} Group order 171 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, y * x * z * y * x * z^-1 * x * z ] T58.81 : Triangle type {9,9,9} Group order 171 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * y^-2, y * z^-1 * x^2 * y^-1 * z^-1, (y^-1 * x)^3 ] T58.82 : Triangle type {9,45,45} Group order 135 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^-2 * z * y^-1 * z * y^-3 * z * y^-3 * z^3 ] T58.83 : Triangle type {9,45,45} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T58.84 : Triangle type {10,14,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-6 * y^4 * z^-4 ] T58.85 : Triangle type {10,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y^7 * z^-2 ] T58.86 : Triangle type {10,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y^9 ] T58.87 : Triangle type {10,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y^5 * z^-4 ] T58.88 : Triangle type {12,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x * y^-1 * x^3 * y^-1 * z^-2 ] T58.89 : Triangle type {12,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^-1 * y^-1 * x^3 * z * y * z^-1 ] T58.90 : Triangle type {12,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^3 * x^-1 * y^-1 * z * y ] T58.91 : Triangle type {12,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-2 * x^-1 * y^-1 * z^-4 * x^-1 * y * z^-4 ] T58.92 : Triangle type {12,12,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, y * x^-1 * z * y * z^-4 * x^-1 * y * x^-1 * z^4 ] T58.93 : Triangle type {12,16,16} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^-1 * y, x^-1 * z * y^-1 * x * z^2 ] T58.94 : Triangle type {12,22,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^5 * z^-4, x^-4 * y^4 * x^-2 * z^4 * x^-2 ] T58.95 : Triangle type {12,33,44} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^3 * z^-4, x^-2 * y * x^-1 * y^5 * x^-1 * y^5 ] T58.96 : Triangle type {14,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-2 * y^5 * x^-2 * y^4 ] T58.97 : Triangle type {14,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, y^2 * x^-1 * y * x^-1 * y^5 * x^-6 * y ] T58.98 : Triangle type {14,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-1 * y^5, z^-1 * x * z^-4 * x^2 * z^-4 ] T58.99 : Triangle type {14,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-2 * y * x^-1 * y^5 * x^-3 * y^3 ] T58.100 : Triangle type {14,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-5 * y^4 * x^-2 * z^4 * x^-3 ] T58.101 : Triangle type {18,42,63} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x * z^-1 * x * z^-4 * x^6 * z^-2 ] T58.102 : Triangle type {18,42,63} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^2 * z^-1 * x * z^-1 * x * y^-3 * x^7 * z^-1 * x^4 ] T58.103 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, z * x^-6 * z^5 ] T58.104 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T58.105 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-8 * y * x^-8 * z * x^-4 ] T58.106 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z * y^-1 * z * x^-1 * y^-1 * z^2, x^5 * y^-1 * x * z^-1 ] T58.107 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1 ] T58.108 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^5 * y^-1 * x * z^-1 ] T58.109 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-4 * y^-1 * x * z, x * y^-2 * z * y^-1 * x * y^-6 ] T58.110 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, z^2 * x^-3 * z^4 ] T58.111 : Triangle type {21,42,42} Group order 126 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^8 * z^-2 * x^8 * z^-1 * x * y^-1 * x^2 ] T58.112 : Triangle type {30,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-2 * x^-1 * z^4, x * y^-4 * x^6 ] T58.113 : Triangle type {30,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^4 * y^-4 * x^9 ] T58.114 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-5 * z, x * y^-5 * x * y^-4 ] T58.115 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^35 * y^-1 * x * y^-1 * x * y^-1 * x ] T58.116 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 ] T58.117 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-15 * z^2 * y^-4 ] T58.118 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^15 * y^-1 * x * y^-1 * x * y^-1 * x ] T58.119 : Triangle type {40,60,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-4 * z^4 * x^-5 * y * x^-1 ] T58.120 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-19 * z * y^-10 ] T58.121 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-31 * x^2 * y^-7 ] T58.122 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-2 * y * x^-5 * y^6 * x^-1 * y * x^-1 ] T58.123 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-11 * x * y^-1 * x * y^-1 * x ] T58.124 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-2 * z^4, x * y^-4 * x^6 ] T58.125 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 ] T58.126 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-6, x^-3 * z^4 * x^-6 ] T58.127 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-6 * x^6 ] T58.128 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-1 * z^4, x * y^-5 * x^2 * y^-3 ] T58.129 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-3 * x * y^-4, x^-2 * z^2 * x^-8 ] T58.130 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-4 * z^2, y * x^-5 * y^7 ] T58.131 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^-3 * z^2 * y^-3 * x * y^-4 ] T58.132 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^4 * z^-3 * x^7 * y^-1 * x^2 ] T58.133 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-5 * z, x^3 * y^-5 * x^2 * z^-3 * x^3 ] T58.134 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-2 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 ] T58.135 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^4 * z^-2 * y^12 ] T58.136 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z * x^-1 * z^5 * x^-2 * z^4 ] T58.137 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x^2 * y^-5 ] T58.138 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-2 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T58.139 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-1 * x * z^-1 * x^10 * y^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T58.140 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-5 * z * y^-1 ] T58.141 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-5 * z, x^2 * y^-5 * x^2 * z^-3 * x^2 ] T58.142 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^5 * y^-1 * z^12 * y^-1 * x^-1 * z^5 ] T58.143 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^9 * z^-2 * x * z^-1 * x^10 * z^-1 * x * z^-1 * x * z^-1 * x^3 ] T58.144 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^9 * x^-6 * z ] T58.145 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-2 * x * y^-4, x^-2 * z^5 * x^-5 * z ] T58.146 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^9 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T58.147 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-3 * z * y^-1 * z^4 * y^-2 * x^3 * y^-3 ] T58.148 : Triangle type {59,118,118} Group order 118 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-59, y * z^-1 ] T58.149 : Triangle type {60,60,60} Group order 120 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-1 * x * y^-2 * z * y^-1 ] T58.150 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x^-2 * y^-1, y^-52 * x * y^-6, x * z^-1 ] T58.151 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-9 * z * y^-3 * x^2 * y^-6 ] T58.152 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x * z^-1 * x^16 * z^-1 * x * z^-1 * x^3 ] T58.153 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y^4 * x^-2 * y^2 * z^-4 * y * z^-1 * y^3 ] T58.154 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * y^-2 * x^-1 * z^4, x * y^-4 * x^6 ] T58.155 : Triangle type {117,117,117} Group order 117 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-9 * z * x^-4 ] Genus 59 T59.1 : Triangle type {2,4,8} Group order 928 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x * z * y^-2 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^2 ] T59.2 : Triangle type {2,4,8} Group order 928 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x * z * y^-2 * z * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 ] T59.3 : Triangle type {2,4,12} Group order 696 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T59.4 : Triangle type {2,4,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-120 ] T59.5 : Triangle type {2,4,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-45 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T59.6 : Triangle type {2,4,236} Group order 472 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-18 * x * y^-1 * z^-99 ] T59.7 : Triangle type {2,6,177} Group order 354 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^47 * y * x * y^-1 * z^-9 * x * z ] T59.8 : Triangle type {2,7,14} Group order 406 Chiral action Defining relators: [ x^2, x * y * z, y^-7, x * z * y^-2 * z^-1 * y * z^-1 ] T59.9 : Triangle type {2,7,14} Group order 406 Chiral action Defining relators: [ x^2, x * y * z, y^-7, x * z^2 * y^-2 * z^-1 * y * z^-2, y * x * z * y^3 * z^-4 ] T59.10 : Triangle type {2,7,14} Group order 406 Chiral action Defining relators: [ x^2, x * y * z, y^-7, z * y * z^-1 * y^3 * z^-1 * y^2 * x ] T59.11 : Triangle type {2,8,8} Group order 464 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T59.12 : Triangle type {2,8,8} Group order 464 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T59.13 : Triangle type {2,8,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^22 * y * x * z * y * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-3 * x * z^5 ] T59.14 : Triangle type {2,8,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^11 * y * x * z^17 * y * x * y * z^-7 * x * z^2 ] T59.15 : Triangle type {2,12,12} Group order 348 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-2 * y ] T59.16 : Triangle type {2,20,28} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x ] T59.17 : Triangle type {2,119,238} Group order 238 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^105 * z^-14 ] T59.18 : Triangle type {2,120,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^2 * z^-29 * y^12 * z^-1 * y^16 ] T59.19 : Triangle type {2,120,120} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^14 * y^-105 ] T59.20 : Triangle type {2,236,236} Group order 236 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-104 ] T59.21 : Triangle type {3,4,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y * z^-1, x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z * y * z^-3 ] T59.22 : Triangle type {3,4,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-2)^2, (x * z * y^-1 * z^-1)^2, y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T59.23 : Triangle type {3,4,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y^-1 ] T59.24 : Triangle type {3,177,177} Group order 177 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-48 * z * y^-10 ] T59.25 : Triangle type {4,4,4} Group order 464 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T59.26 : Triangle type {4,4,4} Group order 464 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T59.27 : Triangle type {4,4,6} Group order 348 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^2 * x * z * x^-1 ] T59.28 : Triangle type {4,4,60} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * y * x^-1 * y^-1 * x * z^3 ] T59.29 : Triangle type {4,4,60} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^10 * y * x^-1 * y * x^-1 ] T59.30 : Triangle type {4,4,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^47 * y * x^-1 * y * x^-1 * z^11 ] T59.31 : Triangle type {4,4,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-19 * x^-1 * z^3 * y * z^-1 * x * z * y^-1 * z^-4 ] T59.32 : Triangle type {4,4,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-19 * x^-1 * z^3 * y * z^-7 ] T59.33 : Triangle type {4,4,118} Group order 236 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-47 * x * y^-1 * z^-11 ] T59.34 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z^10 ] T59.35 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3 ] T59.36 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z * y^2 * x^-1 * z^3 ] T59.37 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * z^3 ] T59.38 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z^3 * y * x^-1 * z^2 * y^-1 * z^-1 ] T59.39 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T59.40 : Triangle type {4,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, (y * z^-1 * y)^2, (y * z^-3)^2 ] T59.41 : Triangle type {4,8,8} Group order 232 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T59.42 : Triangle type {4,8,8} Group order 232 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z * y ] T59.43 : Triangle type {4,8,48} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^2 * y^-1 * z^-3 * x^-1 * z^6 ] T59.44 : Triangle type {4,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^7 * y^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-7 * x^-1 ] T59.45 : Triangle type {4,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^7 * y^-1 * z^-5 * x^-1 * z^4 * y^-1 * z^-3 * x * z^3 ] T59.46 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^3 * y * x^-1 * y^-1 * z^-1 * x * z * y ] T59.47 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^4 * x * z^-1 * x * z^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T59.48 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y * z^-1 * x^-1 * z^4, y * x * z * y * x^-1 * z * x * y^-1 * z^-1 * x * z * y^5 ] T59.49 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, y^-2 * z^-1 * x^-1 * z * y^2 * x * y^-3 * z^-1 * x^-1 * y^-2 ] T59.50 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^3 * y * x^-1 * z^6 * y * x^-1 * z^5 ] T59.51 : Triangle type {4,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^3 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T59.52 : Triangle type {4,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z * y^-1 * z^2 * y^-2 * z * y^-1 * z^2 ] T59.53 : Triangle type {4,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^12 * z^-3 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y^5 * z^-3 * y * z^-1 * y ] T59.54 : Triangle type {4,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-12 * z * y^-1 * z^4 * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T59.55 : Triangle type {5,15,33} Group order 165 Chiral action Defining relators: [ x * y * z, x^-5, z * y^-1 * x^2 * y^-1 * x ] T59.56 : Triangle type {5,15,33} Group order 165 Chiral action Defining relators: [ x * y * z, z^-1 * y * x * z^-1, x^-5 ] T59.57 : Triangle type {6,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-4 ] T59.58 : Triangle type {6,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z^2 * y^-1 * z * y^-5 * z ] T59.59 : Triangle type {7,7,7} Group order 203 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * x, y^-3 * x * z * x^-1, z^-1 * y^2 * x^-1 * z * y ] T59.60 : Triangle type {7,7,7} Group order 203 Chiral action Defining relators: [ x * y * z, x^-7, z^-1 * y * x^-2 * z * x^-1 * y, y * z^-1 * x^-2 * y^-2 * z, x^-1 * z * x^-2 * y * x^-1 * y ] T59.61 : Triangle type {7,7,7} Group order 203 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z^-1, x^-7, y * x^-3 * z * x^-1 * y ] T59.62 : Triangle type {7,7,7} Group order 203 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * y^-2, z^-1 * x^-1 * y^-1 * x * y^-1 * x, x^-7 ] T59.63 : Triangle type {8,8,40} Group order 160 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1 ] T59.64 : Triangle type {8,8,40} Group order 160 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, (x * z * y^-1)^2 ] T59.65 : Triangle type {8,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^5 * y * x * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^2 ] T59.66 : Triangle type {8,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^13 * y * x^-1 * y * x^-1 * z^5 ] T59.67 : Triangle type {8,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^5 * y * x^-1 * z^4 ] T59.68 : Triangle type {8,8,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^-1 * x * z^4 * y * x * z^2 * y^-1 * z^-1 ] T59.69 : Triangle type {8,10,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^10 ] T59.70 : Triangle type {8,10,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^10 ] T59.71 : Triangle type {8,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z ] T59.72 : Triangle type {8,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^9 * y^-1 * z * y^-4 * z^2 ] T59.73 : Triangle type {8,68,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 ] T59.74 : Triangle type {8,68,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 ] T59.75 : Triangle type {10,28,28} Group order 140 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 * y ] T59.76 : Triangle type {12,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^2 * y * x^-1 * z * y^-1 ] T59.77 : Triangle type {12,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, z^-2 * y * x^-1 * y * z^-1 * y ] T59.78 : Triangle type {12,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^-1 * x^3 * y^-1 * z^-1 * x ] T59.79 : Triangle type {12,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-1 * y ] T59.80 : Triangle type {12,33,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^6 * z^-3, x^-4 * y^4 * x^-2 * z^4 * x^-2 ] T59.81 : Triangle type {12,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^2 * z^-4, x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T59.82 : Triangle type {14,20,20} Group order 140 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x * z^-1 * y * z^-1 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 * y ] T59.83 : Triangle type {16,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-6 * y ] T59.84 : Triangle type {16,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, x^-7 * z * y ] T59.85 : Triangle type {16,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3, x^-7 * z * y ] T59.86 : Triangle type {16,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^2 * x^-6 * z^6 ] T59.87 : Triangle type {18,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-3 * y^3, z * x^-7 * z^6 ] T59.88 : Triangle type {18,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^3 * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T59.89 : Triangle type {18,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-7 ] T59.90 : Triangle type {60,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-4 * z^2, x^3 * y^-5 * x^2 * z^-3 * x^3 ] T59.91 : Triangle type {60,120,120} Group order 120 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-60, y * z^-1 ] T59.92 : Triangle type {60,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^8 * y^-2 * x^-1 * z^4 ] T59.93 : Triangle type {60,120,120} Group order 120 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^16 * y^-1 * x^8 * y^-1 * x^5 ] T59.94 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x^-2 * y^-1, y^-53 * x * y^-6, x * z^-1 ] T59.95 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * y^-1, y^-1 * z * y^-1 * z^4 * y^-2 * z^4 ] T59.96 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^-1 * z * x^-1 * z^5 * x^-5 * z ] T59.97 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-2 * z^4, y * x^-5 * y^7 ] T59.98 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-30 * x^4 * y^-7 ] T59.99 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^3 * y^-4 * x^8 ] T59.100 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * z^-1, z^2 * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T59.101 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, z^-1 * x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x^3 ] T59.102 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * y * z^-5 * y^2 * z^-12 ] T59.103 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-10 * y^3 * x^-3 ] T59.104 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^10 * y^-2 * x * y^-1 * x * y^-1 * x * y^-6 * x * y^-4 * x * y^-1 * x * y^-1 * x ] T59.105 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x * z^-2 * x^16 * z^-1 * x * z^-1 * x * z^-2 ] T59.106 : Triangle type {119,119,119} Group order 119 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-2 * x^-1 * z^4, x^-10 * y ] Genus 60 T60.1 : Triangle type {2,4,63} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-47 * x * z^8 * y^-1 * z^-7 ] T60.2 : Triangle type {2,4,122} Group order 488 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-122 ] T60.3 : Triangle type {2,4,240} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-19 * x * y^-1 * z^-100 ] T60.4 : Triangle type {2,6,62} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-32 * x * z^19 * y * z^-1 * x * y^-1 * z^-8 ] T60.5 : Triangle type {2,8,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^9 * y^-1 * z^-2 * x * y^-1 * z^-7 ] T60.6 : Triangle type {2,8,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^26 * y * x * z^5 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^3 ] T60.7 : Triangle type {2,10,32} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^14 * y * x * z * y * z^-1 * x * y^-1 * z^-3 * x * z^10 ] T60.8 : Triangle type {2,12,26} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^8 * y * x * z * y^-1 * z^-5 * x * z^10 ] T60.9 : Triangle type {2,14,22} Group order 308 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^6 * y * x * z * y^-1 * z^-5 * x * z^8 ] T60.10 : Triangle type {2,14,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^3 * y^-5 * z^3, z^-1 * x * z^3 * y * z^-2 * x * z^5 * y * z^-1 * x * z * y^-1 * z^-4 ] T60.11 : Triangle type {2,16,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^16, z^-2 * x * z^6 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-1 ] T60.12 : Triangle type {2,22,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-10 * z^3 * y^-5 * z^3 * y^-1 ] T60.13 : Triangle type {2,26,130} Group order 260 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-14 * z^3 * y^-5 * z^3 * y^-1 ] T60.14 : Triangle type {2,33,44} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^-1 * z * y^-4 * z * y^-1 * z * y^-1 * z ] T60.15 : Triangle type {2,62,124} Group order 248 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-32 * y^12 * z^-1 * y^15 * z^-1 ] T60.16 : Triangle type {2,63,63} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-49 * y^11 * z^-1 ] T60.17 : Triangle type {2,82,123} Group order 246 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-11 * y^11 * z^-3 * y^15 * z^-1 ] T60.18 : Triangle type {2,121,242} Group order 242 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^106 * z^-14 * y ] T60.19 : Triangle type {2,122,122} Group order 244 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-105 * z ] T60.20 : Triangle type {2,240,240} Group order 240 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^14 * y^-104 * z ] T60.21 : Triangle type {3,3,62} Group order 372 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-6 * x^-1 * y^-1 * x * z^3 * y * z^-2 ] T60.22 : Triangle type {3,61,183} Group order 183 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-50 * z * y^-8 * z^2 ] T60.23 : Triangle type {3,62,62} Group order 186 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^49 * y^-10 * z * y^-1 ] T60.24 : Triangle type {3,180,180} Group order 180 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-49 * z * y^-9 * z ] T60.25 : Triangle type {4,4,61} Group order 244 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z^5 * y^-1 * z^-1 ] T60.26 : Triangle type {4,4,61} Group order 244 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^48 * y * x^-1 * y * x^-1 * z^11 ] T60.27 : Triangle type {4,4,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^47 * y * x^-1 * z^12 ] T60.28 : Triangle type {4,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-5 * z * y^-7 * z ] T60.29 : Triangle type {4,41,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-13 * z * y^-1 * z^4 * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T60.30 : Triangle type {4,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^6 * z^-3 * y^2 * z^-1 * y^8 * z^-1 ] T60.31 : Triangle type {4,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-11 * z^3 * y^-1 * z * y^-2 * z^3 * y^-5 * z * y^-1 * z * y^-11 ] T60.32 : Triangle type {4,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-12 * z * y^-1 * z^4 * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T60.33 : Triangle type {5,5,41} Group order 205 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2, z^-1 * x^-1 * y * x^-1 * z * x^-1 * y ] T60.34 : Triangle type {5,5,41} Group order 205 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z^-1 * y, y^-5, x * z^-1 * y * x^-1 * y^-1 * z^-1 ] T60.35 : Triangle type {5,31,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T60.36 : Triangle type {5,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, z^18 * y^-1 * z * y^-2 * z * y^-6 * z * y^-1 * z ] T60.37 : Triangle type {5,32,32} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y * z^-4 * y^3 * z^-1 * y^9 * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 * y^3 ] T60.38 : Triangle type {5,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^6 * z^-4 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T60.39 : Triangle type {5,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T60.40 : Triangle type {6,6,31} Group order 186 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z * y^-1 * z * x^-1 * z^3 ] T60.41 : Triangle type {6,6,31} Group order 186 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^-3 * x^-1 * y^-1 * z^-2 ] T60.42 : Triangle type {6,6,31} Group order 186 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^17 * y^-1 * x * y * z^-5 * x^-1 * z^7 ] T60.43 : Triangle type {6,25,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-4 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T60.44 : Triangle type {6,26,26} Group order 156 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-2 * y^10 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T60.45 : Triangle type {6,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T60.46 : Triangle type {7,22,22} Group order 154 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^9 * z^-1 * y * z^-1 * y^2 * x * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 ] T60.47 : Triangle type {7,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 * y^3 * x^-1 * y^6 ] T60.48 : Triangle type {7,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 * y^6 * z^-1 * y * z^-1 ] T60.49 : Triangle type {7,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-8 * z^3 * y^-1 * z * y^-1 * z^4 ] T60.50 : Triangle type {8,8,21} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-7 * x * y^-1 * x * y * z^-5 * x^-1 * z * y * z^-5 ] T60.51 : Triangle type {8,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z * y^-1 * z * y^-1 * z * y^-1 * x * y^-3 * z * y^-6 * z * y^-1 ] T60.52 : Triangle type {9,16,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-4 * y^4 * z^-3 ] T60.53 : Triangle type {9,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 ] T60.54 : Triangle type {9,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-2 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T60.55 : Triangle type {9,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^3 * z^-1 * y * z^-1 * y^9 ] T60.56 : Triangle type {10,10,16} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-10 * x^-1 * y * x * y^-1 * z^-4 ] T60.57 : Triangle type {11,13,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-7 * y^2 * z^-4 ] T60.58 : Triangle type {11,14,14} Group order 154 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-11, (y^4 * z^-1 * y * z^-1)^2 ] T60.59 : Triangle type {11,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x^-11 ] T60.60 : Triangle type {11,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^5 * z^-4, x^-11 ] T60.61 : Triangle type {11,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^6 * z^-3, x^-11 ] T60.62 : Triangle type {11,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, x^-11 ] T60.63 : Triangle type {11,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y^5 * z^-4, x^-11 ] T60.64 : Triangle type {12,12,13} Group order 156 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, z^-1 * x^-3 * y^-1 * x * y^-1, y^2 * x^-1 * y^2 * x^-5 * y^2 ] T60.65 : Triangle type {12,12,13} Group order 156 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z * y * z^-1 * x * z^2, x * y^-2 * x^2 * y^-2 * x^2 * y^-1 * x^2 ] T60.66 : Triangle type {12,12,13} Group order 156 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, z * x^-3 * y^-1 * x * y^-1, (x^-2 * y * x^-3)^2 ] T60.67 : Triangle type {12,12,13} Group order 156 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, z^2 * x^-1 * y^-1 * z, x^-2 * y * x^-8 * y ] T60.68 : Triangle type {12,12,13} Group order 156 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, y^-1 * z^-1 * x^-1 * z^2, x^-1 * y * x^-7 * y * x^-1 * y ] T60.69 : Triangle type {12,12,13} Group order 156 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z^8 * y * x * z^4 ] T60.70 : Triangle type {12,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-1 * y^5 * x^-1 * y^5, z^-6 * y * z^-4 ] T60.71 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-4 * y^5 * x^-1 * y^5 * x^-1 ] T60.72 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-3 * z^4 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 ] T60.73 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-1 * y * x^-1 * y^5 * x^-2 * y^4 ] T60.74 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^-4 * y^5 * x^-2 * z^4 * x^-1 * z * x^-1 ] T60.75 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * x^-1 * y^5, z^-6 * x^2 * z^-4 ] T60.76 : Triangle type {13,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-4 * y^5 * x^-2 * z^4 * x^-1 * z * x^-1 ] T60.77 : Triangle type {14,14,70} Group order 140 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^2 * y * z^-3 * x^-1 * z^4 ] T60.78 : Triangle type {14,14,70} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^5 * y * z^-2 * x^-1 * z^2 ] T60.79 : Triangle type {14,14,70} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, x^-1 * y^-1 * z^-4 * x^-1 * y * z^-4 ] T60.80 : Triangle type {16,16,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * y * z^-4 * x^-1 * y * x^-1 * y * x^-1 * y * z^-1 ] T60.81 : Triangle type {16,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-6 * y ] T60.82 : Triangle type {16,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-2 * x * z^-4 * x^6 * z^-2 ] T60.83 : Triangle type {16,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 ] T60.84 : Triangle type {16,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * y^3, x * z^-4 * x^2 * z^-4 ] T60.85 : Triangle type {21,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T60.86 : Triangle type {21,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-3 ] T60.87 : Triangle type {21,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-4 * x^4 * z^-2 ] T60.88 : Triangle type {21,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-5 * y * x^-1 * y * x^-1 * z * x^-8 * z * x^-4 ] T60.89 : Triangle type {21,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-7 * y * x^2 * z^-4 ] T60.90 : Triangle type {22,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^3 * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y ] T60.91 : Triangle type {22,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T60.92 : Triangle type {22,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3 ] T60.93 : Triangle type {22,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1 ] T60.94 : Triangle type {22,22,66} Group order 132 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * y * z^-4 * y * x * z^-4 ] T60.95 : Triangle type {22,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3, y^3 * x^-1 * y * z^-2 ] T60.96 : Triangle type {22,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, y * z^-1 * y * x^-1 * z * y, (z^-1 * x * z^-1)^3 ] T60.97 : Triangle type {22,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x^-3 * y^3 * x^-7 ] T60.98 : Triangle type {22,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x * z^-1 * y * x * z^-3 ] T60.99 : Triangle type {22,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * y^3 ] T60.100 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^2 * y^-6 * x * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T60.101 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-3 * x * z^-4 * x^6 * z^-3 ] T60.102 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-1 * y^5, x * z^-4 * x^5 * z^-1 ] T60.103 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-3 * y^5 * x^-6 ] T60.104 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^3 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * y^-1 * x^10 * z^-1 * x * z^-1 * x^2 ] T60.105 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^10 * y^-2 * x^8 * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T60.106 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-2 * x^6 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T60.107 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^2 * z^-4 * x^6 * z^-1 ] T60.108 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-6, z^-6 * x * z^-4 ] T60.109 : Triangle type {25,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^2 * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-8 ] T60.110 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^2 * x^-1 * y * x^-1 * y * z^-3 ] T60.111 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T60.112 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z^2 * y, z * y^-3 * x^-1 * z^3 ] T60.113 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^2 * y^-1 * x * z^2 ] T60.114 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^8 * y^-2 ] T60.115 : Triangle type {26,26,65} Group order 130 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^-2 * x * z^-1 * y * z^-4 * y^2 * z^-4 ] T60.116 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^6 * z^-1 * y^9 ] T60.117 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-1 * x * y^-5 * x * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T60.118 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-3 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 ] T60.119 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^4 * y^-1 * x * y^-5 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T60.120 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x * z^-4 * x^6 ] T60.121 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^-3 * y * x^-5 * z^4 * x^-1 * z * x^-1 ] T60.122 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^13 * z^-1 * x * z^-1 * x^11 * z^-1 * x * z^-1 * x^2 ] T60.123 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^4 * x^-6, z^-3 * y^5 * z^-4 ] T60.124 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^7 * x^-1 * y^5 ] T60.125 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-4 * x^2 * z^-4 ] T60.126 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^6 * z^-3, x^-3 * y^4 * x^-6 ] T60.127 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-4 * y * x^-5 * z^4 * x^-1 * z * x^-2 ] T60.128 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-9 * z^4 * x^-3 ] T60.129 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^6 * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 ] T60.130 : Triangle type {31,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-18 * z * x^-8 * y * x^-4 ] T60.131 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^6 * z^-1 * y^14 ] T60.132 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x * y^-1 * x * y^-6 * x^5 * y^-2 ] T60.133 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^10 * y^-2 * x * y^-1 * x * y^-1 * x * y^-6 * x * y^-4 * x * y^-1 * x * y^-1 * x ] T60.134 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^-4 * z^4 * x^-5 * y * x^-1 ] T60.135 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-6 * z^2 ] T60.136 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T60.137 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-2 * y * x^-8 * y^2 * x^-2 ] T60.138 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^4, x^-6 * y^6 * x^-1 ] T60.139 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-5 * z, x^-8 * y^3 * x^-1 ] T60.140 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^4 * z^-3 * y^3 * z^-4 * y * z^-1 * y^5 ] T60.141 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^8 * x^-1 * z^4 ] T60.142 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-3 * y^4 * z^-4 * y * z^-1 * y * z^-1 * y * z^-2 ] T60.143 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^-1 * y * x^-5 * y^5 * x^-3 ] T60.144 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^20 * z^-1 * x^5 * y^-1 * x^15 ] T60.145 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^-3 * z * y^-1 * z^4 * y^-2 * x * y^-4 ] T60.146 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^-15 * x^6 * y^-6 ] T60.147 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-2 * z^4, y^-3 * z^2 * y^-3 * x * y^-4 ] T60.148 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-7, y^-2 * z^4 * y^-2 * x * y^-4 ] T60.149 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * y^-1, x^-2 * z^5 * x^-2 * z^4 ] T60.150 : Triangle type {41,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^7 * z^-2 * x^7 * z^-1 * x^5 ] T60.151 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-11 * x^4 * y^-1 * x * y^-1 * x * y^-2 * x^8 * y^-1 * x * y^-1 * x * y^-1 * x ] T60.152 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^6 * z^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x ] T60.153 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^4 * y^-4 * x^4 * z^-2 * x^4 ] T60.154 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-3 * z^3, x^3 * y^-5 * x^2 * z^-3 * x^3 ] T60.155 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-3 * z^3, x^2 * y^-5 * x^2 * z^-3 * x^2 ] T60.156 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-6, y^-2 * z * y^-1 * z^4 * y^-3 * z^3 ] T60.157 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-4 * z^2, x * y^-6 * x * y^-4 ] T60.158 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^3 * x^-4 * y^2 * z^-4 * y * z^-1 * y^3 ] T60.159 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^6 * y^-1 * z^4 * y^-2 * x^-1 * z^5 ] T60.160 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-1 * z^4, y^-3 * z^2 * y^-3 * x * y^-4 ] T60.161 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, y * z^-5 * y^5 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T60.162 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-8 * x^4 * y^-2 ] T60.163 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-3 * x * y^-4, x^-2 * z^5 * x^-3 * z^3 ] T60.164 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-11 * y^4 * z^-11 ] T60.165 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-4 ] T60.166 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T60.167 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-2 * z^4, x^-6 * y^6 * x^-1 ] T60.168 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^7 * z^-5 * x * z^-1 * x^2 ] T60.169 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-12 * x * z^-6 * y * x * z^-11 ] T60.170 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^2 * y^-2 * x * y^-1 * x * y^-1 * x * y^-11 * x * y^-1 * x * y^-1 * x ] T60.171 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-2 * x^-1 * z^4, x^2 * y^-4 * x^7 ] T60.172 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-3 * z * y^-1 * z^4 * y^-2 * x^3 * y^-3 ] T60.173 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^11 * x^-1 * y^-2 * z^5 ] T60.174 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y * x^-1 * y * x^-5 * y^6 * x^-1 * y^2 ] T60.175 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^3 * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T60.176 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^8 * x^-1 * z^4 ] T60.177 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-6, x^-1 * z * x^-1 * z^5 * x^-6 ] T60.178 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x * z^-2 ] T60.179 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-36 * x * z^-4 ] T60.180 : Triangle type {61,122,122} Group order 122 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-61, y * z^-1 ] T60.181 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-19 * x^2 * y^-11 ] T60.182 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-5 * z * y^-3 * x * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T60.183 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^4 * x^-1 * y^5 * x^-1 * y^5 ] T60.184 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^-1 * y * x^-1 * y^5 * x^-6 ] T60.185 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x^-2 * y^2 * x^-8 ] T60.186 : Triangle type {62,62,62} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^2 * z^-1 * y * z^-1 * y^7 * z^-2 ] T60.187 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x^-2 * y^-1, y^-53 * x * y^-7, x * z^-1 ] T60.188 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * z^-3 * x^6 * z^-1 * x^5 ] T60.189 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-1, y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 ] T60.190 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^-1 * y * x^-5 * y^6 * x^-2 ] T60.191 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-10 * z^3 * x^-4 ] T60.192 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, x^2 * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-4 ] T60.193 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-32 * x^2 * y^-7 ] T60.194 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y, z^-1 * y^6 * z^-4 * y^3 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T60.195 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^9 * x^-1 * z^4 ] T60.196 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-3 * z^3, x^-2 * z^5 * x^-6 ] T60.197 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-3 * z^4 * y^-2 * x * y^-4 ] T60.198 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^5 * z^-2 * x^8 * y^-1 * x^3 ] T60.199 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x^2 * y^-5 ] T60.200 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-2 * z * x^-4 * y^6 * x^-2 ] T60.201 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^7 * z^-5 * x * z^-1 * x * z^-1 ] T60.202 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^10 * y^-2 * x^7 * y^-1 * x^6 ] T60.203 : Triangle type {121,121,121} Group order 121 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-9 * x * z^-7 * x^2 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 ] Genus 61 T61.1 : Triangle type {2,4,6} Group order 1440 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z, y^-1 * z * y * x * z^2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T61.2 : Triangle type {2,4,6} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^6, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2, z^-1 * x * z * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y ] T61.3 : Triangle type {2,4,6} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2, z^-1 * y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^2 * y^-1 * z^-2 ] T61.4 : Triangle type {2,4,12} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z * y^-1 * z, z^12 ] T61.5 : Triangle type {2,4,14} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T61.6 : Triangle type {2,4,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x, z^-2 * x * z^3 * y * x * z * y * z^-3 * x * z * y^-1 * z^-3 ] T61.7 : Triangle type {2,4,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T61.8 : Triangle type {2,4,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y * z^-4 * x * y^-1 * z^6 ] T61.9 : Triangle type {2,4,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-1 * x * y^-1 * z * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-3 ] T61.10 : Triangle type {2,4,28} Group order 560 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-7 * x * z^9 * y * z^-1 * x * y^-1 * z^-7 * x * z * y^-1 ] T61.11 : Triangle type {2,4,52} Group order 520 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-7 * x * z^4 * y * z^-1 * x * z^2 * y * x * y^-1 * z^-9 ] T61.12 : Triangle type {2,4,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-49 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T61.13 : Triangle type {2,4,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-12 * x * z^11 * y * z^-1 * x * y^-1 * z^-6 ] T61.14 : Triangle type {2,4,124} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-124 ] T61.15 : Triangle type {2,4,244} Group order 488 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-20 * x * y^-1 * z^-101 ] T61.16 : Triangle type {2,5,10} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-1 * x * y^-1 * z^-2 * x, z^10 ] T61.17 : Triangle type {2,5,10} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-4)^2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T61.18 : Triangle type {2,6,6} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5 ] T61.19 : Triangle type {2,6,6} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1, z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 ] T61.20 : Triangle type {2,6,6} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T61.21 : Triangle type {2,6,6} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, y * x * y^-1 * z * y^3 * z^-2 * x * z^2 ] T61.22 : Triangle type {2,6,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T61.23 : Triangle type {2,6,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y^-1 * z^2 * y^-2 * z^-3 * x ] T61.24 : Triangle type {2,6,18} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y^-2 * z * y^3 * z^-1 * x * y^-1 * z^-1 * x ] T61.25 : Triangle type {2,6,18} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^6 * y * x * y * z^-10 ] T61.26 : Triangle type {2,6,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-6 * x * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T61.27 : Triangle type {2,6,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T61.28 : Triangle type {2,6,63} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^3 * y * x * z^2 * y * x * z^3 * y^-1 * z^-8 ] T61.29 : Triangle type {2,6,63} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^31 * y * x * z^17 * y * z^-1 * x * y^-1 * z^-9 * x * z^2 ] T61.30 : Triangle type {2,6,183} Group order 366 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-30 * x * z^17 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-1 ] T61.31 : Triangle type {2,10,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y^-2 * z)^3, y^10 ] T61.32 : Triangle type {2,12,12} Group order 360 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * y^2 * x * y^-1 * z^-1 * x, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T61.33 : Triangle type {2,12,12} Group order 360 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^2 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T61.34 : Triangle type {2,14,14} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, (y * z^-2 * y^2)^2 ] T61.35 : Triangle type {2,16,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, z * y * x * z * y^2 * z^-1 * x * z * y^-1 ] T61.36 : Triangle type {2,16,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z^-1 * x * z ] T61.37 : Triangle type {2,16,16} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, z^4 * y^-1 * z * y^-7 * z * y^-2 ] T61.38 : Triangle type {2,18,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-18 ] T61.39 : Triangle type {2,18,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^-1 * z^4 * y^-1 * z * y^-7 * z * y^-3 ] T61.40 : Triangle type {2,24,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, (y * z^-1 * y^4)^2, y * x * y^-5 * z^-1 * y^2 * x * y^-1 * z^-1 * y ] T61.41 : Triangle type {2,24,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-1 * z * y^6 * x * y^-4, z^8 * y^-1 * z^2 * y^-4 * z * y^-6 * z * y^-1 ] T61.42 : Triangle type {2,24,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z^3 * y * x * z * y * x * z * y^3 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T61.43 : Triangle type {2,24,24} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-1 * z * y^10 * x, z^6 * y * z^-5 * x ] T61.44 : Triangle type {2,28,28} Group order 280 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^5 * y^-4 * z^2 * y^-11 * z^4 * y^-1 * z ] T61.45 : Triangle type {2,30,45} Group order 270 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-2 * y * z^-1, y^2 * z^-1 * y * z^-1 * y^7 * z^-3 ] T61.46 : Triangle type {2,30,45} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-2 * z^3 * y^-4 * z^4 ] T61.47 : Triangle type {2,33,66} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-33 ] T61.48 : Triangle type {2,52,52} Group order 260 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-2 * z * y^-4 * z^2 * y^-1 * z * y^-7 * z * y^-1 * z * y^-2 * z^3 ] T61.49 : Triangle type {2,64,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-34 * y^12 * z^-1 * y^14 * z^-1 * y ] T61.50 : Triangle type {2,64,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-1 * y^10 * z^-3 * y^17 ] T61.51 : Triangle type {2,64,64} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-15 * z^3 * y^-9 * z^2 * y^-1 ] T61.52 : Triangle type {2,123,246} Group order 246 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^107 * z^-16 ] T61.53 : Triangle type {2,124,124} Group order 248 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^16 * y^-107 ] T61.54 : Triangle type {2,244,244} Group order 244 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-106 ] T61.55 : Triangle type {3,4,4} Group order 720 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, y^-1 * z * y * z^-1 * y * x^-1 * z * y * x * z, (z^-1 * y)^5 ] T61.56 : Triangle type {3,4,4} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (y * z^-1)^4, (x * z * y^-1 * z^-1 * y)^2, y^-1 * z^-1 * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * z * y^-1 ] T61.57 : Triangle type {3,4,4} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (y * x^-1 * z)^3, (x * z * y^-1 * z^-1 * y)^2, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * z ] T61.58 : Triangle type {3,4,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T61.59 : Triangle type {3,5,15} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, (x^-1 * z * y)^2, z^-3 * x^-1 * z^2 * y^-1 ] T61.60 : Triangle type {3,6,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T61.61 : Triangle type {3,6,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * y^-1 * z^-1 * y * x * z * y * z^-1 ] T61.62 : Triangle type {3,6,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, (z^-1 * y)^3, y^-1 * z^-1 * y^2 * x * z * y * x^-1 ] T61.63 : Triangle type {3,6,6} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * y^2 * x * z * y * x^-1 ] T61.64 : Triangle type {3,6,7} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, x * z * x^-1 * y^-1 * x * y^-1 * z^-1 * y, z^3 * y^-1 * x^-1 * z^3, z^3 * y * x^-1 * z^2 * y^-1 ] T61.65 : Triangle type {3,6,12} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, y * x^-1 * y^-2 * x * z * y * z^-1 ] T61.66 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y^2 * x * z^3 ] T61.67 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * y^2 * x^-1 * y^-1 * z^-2, z * y^2 * x^-1 * y * z^-1 * x ] T61.68 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T61.69 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-4 * x^-1 * z^3 * y^-1 ] T61.70 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z, z^2 * y^2 * x^-1 * z^3 ] T61.71 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x^-1 * z^3 ] T61.72 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2 ] T61.73 : Triangle type {3,6,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-3 * x^-1 * y^-1 * z * y, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-2 * x * z * y^-1 * z, (y * z^-2 * y)^2 ] T61.74 : Triangle type {3,12,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, (y * z^-1 * y^2)^2 ] T61.75 : Triangle type {3,12,12} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y * x^-1 * y * x^-1 * y^-1 * x * z, z * y^2 * x^-1 * y^-3 ] T61.76 : Triangle type {3,18,18} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z ] T61.77 : Triangle type {3,18,18} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-1 * y * x^-1 * y^3 ] T61.78 : Triangle type {3,18,18} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y * z^-5 * y * z^-1 * y^2 * z^-1 * y * z^-4 ] T61.79 : Triangle type {3,18,18} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-1 * y^11 * z^-1 * y^3 * z^-1 ] T61.80 : Triangle type {3,22,66} Group order 198 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-5 * y * z^-2 * y^6 * z^-4 * y * z^-1 * y ] T61.81 : Triangle type {3,48,48} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-4 * y * z^-2 * y^3 * z^-2 * y^3 ] T61.82 : Triangle type {3,48,48} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, (y * z^-2 * y)^2 ] T61.83 : Triangle type {3,62,186} Group order 186 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-51 * z * y^-8 * z^2 ] T61.84 : Triangle type {3,63,63} Group order 189 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-4 * y * z^-2 * y^2 * z^-1 * y^6 * z^-1 * y^3 * z^-1 ] T61.85 : Triangle type {3,63,63} Group order 189 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-52 * z * y^-8 * z^2 ] T61.86 : Triangle type {3,183,183} Group order 183 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-50 * z * y^-9 * z ] T61.87 : Triangle type {4,4,6} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^6, x * z^-1 * y * x^-2 * y^-1 * z * y^-1 * z^-1 ] T61.88 : Triangle type {4,4,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y^-1 * z^-1 * x^-1 * z * y * x, z * x^-1 * y * x^2 * y^-1 * z * y^-1 ] T61.89 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x * z^2, y * z^-1 * y * x^2 * z * y^-1 * z^-1 ] T61.90 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x^2 * z^2 * y^-1 ] T61.91 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z, z^-1 * y * x * y^-1 * x * y^-1 * z^-2 ] T61.92 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z * y * x * z * y * x^-1 * z * y^-1 * z * y^-1 ] T61.93 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y^2 * z^-1 * x^-1 * z * y^-1 ] T61.94 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y * x * z * y^-1 * z * y^-1 ] T61.95 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1 ] T61.96 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y^-1 * z^2 * y * z^-1 * y * z^-1 * x^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 ] T61.97 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y^-1 * z^2 * y * z^-1 * y * z^-1 * x^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T61.98 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y * x^-1 * z * y^-1 * z * y^-1 ] T61.99 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z * y * x * z * y * x * z * y^-1 * z * y^-1 ] T61.100 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y^2 * z^-1 * x * z * y^-1 ] T61.101 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z * y * x * z * y^2 * z^-1 * x^-1 * z * y^-1 ] T61.102 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, y * x * y^-1 * x * y^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 ] T61.103 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1)^4, y * x * y^-1 * x * y^-1 * x * z * x^-1 * y^-1 * z ] T61.104 : Triangle type {4,4,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, y * x * y^-1 * x * y^-1 * x * z * x^-1 * y^-1 * z ] T61.105 : Triangle type {4,4,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T61.106 : Triangle type {4,4,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z * y^-1 * x * y^-1 * x * z^3 ] T61.107 : Triangle type {4,4,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * z^3 * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 * z ] T61.108 : Triangle type {4,4,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z * x^-1 * y * x^-2 * z^4 ] T61.109 : Triangle type {4,4,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * z^-1 * x^-1 * z^3 * x^-1 * z^4 * y^-1 ] T61.110 : Triangle type {4,4,14} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-2 * x^-1 * z^3 * y^-1 * z^-1 * x^-1 * y^-1 * x^-1 * y^-1 * z^-5 ] T61.111 : Triangle type {4,4,26} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z * y^-1 * z^-3 * x^-1 * y * x * y^-1 * z^-4 * x * z^2 ] T61.112 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-5 * x * y * x^-1 * z^8 ] T61.113 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-32 ] T61.114 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^2 * y * z^-6 * x * y^-1 * z^-1 * x^-1 * z^5 ] T61.115 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-5 * x * z^9 ] T61.116 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-32 ] T61.117 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-3 * x^-1 * z^2 * y^-1 * x * z * y * z^-3 * x^-1 * z^3 * y * z^-1 ] T61.118 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x * z^5 * y^-1 * z^-2 * x^-1 * y^-1 * z^-4 ] T61.119 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x * z * y * z^-3 * x^-1 * y * x^-1 * z^7 * y^-1 ] T61.120 : Triangle type {4,4,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x * z * y * z^-3 * x^-1 * y * x^-1 * z^7 * y^-1 ] T61.121 : Triangle type {4,4,62} Group order 248 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-48 * x * y^-1 * x * y^-1 * z^-12 ] T61.122 : Triangle type {4,4,122} Group order 244 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^48 * y * x^-1 * z^12 ] T61.123 : Triangle type {4,5,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T61.124 : Triangle type {4,6,6} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^6, z^6, z * x^-1 * y * x^-1 * y^-2 * z ] T61.125 : Triangle type {4,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (y * z^-1 * y)^2, (z^-1 * x)^3 ] T61.126 : Triangle type {4,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^6, (x * z^-1 * y^2)^2 ] T61.127 : Triangle type {4,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 ] T61.128 : Triangle type {4,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T61.129 : Triangle type {4,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T61.130 : Triangle type {4,6,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, z^2 * y * x * z * y^-1 ] T61.131 : Triangle type {4,6,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-1 * x * z^-1 * x^2 * z * y * x * z ] T61.132 : Triangle type {4,6,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x^-1 * z^3 ] T61.133 : Triangle type {4,6,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y, z * y^2 * x^2 * z^2 * x^-1 ] T61.134 : Triangle type {4,6,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T61.135 : Triangle type {4,6,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z * y * x * z^4 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^8 ] T61.136 : Triangle type {4,6,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^9 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x^-1 * z ] T61.137 : Triangle type {4,9,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, z^-2 * y * x^-1 * y^-1 * z^-1, y * z^-1 * x^-2 * z^2 * x^-1, x * z * y * x^-1 * y * z^-1 * y ] T61.138 : Triangle type {4,9,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3, y^-9 ] T61.139 : Triangle type {4,10,20} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^-2 * z^-1, x * z^2 * y * x * z * y * z^-5 ] T61.140 : Triangle type {4,10,20} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^10 ] T61.141 : Triangle type {4,10,20} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, z^-1 * y^6 * z^-3 ] T61.142 : Triangle type {4,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^5 * x^-1 * y^-4 * z^-1, z^3 * y * z^-1 * x^-1 * z^5 ] T61.143 : Triangle type {4,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * z^-1 * y^3 * z^-3, y^10 ] T61.144 : Triangle type {4,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * y^4 * z^-1 * y * z^-2, z^4 * y^-1 * x * z^5 ] T61.145 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, y^-2 * z * x^-1 * y^-3 ] T61.146 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3 ] T61.147 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * x^-1 * y^-4, y^-1 * z^4 * y^-3 * z^4 ] T61.148 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z^3 * y^-1 * z^-2, y^-1 * z^2 * y^-1 * z^2 * y^-6 ] T61.149 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-1 * z^2 * y^-3 * z^5 ] T61.150 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^4 * z^-1 * y^3 * z^-2 * y * z^-1 ] T61.151 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z^3 * y^-1 * z^-2, (y^-1 * z * y^-3 * z)^2 ] T61.152 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, (y^-1 * z^2)^4 ] T61.153 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * x^-1 * y^-4, (y^-1 * z^2)^4 ] T61.154 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^-5 * z * y^-2 * z * y^-1 * z^2 ] T61.155 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^-5 * z^2 * y^-2 * z^2 * y^-1 ] T61.156 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-1 * z^3 * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 ] T61.157 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-4 * x^-1 * z * y * z^-2 ] T61.158 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * x^-1 * y^-1 * x * z^3 ] T61.159 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2, (y * z^-2)^2, y^2 * x^-2 * y^-1 * z * x^-1 ] T61.160 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^-2 * z * x^-1 * z * y^-1 * z ] T61.161 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, y * z^-1 * x^-2 * z^2 * x^-1 ] T61.162 : Triangle type {4,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-2 ] T61.163 : Triangle type {4,15,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-4 * z^4 ] T61.164 : Triangle type {4,18,36} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z, y^-1 * z * y^-3 * x * z * y^-1 * z * y^-1 ] T61.165 : Triangle type {4,22,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-7 * y^6 * z^-1 * y^8 ] T61.166 : Triangle type {4,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-14 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T61.167 : Triangle type {4,82,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-13 * z * y^-1 * z^4 * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T61.168 : Triangle type {5,5,5} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, y^-5 ] T61.169 : Triangle type {5,5,5} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, y^-5, (z^-1 * x)^3, z^-1 * x^-1 * y * x^2 * z * y^-1 * z^-1 ] T61.170 : Triangle type {5,15,15} Group order 180 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, (y^-1 * x)^3 ] T61.171 : Triangle type {6,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, y^6, (x * z^-1 * y)^2, (x^-1 * z * y)^2, z^6 ] T61.172 : Triangle type {6,6,6} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * y^-1 * x, z^2 * y * x^-1 * z * y^-1 ] T61.173 : Triangle type {6,6,9} Group order 216 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-3 * y^-2 * z * y ] T61.174 : Triangle type {6,6,9} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^4 * y^-1 * x^-1 * z^4 ] T61.175 : Triangle type {6,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, (x * z * y)^2 ] T61.176 : Triangle type {6,6,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^2 * y^-1 * x * y^-1 * x * z^4 ] T61.177 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-1 * x^-2 * z * y^-1 * z ] T61.178 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z * x^-1 * y^-1 * x * z * x^-1, z * y^-1 * z^-1 * x * z * y^-1 ] T61.179 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-2)^2, z * y * x^3 * z * x^-1 * y^-1 ] T61.180 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, (x * z * y)^2 ] T61.181 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, z^-2 * y * x^-1 * z * y^-2, y^8 ] T61.182 : Triangle type {6,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y^8, z^-1 * y^3 * x^-1 * y^4 ] T61.183 : Triangle type {6,12,12} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y^2 * z^-1 * y ] T61.184 : Triangle type {6,12,12} Group order 180 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^-1 * z^2, z^-1 * y * z^-1 * x^-1 * y^3 ] T61.185 : Triangle type {6,12,12} Group order 180 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, x^6, z^-1 * y * x^-2 * y^-2 * x ] T61.186 : Triangle type {6,12,28} Group order 168 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, x^6, y * x^-3 * z * x^-2 ] T61.187 : Triangle type {6,12,28} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-2, (x * y^-2)^2 ] T61.188 : Triangle type {6,12,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^-5 * x^-1 * y * x^-1 * z * y * z^-3 * x^-1 * y * z^-2 ] T61.189 : Triangle type {6,14,21} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^-4 * z^3 ] T61.190 : Triangle type {6,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T61.191 : Triangle type {8,10,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^10 ] T61.192 : Triangle type {8,10,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^10 ] T61.193 : Triangle type {8,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T61.194 : Triangle type {8,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T61.195 : Triangle type {8,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T61.196 : Triangle type {8,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^8 ] T61.197 : Triangle type {8,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^9 * y^-1 * z * y^-3 * z * y^-1 * z ] T61.198 : Triangle type {8,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-6 * x * y^-2 * z^4 * y^-1 * z * y^-4 ] T61.199 : Triangle type {9,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T61.200 : Triangle type {9,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, z^-1 * y^3 * z^-2 ] T61.201 : Triangle type {9,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, x^-9 ] T61.202 : Triangle type {9,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2, x^-9 ] T61.203 : Triangle type {10,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-1 * y * z^-1 * y * z^-4 * y^3 * z^-4 ] T61.204 : Triangle type {10,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * y * x^-1 * y^-2 * z, (x * y^-3)^2 ] T61.205 : Triangle type {10,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, y^-1 * z^-1 * x^3 * y^-3 ] T61.206 : Triangle type {10,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * z * y, x^10 ] T61.207 : Triangle type {10,15,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * y^-1 * z^-1, x^-1 * y * x^-1 * z * y * x^-4 * y^2 * x^-1 ] T61.208 : Triangle type {10,28,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-3 * y^6 * z^-1 * y ] T61.209 : Triangle type {12,16,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, y * x^-1 * y^2 * x^-8 * y ] T61.210 : Triangle type {12,16,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, z^-3 * y^2 * z^-3 ] T61.211 : Triangle type {12,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^2 * z^-3 ] T61.212 : Triangle type {12,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, y^-2 * x^4 * y^-4 ] T61.213 : Triangle type {12,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, (y^-1 * x^2 * y^-1 * x * y^-1 * x)^2 ] T61.214 : Triangle type {12,18,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-2 * y * x^-1 * y * x^-4 * y * x^-1 * y^3 ] T61.215 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-2 * z^2 * y^-1 * z * y^-3 * z^3 ] T61.216 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-2, x^4 * z^-4 * x^2 * y^-4 * x^2 ] T61.217 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, z^-1 * y^2 * x^-1 * y^-3, x^-3 * z * x^-7 * y * x^-1 ] T61.218 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, z^-1 * y^2 * x^-1 * y^-3, y^4 * x^-1 * y * z^-1 * y^2 ] T61.219 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-1 * z * y^-8 * z * y^-1 ] T61.220 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x * y^-2 * x^7 * z^-1 ] T61.221 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T61.222 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * y * z^-1 * y^3 * x * z^-1 * y * z^-1 * y ] T61.223 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^2 * x^-3 * z * y^3 ] T61.224 : Triangle type {12,24,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^3 * x^-1 * y^-1 * z^-1 * y ] T61.225 : Triangle type {14,28,28} Group order 140 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x * y^-2 * x * y^-1 * z^-1, z * y^-1 * z * x^-1 * z * y^-1 * z ] T61.226 : Triangle type {14,28,28} Group order 140 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, (y^2 * x^-1 * y^2)^2 ] T61.227 : Triangle type {14,28,28} Group order 140 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^-6 * y * x^-6 * z * x^-1 ] T61.228 : Triangle type {15,27,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-1 * y * x^-1 * y^5 * x^-3 * y^3 ] T61.229 : Triangle type {15,27,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-5 * y^5 * x^-2 * z^4 * x^-1 * z * x^-2 ] T61.230 : Triangle type {15,45,45} Group order 135 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2, x * y^-3 * x^-1 * y^3, y * x^-1 * y * x^-2 * y^4 ] T61.231 : Triangle type {15,45,45} Group order 135 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y * z^-1 * y^2 * z^-2, x^-5 * y * x^-1 * y^2 ] T61.232 : Triangle type {15,45,45} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-4 * z^4 * x^-2 * z^4 * x^-1 * z * x^-2 ] T61.233 : Triangle type {15,45,45} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^4, z^-1 * x * z^-4 * x^2 * z^-4 ] T61.234 : Triangle type {18,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, z^-1 * x^3 * z^-2, z^2 * y^-1 * x^2 * y^-6 ] T61.235 : Triangle type {18,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * y * x^2 * y^-1 * z^-1 ] T61.236 : Triangle type {18,18,18} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z^-1 * y, (x * z * y)^2, y^-3 * x * y^-1 * x * y^-4 ] T61.237 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-15 * z * x^-4 ] T61.238 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-4 * z * x^-1 * z^2 * x^-6 * z * x^-3 ] T61.239 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-4 * y * x^-1 * z^3 * x^-5 * z^2 * x^-3 ] T61.240 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-4 * z * x^-1 * z * x^-8 * z * x^-1 * z ] T61.241 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T61.242 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x^6 * y^-4 ] T61.243 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-6 * x * z^-1 * x * z^-4 * x * y * z^-8 ] T61.244 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x^3 * z^-3 * y * x^2 * z^-4 ] T61.245 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, x^3 * z^-3 * y * x^2 * z^-4 ] T61.246 : Triangle type {32,64,64} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, z^-6 * y^2 * z^-4 ] T61.247 : Triangle type {33,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-9 * x^3 * y^-6 ] T61.248 : Triangle type {33,33,33} Group order 132 Reflexible action Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-1 * z^-1, y^2 * x^2 * z^2, y^-1 * z * y^-2 * x^-1 * z^3 ] T61.249 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * y^-2 * x^9 * z^-1 * x * z^-1 * x^2 ] T61.250 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^11 * x^-2 * y^4 ] T61.251 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^7 * y^-5 * x * y^-1 * x^2 ] T61.252 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-24 * y * x^-1 * y * x^-1 * y * x^-1 * z * x^-8 * y * x^-4 ] T61.253 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^14 * y^-2 * x * y^-4 * x^3 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T61.254 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x^-3 * y^3 * x^-7 ] T61.255 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * z^-8 ] T61.256 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, x^-2 * y * x^-1 * y^5 * x^-3 * y^3 ] T61.257 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^3 * x^-7, z^-6 * y^2 * z^-4 ] T61.258 : Triangle type {42,63,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z * x^-1 * z * x^-7 * z^4 * x^-1 * z^3 ] T61.259 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^3 * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T61.260 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-29 * x * y^-5 * x * y^-6 ] T61.261 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-3 * y^2 * x^-4 * z^4 * x^-2 ] T61.262 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^-2 * y^5 * x^-1 * y^5 ] T61.263 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T61.264 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^6 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T61.265 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^2 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T61.266 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^4 * x^-6, z^-6 * x * z^-4 ] T61.267 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-5 * z^2 * y^-3 * z * y^-15 ] T61.268 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z * y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T61.269 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^6 * z^-3, x^-2 * y^2 * x^-4 * z^4 * x^-1 ] T61.270 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-3 ] T61.271 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-2 * y^5 * x^-5 * y ] T61.272 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-4 * y^2, z^2 * x^-6 * z^6 ] T61.273 : Triangle type {62,124,124} Group order 124 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-62, y * z^-1 ] T61.274 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x^-2 * y^-1, y^-54 * x * y^-7, x * z^-1 ] T61.275 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^3 * x^-4 * y^2 * z^-3 * y^5 ] T61.276 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-2 * z^4, y^-2 * z^2 * y^-3 * x * y^-4 ] T61.277 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x * y^-3 * x * y^-1 * x * y^-1 * x * y^-11 * x * y^-1 * x * y^-1 * x ] T61.278 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-2 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T61.279 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 ] T61.280 : Triangle type {123,123,123} Group order 123 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-3 * z^3, y * x^-5 * y^7 ] Genus 62 T62.1 : Triangle type {2,4,126} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-126 ] T62.2 : Triangle type {2,4,248} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-21 * x * y^-1 * z^-102 ] T62.3 : Triangle type {2,5,10} Group order 610 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, x * z * y * x * y^-2 * z^-1 * y * x * y^-1 * z^-1 ] T62.4 : Triangle type {2,5,10} Group order 610 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T62.5 : Triangle type {2,6,6} Group order 732 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, x * z * y^-1 * z^2 * y * z^-1 * x * z^2 * y^-2 * z^-1 * x * z * y^-1 * z^-3 * y * z^-2 * y * z^-1 * x * y^-1 ] T62.6 : Triangle type {2,6,64} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-33 * x * z^17 * y * x * z * y * x * y^-1 * z^-10 ] T62.7 : Triangle type {2,6,186} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-31 * x * z^17 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-3 ] T62.8 : Triangle type {2,8,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^32 * y * x * y^-1 * z^-1 * x * z^7 ] T62.9 : Triangle type {2,10,155} Group order 310 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^21 * y * z^-7 * x * z^2 ] T62.10 : Triangle type {2,20,70} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * x * z^3 * y^-1 * z^-1 * x ] T62.11 : Triangle type {2,44,66} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-10 * z^3 * y^-6 * z^3 ] T62.12 : Triangle type {2,125,250} Group order 250 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^108 * z^-16 * y ] T62.13 : Triangle type {2,126,126} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-107 * z ] T62.14 : Triangle type {2,248,248} Group order 248 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^16 * y^-106 * z ] T62.15 : Triangle type {3,6,6} Group order 366 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * z^2 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T62.16 : Triangle type {3,6,6} Group order 366 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-2 * z ] T62.17 : Triangle type {3,64,64} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^51 * y^-10 * z * y^-1 ] T62.18 : Triangle type {3,186,186} Group order 186 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-51 * z * y^-10 ] T62.19 : Triangle type {4,4,63} Group order 252 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-49 * x * y^-1 * x * y^-1 * z^-12 ] T62.20 : Triangle type {4,4,124} Group order 248 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-48 * x * y^-1 * z^-13 ] T62.21 : Triangle type {4,8,26} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-7 * x * z^5 * y^-1 * x * z * y^-1 * z^-11 ] T62.22 : Triangle type {4,12,32} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z * y * x * z^8 * y * x^-1 * z^5 ] T62.23 : Triangle type {4,20,45} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^-1 * z^2 * y^-2 * z^-3 * y, y * z^-1 * y^7 * z^-1, z^3 * y * z^-1 * x * z^4 ] T62.24 : Triangle type {4,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-4 * y^9 * z^-1 * y^7 * z^-1 ] T62.25 : Triangle type {4,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-12 * z^3 * y^-1 * z * y^-2 * z^3 * y^-5 * z * y^-1 * z * y^-11 ] T62.26 : Triangle type {5,5,5} Group order 305 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, x^-1 * z * y^-1 * x^2 * z * x^-1 * z ] T62.27 : Triangle type {5,5,5} Group order 305 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, y * z^-1 * y * x^-1 * z * x^-1 * z ] T62.28 : Triangle type {5,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^6, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T62.29 : Triangle type {5,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y^6, (y * z^-2)^2, y * z^-1 * x * y^-1 * x * y^-2 * z ] T62.30 : Triangle type {5,32,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T62.31 : Triangle type {5,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y ] T62.32 : Triangle type {5,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T62.33 : Triangle type {6,6,32} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^18 * y^-1 * x * y * z^-5 * x^-1 * z^7 ] T62.34 : Triangle type {6,6,93} Group order 186 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^16 * y^-1 * z^-1 * x * z * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 ] T62.35 : Triangle type {6,12,42} Group order 168 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^-1 * z^-3 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^6 ] T62.36 : Triangle type {6,14,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-3 * y * z^-1 * y^2 * z^-1 * y * z^-2 * y^2 * z^-1 ] T62.37 : Triangle type {6,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T62.38 : Triangle type {6,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^6 * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T62.39 : Triangle type {8,8,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-7 * x * y^-1 * x * y^-1 * z^-12 ] T62.40 : Triangle type {10,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-3 * y^6 * z^-2 ] T62.41 : Triangle type {10,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^4 * z^-2 * y^8 ] T62.42 : Triangle type {12,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2, x * y^-1 * x^3 * y^-1 * z^-2 ] T62.43 : Triangle type {12,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x * y^-1 * x^3 * y^-1 * z^-2 ] T62.44 : Triangle type {14,20,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, y * x^-1 * y * x^-1 * y^6 * x^-5 * y^2 ] T62.45 : Triangle type {16,16,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z^3 * y^-1 * z^-1 * x * y^-1 * x * z^3 ] T62.46 : Triangle type {18,18,24} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T62.47 : Triangle type {20,20,35} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, y^-3 * x^2 * y^-3, z^3 * y * x * z^3 ] T62.48 : Triangle type {20,20,35} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x * z * y * z^-3 ] T62.49 : Triangle type {22,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, z * x^-6 * z^5 ] T62.50 : Triangle type {22,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^4 * x^-6 * z^8 ] T62.51 : Triangle type {22,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-8 * y * x^-7 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T62.52 : Triangle type {22,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^3 * x^-5 * y^-3 * z^6 ] T62.53 : Triangle type {22,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y^5 * z^-4, x^-1 * y * x^-1 * y^5 * x^-6 ] T62.54 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T62.55 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-8 * z^4 * x^-1 * z ] T62.56 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-2 * z * x^-1 * z^5 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z^3 ] T62.57 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x * z^-1 * x^5 * y^-5 * x * y^-1 * x^2 ] T62.58 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^6 * x^-2 ] T62.59 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, x * y^-1 * z^2 * y^-3 * x * y^-5 * x * y^-1 * x * y^-3 ] T62.60 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-13 * y^2 * x^-6 * z^2 * x^-5 ] T62.61 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^2 * x^-8 * y * x^-12 * y * x^-1 * y ] T62.62 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * y, z^-2 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T62.63 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * y^5)^2, x^-7 * z^5 ] T62.64 : Triangle type {26,65,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^5 * y^-3 * x^-1 * z^4 * x^-1 * z^3 ] T62.65 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^-3 * y * x^-5 * z^4 * x^-1 * z * x^-1 ] T62.66 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-2 * x * z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-5 * x * z^-3 ] T62.67 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-3 * z * y^-7 * z * y^-1 * z * y^-6 ] T62.68 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^5 * z^-4, x^-3 * y^4 * x^-6 ] T62.69 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-15 * y * x^-1 * y * x^-1 * y * x^-10 * y * x^-2 ] T62.70 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 * x^-2 ] T62.71 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * x^-2 * y^-4 * z * y^-1 * z * y^-1 * z^3 ] T62.72 : Triangle type {32,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-4 * x^6 ] T62.73 : Triangle type {33,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, x^2 * z^-1 * x^2 * z^-3 ] T62.74 : Triangle type {33,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2, y * x^-4 * y * x^-1 * y^2 ] T62.75 : Triangle type {33,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, x^6 * y^-4 ] T62.76 : Triangle type {33,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^2 * z^-3 * x^4 * z^-1 * x^2 ] T62.77 : Triangle type {33,44,44} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-7 * z * x^-2 ] T62.78 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-6 * x * z^-4 ] T62.79 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-24 * y * z^-7 ] T62.80 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T62.81 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-3 * y^2 * x^-4 * z^4 * x^-2 ] T62.82 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^8 * y^-5 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T62.83 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T62.84 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-8 * y * x^-6 * y^3 * x^-5 ] T62.85 : Triangle type {63,126,126} Group order 126 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-63, y * z^-1 ] T62.86 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-37 * x * z^-4 ] T62.87 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^4 * z^-4, x^2 * z^-4 * x^3 * y^-3 * x^3 ] T62.88 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * y^-1 * x, y * z^-1 * y * z^-1 * y^5 * z^-4 ] T62.89 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-2 * y * x^-1 * y^5 * x^-2 * y^4 ] T62.90 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, x^-2 * y * x^-1 * y^5 * x^-2 * y^4 ] T62.91 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * x^-1 * y^5 ] T62.92 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x^-2 * y^-1, y^-54 * x * y^-8, x * z^-1 ] T62.93 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^2 * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T62.94 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 * y ] T62.95 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-1 * y, x^-2 * z^4 * y^-1 * x^-1 * z^4 * x^-2 ] T62.96 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^2 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T62.97 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-9 * x^2 * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T62.98 : Triangle type {125,125,125} Group order 125 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-9 * x^3 * y * z^-7 ] Genus 63 T63.1 : Triangle type {2,3,12} Group order 1488 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z * y^-1 * z^2 * y * x * z^2 * y * z^-1 * x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 ] T63.2 : Triangle type {2,4,66} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-50 * x * z^8 * y^-1 * z^-7 ] T63.3 : Triangle type {2,4,128} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-128 ] T63.4 : Triangle type {2,4,128} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-49 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T63.5 : Triangle type {2,4,252} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-22 * x * y^-1 * z^-103 ] T63.6 : Triangle type {2,7,9} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, y * x * z * y^2 * x * y^-1 * z^-1, z^-4 * x * y * z^-4 ] T63.7 : Triangle type {2,7,9} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, (y * z^-2 * y)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-2 ] T63.8 : Triangle type {2,7,9} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^-7, z * y * z^-2 * x * y^-1 * z^-3 * x ] T63.9 : Triangle type {2,8,44} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^23 * y * x * z * y * x * y^-1 * z^-5 * x * y^-1 * z^-3 * x * z^8 ] T63.10 : Triangle type {2,8,44} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^30 * y * z^-2 * x * y^-1 * z^-9 * x * z ] T63.11 : Triangle type {2,8,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-13 * x * z^17 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-2 ] T63.12 : Triangle type {2,8,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-12 * x * z^18 * y * x * y * z^-7 * x * z^2 * y^-1 ] T63.13 : Triangle type {2,12,21} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y, y * x * z * y^-3 * z^-2 * x * z^2 ] T63.14 : Triangle type {2,12,52} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^4 * y * x * z^3 * y * x * z * y^-1 * z^-6 * x * y^-1 * z^-3 * x * z^5 ] T63.15 : Triangle type {2,16,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * z * y^10 * x * y^-1 * z^-1 * y, z^10 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z ] T63.16 : Triangle type {2,16,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-1 * x * z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-3 ] T63.17 : Triangle type {2,16,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-5 * z^3)^2, z^-3 * x * z^7 * y * z^-1 * x * z * y^-1 * z^-4 ] T63.18 : Triangle type {2,16,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-5 * z^3)^2, z^3 * y * z^-2 * x * z^6 * y * x * z^3 * y^-1 * z^-1 * x ] T63.19 : Triangle type {2,20,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * z^4 * y * z^-1 * x * z^2 * y^-1 * z^-3, y^-8 * z^3 * y^-5 * z^3 * y^-1 ] T63.20 : Triangle type {2,35,35} Group order 280 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-2 * y, y^-3 * z^15 * y^-1 * z * y^-1 * z^2 * y^-10 * z^2 ] T63.21 : Triangle type {2,38,133} Group order 266 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * x * z^3 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-7 * z^3 * y^-4 * z^4 * y^-1 ] T63.22 : Triangle type {2,44,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-13 * y^11 * z^-3 * y^13 * z^-2 * y ] T63.23 : Triangle type {2,66,66} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-52 * y^11 * z^-1 ] T63.24 : Triangle type {2,86,129} Group order 258 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-12 * y^11 * z^-3 * y^16 ] T63.25 : Triangle type {2,127,254} Group order 254 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^109 * z^-18 ] T63.26 : Triangle type {2,128,128} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-34 * y^12 * z^-1 * y^15 * z^-1 ] T63.27 : Triangle type {2,128,128} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-109 ] T63.28 : Triangle type {2,252,252} Group order 252 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-108 ] T63.29 : Triangle type {3,3,6} Group order 744 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, x * z^-1 * x * z * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z * y * x * z * y ] T63.30 : Triangle type {3,3,127} Group order 381 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * x^-1 * z^2 * y^-1 * z^-3 * x^-1 * z^3 * y^-1 * z^-2 ] T63.31 : Triangle type {3,4,12} Group order 372 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * z^-2 ] T63.32 : Triangle type {3,64,192} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-53 * z * y^-8 * z^2 ] T63.33 : Triangle type {3,189,189} Group order 189 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-52 * z * y^-10 ] T63.34 : Triangle type {4,4,33} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-26 * x^-1 * y^-1 * x * z * y * z^-4 ] T63.35 : Triangle type {4,4,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-21 * x^-1 * z^3 * y * z^-7 ] T63.36 : Triangle type {4,4,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-21 * x * z^3 * y^-1 * z^-1 * x * z * y * z^-4 ] T63.37 : Triangle type {4,4,64} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-50 * x * y^-1 * x * y^-1 * z^-12 ] T63.38 : Triangle type {4,4,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-21 * x^-1 * z^3 * y * z^-1 * x * z * y^-1 * z^-4 ] T63.39 : Triangle type {4,4,126} Group order 252 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-49 * x * y^-1 * z^-13 ] T63.40 : Triangle type {4,6,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, z * y * z^-1 * y^2 * z^-1 * x * z ] T63.41 : Triangle type {4,8,14} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * z ] T63.42 : Triangle type {4,8,14} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^14 ] T63.43 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z^4 * y * z^-1, y^-1 * z * y^-1 * z * y^-8 ] T63.44 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z^4 * y * z^-1, y^-1 * z * y^-1 * z * y^-5 * z * y^-1 * z ] T63.45 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, (z^2 * y * x^-1 * z^5)^2 ] T63.46 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T63.47 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^3 * y * x^-1 * z^4 ] T63.48 : Triangle type {4,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y * x^-1 * z^4 ] T63.49 : Triangle type {4,16,24} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y * x^-1 * z * y * x * z^3 ] T63.50 : Triangle type {4,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-1 * z * y^4 * x^-1 * y^-2, x^-1 * z^6 * y * x^-1 * z * y^-1 * z^-3 ] T63.51 : Triangle type {4,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^4 * x^-1 * y^-3 * z, z * y * x^-1 * y * z^-4 * x * y * z^-1 * x * z^3 ] T63.52 : Triangle type {4,20,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^-1 * z^2 * y^-2 * z^-3 * y, y * z^-1 * y^7 * z^-1, z^3 * y * z^-1 * x^-1 * z^4 ] T63.53 : Triangle type {4,43,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^15 * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 ] T63.54 : Triangle type {4,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-21 * z^3 * y^-5 * z * y^-1 * z * y^-11 ] T63.55 : Triangle type {4,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^16 * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 ] T63.56 : Triangle type {4,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-7 * y^3 * z^-1 * y * z^-2 * y^8 ] T63.57 : Triangle type {4,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-14 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T63.58 : Triangle type {4,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-13 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T63.59 : Triangle type {6,8,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T63.60 : Triangle type {6,8,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T63.61 : Triangle type {6,12,84} Group order 168 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * z^-2 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * x * z^3 * y * z^-1 ] T63.62 : Triangle type {6,14,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * y * x * z^-3 ] T63.63 : Triangle type {6,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-1 * z^2, z * y^-3 * x * z^2 * y^-1 ] T63.64 : Triangle type {6,21,21} Group order 168 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y^-1 * z * y^-2 * x * z^2 * y^-1 ] T63.65 : Triangle type {6,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T63.66 : Triangle type {7,22,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^4 * z^-1 * y * z^-1 * y * z^-5 * y^9 ] T63.67 : Triangle type {7,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y ] T63.68 : Triangle type {7,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z * y^-5 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T63.69 : Triangle type {7,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-6 * y * z^-4 * y^7 * z^-1 * y * z^-1 ] T63.70 : Triangle type {8,8,22} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^3 * y^-1 * z^-7 * x^-1 * z * y * z^-1 ] T63.71 : Triangle type {8,8,22} Group order 176 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^7 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z^5 ] T63.72 : Triangle type {8,8,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-7 * x * y^-1 * z^-5 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T63.73 : Triangle type {8,8,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-3 * x^-1 * z^3 * y^-1 * z^-6 * x^-1 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T63.74 : Triangle type {8,19,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 ] T63.75 : Triangle type {8,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^6 * z^-1 * y^2 * z^-1 ] T63.76 : Triangle type {8,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^2 * z^-1 * y^2 * x^-1 * y * z^-1 * y * z^-1 * y ] T63.77 : Triangle type {8,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, z^-8 * y * z^-1 * y^2 * z^-1 * y^5 * z^-2 ] T63.78 : Triangle type {8,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^-1 * z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-7 * z ] T63.79 : Triangle type {8,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-3 * y * z^-1 * y * z^-4 * y^7 * z^-1 ] T63.80 : Triangle type {8,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^4 * z^-1 * y * z^-4 * y^8 ] T63.81 : Triangle type {8,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-8 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z ] T63.82 : Triangle type {9,9,19} Group order 171 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * x, z * y * x^2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^2, x^-9 ] T63.83 : Triangle type {9,9,19} Group order 171 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y * z^-1 * x * z^2, x^-9 ] T63.84 : Triangle type {9,9,19} Group order 171 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, y * z^-1 * x^2 * z^-1 * x^-1, x^-9 ] T63.85 : Triangle type {9,9,19} Group order 171 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, y^2 * x^3 * z^2 * y, x^-9 ] T63.86 : Triangle type {9,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-4 * y^7 ] T63.87 : Triangle type {9,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-4 * y * z^-4 * y^3 * z^-4 ] T63.88 : Triangle type {10,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, y^2 * z^-4 * y * z^-2 * y^4 * z^-2 * y ] T63.89 : Triangle type {10,16,16} Group order 160 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^-4 * z * x^-1 * y, y^2 * z^-1 * y * x^-1 * y^2 * z^-2 ] T63.90 : Triangle type {10,16,16} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^6 * z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-1 ] T63.91 : Triangle type {10,16,16} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^10 ] T63.92 : Triangle type {10,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-3 * y^5 * z^-3 ] T63.93 : Triangle type {10,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-7 * y^3 * z^-4 ] T63.94 : Triangle type {12,12,26} Group order 156 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y^-1 * x^3 * y^-2 ] T63.95 : Triangle type {12,12,26} Group order 156 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, (y^-1 * x)^3, y * x^-3 * y * x^-1 * z ] T63.96 : Triangle type {12,12,26} Group order 156 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, y * z^-1 * x^-1 * z * y * z^-4 * x^-1 * y * x^-1 * z^4 ] T63.97 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, (y * z^-1 * y)^2 ] T63.98 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x * y^-1 * x * y^-1 * z^-1, (y * z^-1 * y)^2 ] T63.99 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-2 * z^2 * y^-1 * z * y^-4 * z * y^-1 ] T63.100 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^7, x^4 * z^-4 * x^2 * y^-4 * x^2 ] T63.101 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^-2 * z * x^-4 * z * x^-1 * z^3 * x^-1 * z ] T63.102 : Triangle type {12,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3, y^-1 * x * y^-1 * x^3 * y^-4 ] T63.103 : Triangle type {15,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-1 * y^5, z^2 * x^-5 * y^-1 * z^6 ] T63.104 : Triangle type {15,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, z^-7 * x^7 * z^-2 ] T63.105 : Triangle type {15,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, y^2 * x^-1 * y * x^-1 * y^5 * x^-6 * y ] T63.106 : Triangle type {16,16,72} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * y * z^-2 * x^2 * z^-1 * y * z^-2, z * y * z^-3 * x^-1 * y * z^-2 * x * z ] T63.107 : Triangle type {16,16,72} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * y * z^-2 * x^2 * z^-1 * y * z^-2, z^4 * y^-1 * x * z^4 ] T63.108 : Triangle type {16,16,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-3 * x * z^4 ] T63.109 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y^2, z * x^-7 * z^6 ] T63.110 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^3 * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T63.111 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * z^-1 * x * y^-3 * x^5 * z^-2 * x^6 ] T63.112 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^-1 * z * x^-7 * z^4 * x^-1 * z^2 ] T63.113 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^9 * y^-5 * x * y^-1 * x * y^-1 * x^3 ] T63.114 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-7 ] T63.115 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-3 * y^3, x * z^-1 * x * z^-4 * x^6 * z^-2 ] T63.116 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, y^9 * x^-1 * y^5 ] T63.117 : Triangle type {19,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-4 * y^2, z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T63.118 : Triangle type {20,20,70} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, z^-1 * x * z^-1 * y * z^-2 * x^2 * z^-4 ] T63.119 : Triangle type {20,20,70} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^6 * y^-2, z * y^-1 * z^-2 * x * z^3 ] T63.120 : Triangle type {20,28,35} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-4 * y, z^-6 * y^4 * z^-4 ] T63.121 : Triangle type {22,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^2 * x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T63.122 : Triangle type {22,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T63.123 : Triangle type {22,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^6 * z^-3, x^2 * z^-4 * x^5 * z^-2 ] T63.124 : Triangle type {22,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-1 * y^5 * x^-7 * y^2 ] T63.125 : Triangle type {22,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y * x^-7 * y^2 * x^-5 * y^3 * x^-5 ] T63.126 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^2 * x^-1 * z * x^-1 * z^4 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T63.127 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^7 * x^-1 * y * x^-1 * y^5 * x^-1 * y^7 ] T63.128 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T63.129 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, y^-1 * z^4 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T63.130 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-5 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T63.131 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, x^-7 * z^4 * x^-1 ] T63.132 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-16 * y * x^-1 * y * x^-1 * y * x^-10 * y * x^-2 ] T63.133 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T63.134 : Triangle type {33,44,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y^5 * z^-4, x^-3 * y^4 * x^-6 ] T63.135 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-12 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-3 * y^6 ] T63.136 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-1 * x^7 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T63.137 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^7 * x^-1 * y^5 ] T63.138 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x * z^-1 * x * z^-4 * x^7 * z^-1 ] T63.139 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-10 * x^2 * y * z^-7 ] T63.140 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-13 * y^2 * x^3 * z^-6 ] T63.141 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^3 * z^-3 * x^3 * z^-4 * x * y^-1 * x^3 ] T63.142 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, x^-1 * y * x^-1 * y^5 * x^-3 * y^3 ] T63.143 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-2 * y^4, z^-5 * y^3 * z^-4 ] T63.144 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^5 * z^-1 * y^9 ] T63.145 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-4 * y * z^-1 * y * z^-1 * y^4 * x * z^-6 ] T63.146 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^15 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T63.147 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^3 * z^-4 * x^5 * y^-1 * x^3 ] T63.148 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * y^-9 * z * y^-1 * z * y^-1 * z^3 ] T63.149 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-29 * y * x^-8 * z * x^-5 ] T63.150 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-5 * y, z^-5 * x^2 * z^-4 ] T63.151 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^5 * z^-4, x * z^-3 * x^8 ] T63.152 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-4 * x^5 * y^-1 * x ] T63.153 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y^2 * x^-7 * y * x^-4 ] T63.154 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-2 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T63.155 : Triangle type {43,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x^2 ] T63.156 : Triangle type {44,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, z^-2 * x^3 * z^-2 * x ] T63.157 : Triangle type {44,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * y^-1 * z^-2, y^-3 * x^2 * y^-3 ] T63.158 : Triangle type {44,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^7 * z^-1 * x * z^-1 ] T63.159 : Triangle type {44,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^9 * y^-2 * x^5 ] T63.160 : Triangle type {44,44,66} Group order 132 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^6 * y^-1 * z^4 * x^-1 * z^4 * x^-1 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z ] T63.161 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-64, y * z^-1 ] T63.162 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-15 * y * x^-4 ] T63.163 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-4 * y * x^-1 * z^3 * x^-9 ] T63.164 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^9 * x^-1 * y^5 ] T63.165 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-4 * y^2, z^-2 * x * z^-4 * x^2 * z^-4 ] T63.166 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^15 * z^-1 * y^10 ] T63.167 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^2 * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T63.168 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, y^2 * x^-1 * y^5 * x^-1 * y^5 ] T63.169 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T63.170 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, z^-6 * x * z^-4 ] T63.171 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, x^2 * z^-4 * x^5 * z^-2 ] T63.172 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-38 * x * z^-4 ] T63.173 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x * z^-5 * x * z^-3 ] T63.174 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-8 * z^4 * x^-2 ] T63.175 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^9 * z^-1 ] T63.176 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^2 * x^-8, z^-6 * y^2 * z^-4 ] T63.177 : Triangle type {64,128,128} Group order 128 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^2 * y^-1 * x^7 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T63.178 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x^-2 * y^-1, y^-55 * x * y^-8, x * z^-1 ] T63.179 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-30 * x * y^-5 * x * y^-6 ] T63.180 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^13 * y^-2 * x * y^-4 * x^3 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T63.181 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x * y^-3 * x * y^-5 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T63.182 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-8 * x * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T63.183 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-1 * x^7 * y^-5 * x * y^-1 * x^4 ] T63.184 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-6 * y ] T63.185 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y^5 * x^-5 * y ] T63.186 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-2 * y^5 * x^-1 * y^5 ] T63.187 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y^2, z^-6 * x * z^-4 ] T63.188 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-4 * y^2, z^-2 * x * z^-4 * x * y * z^-4 ] T63.189 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^3 * z^-4 * x^7 * z^-1 * x ] T63.190 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-4 * y^2, z^-2 * y * z^-1 * y^5 * z^-4 ] T63.191 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^5 * z^-4 * x^5 * y^-1 * x^5 ] T63.192 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-6 * y * z^-10 * y^3 * z^-7 ] T63.193 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^3 * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T63.194 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-1 * y, z^-6 * x^5 * z^-2 ] T63.195 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^4 * x^-3 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T63.196 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^4 * z^-4, x^-3 * y^4 * x^-6 ] T63.197 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-6 * z^3 * x^-4 * y^3 * x^-1 * z * x^-1 * z * x^-2 ] T63.198 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^3 * x^-1 * y^5 * x^-1 * y^5 ] T63.199 : Triangle type {127,127,127} Group order 127 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, y * z^-1 * y * z^-1 * y^9 ] Genus 64 T64.1 : Triangle type {2,3,12} Group order 1512 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * x * z^2 * y^2 * z^-1 * x * z^2 * y^-1 * z^-1, x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T64.2 : Triangle type {2,3,18} Group order 1134 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^-5 * x * z * y^-1 * x * z^3 * y^-1 * z^-1, z^-2 * x * z * y * z^-2 * x * z * y^-2 * z^-2 * x * y^-1 * z^-1, z^2 * y * x * z * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x ] T64.3 : Triangle type {2,3,24} Group order 1008 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x, x * z * y * x * z^4 * y * x * z * y^-1 * z^4 * y^-1 * z^-1 ] T64.4 : Triangle type {2,3,24} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-2 * x * z^4 * y * x * z * y^-1 * z^-2 * x * y^-1 * z^-2, z^-1 * x * z * y * z^-1 * x * z^2 * y * x * z * y^-1 * x * z * y^-1 * z^-3 ] T64.5 : Triangle type {2,3,24} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^-1 * x * z^2 * y * z^-1 * x * z^3 * y * x * z * x * z^2 * y^-1 * z^-2 ] T64.6 : Triangle type {2,3,42} Group order 882 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^10 * y * z^-9 * x * z^3 * y^-1 * z^-3 ] T64.7 : Triangle type {2,4,18} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-18 ] T64.8 : Triangle type {2,4,18} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y * z^-1)^6, x * z^8 * y * z^-1 * x * z^3 * y^-1 * z^-4 ] T64.9 : Triangle type {2,4,130} Group order 520 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-130 ] T64.10 : Triangle type {2,4,256} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-23 * x * y^-1 * z^-104 ] T64.11 : Triangle type {2,5,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^8, (z * y^-1 * z)^3, y^-1 * z * y^2 * z^-3 * y * x * y^-1 * z^3 ] T64.12 : Triangle type {2,5,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^8 ] T64.13 : Triangle type {2,6,6} Group order 756 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T64.14 : Triangle type {2,6,6} Group order 756 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z^2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2 * x ] T64.15 : Triangle type {2,6,6} Group order 756 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, y * z^-2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T64.16 : Triangle type {2,6,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^-2 * y * x * y^-1 * z^-2 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T64.17 : Triangle type {2,6,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, y^-1 * z * y^-2 * z * y^-2 * z^-1 * y * x * y^-2 * z^-1 * x ] T64.18 : Triangle type {2,6,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z^2 * y * z^-2 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-1 * x ] T64.19 : Triangle type {2,6,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-4 * y ] T64.20 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, (y * z^-1 * y * z^-1 * y)^2, z^-1 * x * z^2 * y^-2 * z^2 * y^-1 * z^-2 ] T64.21 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, (y * z^-1 * y * z^-1 * y)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T64.22 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-8 * x * z * y * z^-1 * x * z^2 * y * z^-2 * x * z * y^-1 * z^-6 ] T64.23 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^3 * y^-1 * z^-4, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y ] T64.24 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-4 * x * z^6 * y * z^-3 * x * y * z^-9 ] T64.25 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-6 * x * z^2 * y * x * z * y * z^-4 * x * y * z^-6 * x * y^-1 * z^-1 ] T64.26 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T64.27 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-13 * x * y^-1 * z^-6 * x * z * y^-1 * z^-2 ] T64.28 : Triangle type {2,6,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-2 * y * z^-1, z^6 * y^2 * x * z^5 ] T64.29 : Triangle type {2,6,30} Group order 420 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^-2 * y * x * y^-1 * z^-2 * y * z^-1, z^2 * y * z^-1 * x * z * y * z^-2 * x * z^2 ] T64.30 : Triangle type {2,6,30} Group order 420 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^2 * y * x * z * y * x * y * x * z * y^-1 * z^-2 * x ] T64.31 : Triangle type {2,6,66} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-2 * x * z^9 * y * x * y * x * z^4 * y^-1 * z^-4 ] T64.32 : Triangle type {2,6,66} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-33 * x * z^18 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T64.33 : Triangle type {2,6,66} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-66 ] T64.34 : Triangle type {2,6,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^50 * y * z^-1 * x * y^-1 * z^-9 * x * z^2 ] T64.35 : Triangle type {2,8,12} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y * x * z * y^3 * z^-1 * x * z^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T64.36 : Triangle type {2,8,12} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y * z^-2 * y^3 * z^-1 * y * z^-1 * y ] T64.37 : Triangle type {2,8,12} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * x * y^-1 * z ] T64.38 : Triangle type {2,8,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T64.39 : Triangle type {2,8,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, z^-2 * y * x * y^-2 * z^-2 * y * z^-1 * y ] T64.40 : Triangle type {2,9,18} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T64.41 : Triangle type {2,10,34} Group order 340 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^18 * y * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^3 ] T64.42 : Triangle type {2,10,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^19 * y * z^-2 * x * y * z^-7 * x * z^2 ] T64.43 : Triangle type {2,12,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-4 * z^-1 * y^3, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-1 * x * z^7 * y * z^-2 * x * z * y^-1 * z^-2 ] T64.44 : Triangle type {2,12,15} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z * y^-4 * z^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^3 * y^3 * z^-1 * y^2 * x ] T64.45 : Triangle type {2,12,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y^-3 * z^-1 * x * y^-2, y * z^-2 * x * y^-1 * z^-2 * y * z^-1 ] T64.46 : Triangle type {2,12,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, y^-1 * z * y^-3 * z^-1 * x * z * y^-1 ] T64.47 : Triangle type {2,12,78} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^14 * y * z^-3 * x * z^8 ] T64.48 : Triangle type {2,18,18} Group order 324 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * y^-4 * z^-1 * y * z^-2, y^-3 * z * y^-2 * z * y^-6 * z * y^-1 * z^3 ] T64.49 : Triangle type {2,18,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-3 * z^3 * y^-6 * z^2 * y^-2 ] T64.50 : Triangle type {2,18,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z^5 * y^-5 * z * y^-3 * z^2 * y^-1 ] T64.51 : Triangle type {2,18,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-1 * z^2 * y^-1 * z^2 * y^-4 * z * y^-6 * z, y^3 * x * y^-5 * z * y^5 * x * y^-2 * z * y ] T64.52 : Triangle type {2,18,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-2 * z^-2 * x * y^-1 * z ] T64.53 : Triangle type {2,18,18} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z^-6 * x * z^5 * y * z^-1 * x * y^-1 * z^-4, y^-6 * z^-1 * x * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-2 ] T64.54 : Triangle type {2,18,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * z^6 * y * x * z * y^-1 * z^-4, y^-6 * z^3 * y^-5 * z^3 * y^-1 ] T64.55 : Triangle type {2,21,42} Group order 294 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-1 * z * y^-2 * z * y^-16 ] T64.56 : Triangle type {2,21,42} Group order 294 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-2 * z * y^7 * x * y^-4, y^-4 * z * y^-1 * z^2 * y^-4 * z * y^-8 ] T64.57 : Triangle type {2,28,70} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^6 * y^-4 * z^4 ] T64.58 : Triangle type {2,34,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-2 * y^11 * z^-3 * y^17 * z^-1 ] T64.59 : Triangle type {2,45,90} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-16 * y^9 * z^-1 * y * z^-2 * y * z^-13 * y ] T64.60 : Triangle type {2,66,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-36 * y^12 * z^-1 * y^15 * z^-1 ] T64.61 : Triangle type {2,129,258} Group order 258 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^110 * z^-18 * y ] T64.62 : Triangle type {2,130,130} Group order 260 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^19 * y^-109 * z ] T64.63 : Triangle type {2,256,256} Group order 256 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-108 * z ] T64.64 : Triangle type {3,3,6} Group order 756 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 ] T64.65 : Triangle type {3,3,9} Group order 567 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z * y * x * z * x^-1 * z * y * x^-2 * y^-1 * x * z * y * z^-1 * y * x ] T64.66 : Triangle type {3,3,9} Group order 567 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, y * x * z * y * x * z * y * x^-2 * z * y * z^-1 * x^-1 * y^-1 * x * z ] T64.67 : Triangle type {3,3,12} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, x * z * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x * z^-1 ] T64.68 : Triangle type {3,3,12} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2, y^-1 * z^-1 * x^-1 * z * y^-1 * x * z^2 * y * x ] T64.69 : Triangle type {3,3,12} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T64.70 : Triangle type {3,3,12} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1, x^-1 * z^2 * x^-1 * y^-1 * x * z * y^-1 * x * z ] T64.71 : Triangle type {3,3,12} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z * y^-1 * z^-1)^2, (z^-1 * x^-1 * y^-1)^3 ] T64.72 : Triangle type {3,3,21} Group order 441 Chiral action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T64.73 : Triangle type {3,3,21} Group order 441 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x^-1 * z^6 * y^-1 * z^-5 ] T64.74 : Triangle type {3,3,129} Group order 387 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x * z^3 * y^-1 * z^-1 * x * z^-5 ] T64.75 : Triangle type {3,4,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, x^-1 * y^-1 * x * z * y^-1 * z^-1 * x^-1 * z * x * z^-1 * x * z^2 * y^-1 * z^-1 ] T64.76 : Triangle type {3,4,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z^3 * y * x * z^-4, x^-1 * z * y * z^-1 * x^-1 * z * x^-1 * z^-1 * x * z^2 * y * z^-1 ] T64.77 : Triangle type {3,4,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z * y^-1 * x * y^-1 * z^-4 * x * z^5 ] T64.78 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T64.79 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x * z * y * x * z^2 * y ] T64.80 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T64.81 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * x^-1 * z * y * x * z * y^-1 * z^-1 ] T64.82 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^2 * z^-1 * y^2 * x^-1 * y^-1 * z * y^-1 * z^2 ] T64.83 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T64.84 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T64.85 : Triangle type {3,6,6} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * x * z * y * z^-1 * y * z^-1 * x^-1 * y * x * z^-1 * x^-1 * y^-1 * z^-1 * y * z^-1 ] T64.86 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z * y^2 * x^-1 * z^2, x * z * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T64.87 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, (x^-1 * z^2 * y)^2 ] T64.88 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, y^6, x^-1 * z^2 * y^-1 * x * z^3 ] T64.89 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, (y * z^-1 * y)^2 ] T64.90 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, y^-1 * z * y^-2 * x * z * y^-1 * x, (x * z * y^2)^2 ] T64.91 : Triangle type {3,6,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z * y^2 * x^-1 * z^2, y^-1 * z^-2 * y * x^-1 * y^-1 * z^-1 * x * z ] T64.92 : Triangle type {3,6,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z * y^2 * x^-1 * y^-1 * z^-1 * x ] T64.93 : Triangle type {3,6,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, (x * z * y)^2, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T64.94 : Triangle type {3,6,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^6, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T64.95 : Triangle type {3,6,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z * y^-1 * z^-1 * x * z * y^-1 ] T64.96 : Triangle type {3,6,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1 ] T64.97 : Triangle type {3,6,14} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, y^-1 * z^-2 * x^-1 * z^3, y^-1 * z^-1 * y^2 * x * y^-1 * z^-1 * x^-1 ] T64.98 : Triangle type {3,6,14} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, y^-1 * z^-2 * x^-1 * z^3, y * x^-1 * y^-2 * x * y^-2 * z^-1 ] T64.99 : Triangle type {3,6,14} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^2 * y^2 * x^-1 * z^4 ] T64.100 : Triangle type {3,6,86} Group order 258 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * y * x^-1 * y * z^-3 ] T64.101 : Triangle type {3,12,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^-1 * z * y^-2 * z^2 * y^-1 * x^-1 * y^-1 * z^2 * y^-2 ] T64.102 : Triangle type {3,12,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^-2, y * z^-2 * x^-1 * y^-2 * z, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-3 ] T64.103 : Triangle type {3,12,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * x * z^2 * y, y^-2 * z^4 * y^-4 * z^2 ] T64.104 : Triangle type {3,12,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, x^-1 * z * y^-1 * z * y^3 * z^-1 * y * z^-1 * y ] T64.105 : Triangle type {3,12,12} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * y^-1 * z^2, z^2 * y^-1 * z^2 * x^-1 * y^-1 * z^2 * y^-1 * z * y^-1 * z ] T64.106 : Triangle type {3,18,36} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * x^-1 * y * x * z, x^-1 * z * y * x^-1 * z^3 ] T64.107 : Triangle type {3,18,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T64.108 : Triangle type {3,18,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-2 * y^5 * z^-2 * y * z^-2 * y^3 ] T64.109 : Triangle type {3,18,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z^2 * y^-1 * x * z^3, x^-1 * y * x^-1 * y * x^-1 * y * z^-1 * y * z^-1 ] T64.110 : Triangle type {3,18,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-5 * x^-1 * y^-1 * z * y^-1 * z ] T64.111 : Triangle type {3,24,24} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * y^-2, y * x^-1 * y^-1 * x * y^-1 * z^-1, z^5 * y^-1 * z^2 * y^-1 * z^3 * y^-12 ] T64.112 : Triangle type {3,24,24} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z * y^-1 * z, (y * z^-2 * y)^2 ] T64.113 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T64.114 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-7 * y^10 * z^-1 * y^3 * z^-1 * y ] T64.115 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T64.116 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, z^-1 * y^4 * z^-3 ] T64.117 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T64.118 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-7 * y * z^-2 * y^6 * z^-5 * y * z^-1 ] T64.119 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, z^-2 * y^3 * z^-2 * y ] T64.120 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, z^-8 * y^3 * z^-1 * y^6 * z^-1 * y^5 ] T64.121 : Triangle type {3,24,24} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-7 * y * z^-2 * y^2 * z^-1 * y * z^-2 * y^3 * z^-1 * y * z^-2 * y ] T64.122 : Triangle type {3,30,30} Group order 210 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y * x^-1 * y * x^-1 * y * x * z * y^-1, y^-1 * z^2 * y^-1 * z * x^-1 * z * y^-4 ] T64.123 : Triangle type {3,30,30} Group order 210 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z * y^-1 * z, (y * z^-1 * y^3)^2 ] T64.124 : Triangle type {3,34,51} Group order 204 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-1 * y^10 * z^-2 * y^3 ] T64.125 : Triangle type {3,65,195} Group order 195 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-54 * z * y^-8 * z^2 ] T64.126 : Triangle type {3,66,66} Group order 198 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^53 * y^-10 * z * y^-1 ] T64.127 : Triangle type {3,66,66} Group order 198 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-5 * y * z^-2 * y^9 * z^-1 * y^3 ] T64.128 : Triangle type {3,66,66} Group order 198 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-55 * z * y^-8 * z^2 ] T64.129 : Triangle type {3,192,192} Group order 192 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-53 * z * y^-9 * z ] T64.130 : Triangle type {4,4,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-9 ] T64.131 : Triangle type {4,4,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, z^4 * y^-1 * x^-1 * z^4 ] T64.132 : Triangle type {4,4,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y * z^-6 * x * z^4 ] T64.133 : Triangle type {4,4,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * y * z^-1 * x * z^2 ] T64.134 : Triangle type {4,4,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-5 * x * z^-1 * y * z^-2 ] T64.135 : Triangle type {4,4,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z^6 * y^-1 ] T64.136 : Triangle type {4,4,65} Group order 260 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-51 * x * y^-1 * x * y^-1 * z^-12 ] T64.137 : Triangle type {4,4,128} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-50 * x * y^-1 * z^-13 ] T64.138 : Triangle type {4,5,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^-5, z^2 * y^-1 * x^-1 * z^2 ] T64.139 : Triangle type {4,5,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^-5, z^2 * y^-1 * x^-1 * z^2 ] T64.140 : Triangle type {4,5,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^-5, z^2 * y^-1 * x^-1 * z^2, (z^-1 * x)^3, y * z^-1 * y * x^-2 * z * y^-1 * z * x^-1 ] T64.141 : Triangle type {4,6,12} Group order 252 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, y * x * z * y^-1 * z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x * z ] T64.142 : Triangle type {4,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^2 * y^-1 * x * z^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T64.143 : Triangle type {4,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T64.144 : Triangle type {4,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * y^-1 * z * y^-1, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T64.145 : Triangle type {4,8,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-7 * x * z^5 * y^-1 * z^-13 ] T64.146 : Triangle type {4,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * x * z, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-3 * x * y^-4 ] T64.147 : Triangle type {4,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y)^2, x^-1 * y * x^-2 * y^-2 * z^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y * z^-1 * y ] T64.148 : Triangle type {4,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * y^-1 * x * z^-1 ] T64.149 : Triangle type {4,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * z * y^-1, x * z * y^-1 * x * y^-1 * z^-1 ] T64.150 : Triangle type {4,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * y^-2 * x * z^-2, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * y * z^-2 ] T64.151 : Triangle type {4,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * z * y ] T64.152 : Triangle type {4,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T64.153 : Triangle type {4,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y * z^-2, y^-2 * z * x^-1 * y^-3 ] T64.154 : Triangle type {4,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * y * z^-2, y^-2 * z * x^-1 * y^-3, x^-1 * z * y^2 * x * z * y^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T64.155 : Triangle type {4,12,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x * z^7 * y * x^-1 * z^5 ] T64.156 : Triangle type {4,14,28} Group order 196 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^4 * x * z^-1 * y^2 ] T64.157 : Triangle type {4,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * x * y^-3 * z * y^-1 * z^2 ] T64.158 : Triangle type {4,36,45} Group order 180 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-4 * z^3 ] T64.159 : Triangle type {4,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y^-4 * z^3 ] T64.160 : Triangle type {4,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-1 * y * z^-2 * y^6 * z^-1 * y * z^-2 * y^8 ] T64.161 : Triangle type {4,86,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^21 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y^2 ] T64.162 : Triangle type {5,33,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T64.163 : Triangle type {5,34,34} Group order 170 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z * y^-1 * z * y^-1 * z^2 * y^-3 * z * y^-2 * z * y^-1 * z * y^-5 * z * y^-1 * z * y^-11 ] T64.164 : Triangle type {5,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T64.165 : Triangle type {5,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T64.166 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, y * x * z * y * x^-1 * y^-1 * z^-1 * x * z ] T64.167 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * y^-1 * z, y * x * y^-1 * x * z^-2 ] T64.168 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, y^6, z^6, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T64.169 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T64.170 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^6, z * y^-1 * z^-1 * x^-1 * z * y^-2 ] T64.171 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T64.172 : Triangle type {6,6,6} Group order 252 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, z * y^-1 * z * y^2 * x^-1 * z * y^-1 * z * y^-1 * z ] T64.173 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (x * y^-2)^2, (x * z * y^-1)^2, y^6 ] T64.174 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, z^-1 * y * x^2 * z^-1 * y, z^12 ] T64.175 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (x * y^-2)^2, y^6, (x * z * y)^2 ] T64.176 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, z * y * x^2 * z * y^-1 ] T64.177 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, z^-1 * y * x^-2 * y^-2 * x, z * y * x^-2 * y * x * y^-1 ] T64.178 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, (x * z * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T64.179 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1 ] T64.180 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, y^6, x^-1 * z * y * x * y^-1 * z^-1 ] T64.181 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^-4 * x^-1 * y * x * y^-1 * x * z^5 * y ] T64.182 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T64.183 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y^6, y^-1 * z^-1 * y * x * z * x^-1 ] T64.184 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, y^-1 * z^-5 * x^-1 * z * y * z^-3 * x * z ] T64.185 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^12 ] T64.186 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z * y^2 * x^-1 * z * x^-1 ] T64.187 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, y * z^-1 * x * z^4 * y * x^-1 * z^5 ] T64.188 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T64.189 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z^-12 ] T64.190 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^-1 * y * x^-2 * y^-2 * x, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T64.191 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z * y^2 * x^-1 * z * y^-1 * z ] T64.192 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, y^-1 * z^-1 * x * z^2 * y * x * z * y^-1 * x * z^5 ] T64.193 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, x^-1 * z * x^-2 * z * y * z^-1 ] T64.194 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^-1 * x * y^-1 * x * z^2, y^6 ] T64.195 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^-4 * x * y^-1 * x * y^-1 * z^-6 ] T64.196 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, x^6, z^3 * y * z^-3 * x^-1 * z^3 * y^-1 * x * z ] T64.197 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * y^-1 * x)^2, z^2 * y * z^-5 * x * z^4 ] T64.198 : Triangle type {6,6,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * x^2 * z^3 ] T64.199 : Triangle type {6,6,15} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * z^-2, z * y^-2 * x * z * x^-1, x * z * y * x^-1 * z * y * z^-1 ] T64.200 : Triangle type {6,6,15} Group order 210 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 ] T64.201 : Triangle type {6,6,33} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-1 * x * z^2 * y^-1 * z^-2 * x^-1 * z * y * z^-3 ] T64.202 : Triangle type {6,6,33} Group order 198 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-20 * x * z^5 * y^-1 * x^-1 * y * z^-6 ] T64.203 : Triangle type {6,6,33} Group order 198 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^13 * y^-1 * z^-6 * x * z^4 * y * x * z^8 ] T64.204 : Triangle type {6,6,96} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-10 * x^-1 * z^12 * y^-1 * x * z * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z * y ] T64.205 : Triangle type {6,8,8} Group order 216 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^-2 * z^-1 * x^-1 * y^-2 * z ] T64.206 : Triangle type {6,8,8} Group order 216 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T64.207 : Triangle type {6,8,8} Group order 216 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z^-1 * y^2 * x^-1 * z * y^2 ] T64.208 : Triangle type {6,8,8} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, y * x^-1 * y * x^-1 * y^-1 * x * z ] T64.209 : Triangle type {6,8,8} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1 ] T64.210 : Triangle type {6,10,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y * z^-2 * x^-1 * z^3, y^10 ] T64.211 : Triangle type {6,10,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^10 ] T64.212 : Triangle type {6,10,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^10 ] T64.213 : Triangle type {6,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-1 * z * y^-4 * z * y^-1 * z * y^-1 * z ] T64.214 : Triangle type {6,15,15} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-5 * z * y^-2 * x * y^-1 * z * y^-1 * z * y^-1 ] T64.215 : Triangle type {6,15,15} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, (z^-1 * y)^3, y^2 * x^-2 * y^3 ] T64.216 : Triangle type {6,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^-4 * x^-1 * z^3 ] T64.217 : Triangle type {6,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, y^-1 * x * y^-1 * x * y^-1 * z ] T64.218 : Triangle type {6,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, x^6, x * y^-2 * x * z * y^-1, x * z^-1 * y * x * z^-2, z^-1 * y^2 * x^-1 * z * y^2 ] T64.219 : Triangle type {6,27,54} Group order 162 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z * y^-3 * x^-1 * z^4 ] T64.220 : Triangle type {6,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^3 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T64.221 : Triangle type {6,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-4 * z^3 ] T64.222 : Triangle type {6,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-5 * z * y^-1 ] T64.223 : Triangle type {6,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T64.224 : Triangle type {6,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T64.225 : Triangle type {8,12,24} Group order 168 Chiral action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, x^8, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T64.226 : Triangle type {8,12,24} Group order 168 Chiral action Defining relators: [ x * y * z, y * x^-2 * y^2, (z^-1 * x)^3, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T64.227 : Triangle type {9,9,9} Group order 189 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T64.228 : Triangle type {9,9,9} Group order 189 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 ] T64.229 : Triangle type {9,17,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z * y^-6 * z^5 * y^-1 * z * y^-1 * z^2 ] T64.230 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-1 * z * y^-2 * z^2 * y^-1 * z^3 * y^-3 * z * y^-1 * z^2 * y^-1 ] T64.231 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, y * x^2 * z, y^-1 * x^3 * z^-1 * x, y^-4 * z^2 * y^-1 * z * y^-1 * z * y^-7 * z ] T64.232 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, x * y^-2 * x * z^-1 * y, x * z * y^-1 * x * z^-2, (y * z^-2)^2 ] T64.233 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, x * y^-2 * x * z^-1 * y, x * z * y^-1 * x * z^-2, (z^-1 * y)^3 ] T64.234 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y * z^-1 * y^2 * z^-2, x^-9 ] T64.235 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z * y^-1 * z * x^-1 * z^3, x^-9 ] T64.236 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * z, z * y * x^2 * z^2, x^-9 ] T64.237 : Triangle type {9,18,18} Group order 162 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, z^-2 * x^2 * z^-1 * y, z * x^-3 * y^-2 * z ] T64.238 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, y * x^-3 * z * x^-2, x^-9 ] T64.239 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-5 * z * y^-1 ] T64.240 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-9 ] T64.241 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^9, x^-1 * y^-1 * x^4 * z * x^-3 ] T64.242 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-9 ] T64.243 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, (z^-1 * y)^3, y^-1 * z * y * x^-1 * y^-3 ] T64.244 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^-1 * z^-1 * y^2 * x * y^-1 * z^-1 * x ] T64.245 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, (z^-1 * y)^3, y * z^-2 * x^-1 * y^-2 * z ] T64.246 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^-1 * z * y * x^-1 * y^-3, x^-9 ] T64.247 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T64.248 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^-9 ] T64.249 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^3 * z^-2 ] T64.250 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, z^-1 * x * z^-1 * x * z * y^-1 ] T64.251 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3 ] T64.252 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, y * z^-2 * x^-1 * y * z^-2 ] T64.253 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^-1 * z^-1 ] T64.254 : Triangle type {9,18,18} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * x^-1 * y * z^-2 ] T64.255 : Triangle type {9,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^3 * z^-1 * y * z^-4 * y^7 ] T64.256 : Triangle type {9,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-2 ] T64.257 : Triangle type {10,10,17} Group order 170 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-3 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T64.258 : Triangle type {10,10,80} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-2 * x * z^6 * y^-1 * z^-1 * x^-1 * z * y * z^-4 ] T64.259 : Triangle type {10,10,80} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-2 * x * z^2 * y^-1 * z^-4 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-2 ] T64.260 : Triangle type {10,16,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^4 * x^-1 * y^-3 * z^-1, x^10 ] T64.261 : Triangle type {12,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * z * y^-1, y^-1 * z * y^-1 * x * z * x^-1, y * x^-3 * z * x^-2 ] T64.262 : Triangle type {12,12,12} Group order 168 Chiral action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-4 * y * x * z^-1, z * y^2 * x^-1 * z^2 * y^-1 ] T64.263 : Triangle type {12,12,39} Group order 156 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-1 * x^-2 * z * y^-1 * z ] T64.264 : Triangle type {12,12,39} Group order 156 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 * y * x * z^4 ] T64.265 : Triangle type {12,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x * y^-1 * x^3 * y^-1 * z^-2 ] T64.266 : Triangle type {12,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x * y^-1 * x^3 * y^-1 * z^-2 ] T64.267 : Triangle type {12,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^3 * z^-4, x^4 * z^-4 * x^2 * y^-4 * x^2 ] T64.268 : Triangle type {12,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, x^2 * y^-1 * x * z^-1 * x^3 * z^-4 ] T64.269 : Triangle type {12,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-1 * z * y^-5 * x * y^-2 * z * y^-2 ] T64.270 : Triangle type {14,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^4 * z^-3 * x^4 * y^-3 * x^3 ] T64.271 : Triangle type {14,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, y^-2 * x^5 * y^-6 * x * y^-2 ] T64.272 : Triangle type {14,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^-1 * y^6 * x^-1 * y^4 ] T64.273 : Triangle type {16,18,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-1 * y * x^-1 * y^6 * x^-6 * y^2 ] T64.274 : Triangle type {16,24,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3, y^-2 * x^4 * y^-4 ] T64.275 : Triangle type {16,24,48} Group order 144 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-3 * x * z^-1 * y * x * z^-4 ] T64.276 : Triangle type {16,24,48} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^-2 * y * x^-8 * y^2 * x^-4 ] T64.277 : Triangle type {16,24,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3, x^-6 * y^3 ] T64.278 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^2 * x^-7 * z^4 * x^-1 * z^2 ] T64.279 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, z^-6 * x^5 * z^-2 ] T64.280 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T64.281 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-2 * y^4, z^2 * x^-6 * z^6 ] T64.282 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^-2 * y * x^-1 * y^5 * x^-4 * y^2 ] T64.283 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 ] T64.284 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-3 * y * x^-1 * y * x^-1 * z^3 * x^-8 * y * x^-1 ] T64.285 : Triangle type {17,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-2 * z * x^-7 * z^4 * x^-1 * z^3 ] T64.286 : Triangle type {18,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-2 * x^-1 * z^4, y^-4 * x^2 * y^-4 ] T64.287 : Triangle type {18,18,72} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, z^-4 * x^2 * z^-4 ] T64.288 : Triangle type {18,24,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^3 * x^-1 * y * z^-1 * y ] T64.289 : Triangle type {18,24,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^-1 * z * y * x^-1 * z * x^-1 * z ] T64.290 : Triangle type {20,28,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-3 * y * x^-1 * y * x^-1 * z * x^-8 * z * x^-5 ] T64.291 : Triangle type {21,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * x^-1, z^-1 * x^3 * z^-2, y^5 * x^-3 * y^4 ] T64.292 : Triangle type {21,21,21} Group order 147 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * x * y^-1 * x * y^-1 * z, z^-1 * x * y^-1 * x * z^-1 * x ] T64.293 : Triangle type {21,21,21} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^5 * z^-2, x^2 * z^-1 * x * z^-4 * x^4 * z^-2 ] T64.294 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-13 * y * x^-9 * z * x^-4 ] T64.295 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * y, z^-7 * x^5 * z^-3 ] T64.296 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-1 * y^5, x^-7 * z^5 ] T64.297 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x * z^-1 * x * z^-4 * x^8 ] T64.298 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^6 * x^-2 ] T64.299 : Triangle type {27,45,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^2 * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-7 ] T64.300 : Triangle type {28,28,35} Group order 140 Chiral action Defining relators: [ x * y * z, y * x^-2 * y * z^-1, y^2 * x^2 * z^2, x * z^-1 * x^3 * z^-3 ] T64.301 : Triangle type {28,28,35} Group order 140 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * z^-2, y^2 * x^2 * z^2, (y * z^-1 * y)^2 ] T64.302 : Triangle type {28,28,35} Group order 140 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, x * z^-3 * y * z^-3 ] T64.303 : Triangle type {28,28,35} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z^-2 * x^3 * z^-2 * x ] T64.304 : Triangle type {28,28,35} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, y * x^-1 * y * x^-1 * z^3 ] T64.305 : Triangle type {28,28,35} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * y * x * z^-3 ] T64.306 : Triangle type {33,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-5 * x * y^-11 ] T64.307 : Triangle type {33,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-4 * y * x^-5 * z^4 * x^-1 * z * x^-2 ] T64.308 : Triangle type {33,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-3 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-2 * y^7 ] T64.309 : Triangle type {33,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, z^-6 * x^5 * z^-2 ] T64.310 : Triangle type {33,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-20 * z * x^-8 * y * x^-4 ] T64.311 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^8 * y^-2 ] T64.312 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^-1 * y^2 * x^-1 * y^2 * x^-8 ] T64.313 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, x^6 * z^-4 ] T64.314 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-2 * x * z^-3 * y * x^3 * z^-4 * y ] T64.315 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, y * x^4 * z^-4 * y * x^2 * z^-4 ] T64.316 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^5 * x^-2 * y^5 ] T64.317 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^10 * x^-2 * y^6 ] T64.318 : Triangle type {34,34,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, x^6 * y^-4 ] T64.319 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^10 * x^-1 * y^5 * x^-1 * y^6 ] T64.320 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-3 ] T64.321 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-1 * x^7 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T64.322 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^6 * z^-3, x^-3 * y^3 * x^-7 ] T64.323 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 ] T64.324 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^16 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T64.325 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-7 * y^3 * x^2 * z^-5 ] T64.326 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-26 * y * x^-1 * y * x^-1 * y * x^-1 * z * x^-8 * y * x^-4 ] T64.327 : Triangle type {44,66,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-1 * y * x^-1 * y^5 * x^-6 ] T64.328 : Triangle type {45,45,45} Group order 135 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-1 * y * x^-2 * y^4 ] T64.329 : Triangle type {45,45,45} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y * x^-8 * y^3 * x^-6 * z * x^-4 ] T64.330 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^26 * x^-1 * y^6 ] T64.331 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^2 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z^2 ] T64.332 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^2 * x^-8, y^2 * z^-1 * y * z^-1 * y^9 ] T64.333 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-6, z^-3 * y * z^-1 * y^5 * z^-4 ] T64.334 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^30 * x^-1 * y^5 * x^-1 * y^7 ] T64.335 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-7 * x^5 * z^-3 ] T64.336 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T64.337 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^13 * x^-3 * z * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 ] T64.338 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^8 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T64.339 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T64.340 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-2 * y^4, x^-8 * z^6 ] T64.341 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * x^2 * z^-5 * y^2 * z^-1 ] T64.342 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z * x^-1 * z * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T64.343 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-3 * y * x^-1 * y^5 * x^-7 ] T64.344 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^6 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T64.345 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-4 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 ] T64.346 : Triangle type {65,130,130} Group order 130 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-65, y * z^-1 ] T64.347 : Triangle type {66,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^21 * x^-1 * y^5 * x^-1 * y^6 ] T64.348 : Triangle type {66,66,66} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^4 * x^-2 * y^-4 * z * y^-1 * z * y^-1 * z^2 ] T64.349 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x^-2 * y^-1, y^-55 * x * y^-9, x * z^-1 ] T64.350 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^2 * x^-8 * y * x^-12 * y^3 ] T64.351 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-7 * y * x^-1 ] T64.352 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^7 * y^-5 * x^4 ] T64.353 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^4 * z^-4, x^-2 * y * x^-1 * y^5 * x^-3 * y^3 ] T64.354 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * y^3, z^-4 * y^5 * z^-4 ] T64.355 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 ] T64.356 : Triangle type {129,129,129} Group order 129 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * x^-1 * y^5, z^-1 * x * z^-4 * x^2 * z^-4 ] Genus 65 T65.1 : Triangle type {2,3,8} Group order 3072 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * x * z * y * x * z^4 * y * x * z * y * x * y^-1 * z^2 * y^-1 * z^-2 * x * z, z^3 * y * x * z * y * z^-1 * x * y * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 * x ] T65.2 : Triangle type {2,3,10} Group order 1920 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, y * x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z, y * z^-1 * x * z^2 * y * z^-1 * x * z * y * z^-1 * y^-1 * z^-3 * x * z^2 ] T65.3 : Triangle type {2,3,12} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z^-1 * x * z * y * x * z^2 * y * x * z^2 * y^2 * z^-3 * x * y^-1 * z^-1, z * y * z^-1 * x * z * y * z^-2 * x * z^2 * y^2 * z^-1 * x * z * y^-1 * z^-1 * x ] T65.4 : Triangle type {2,4,5} Group order 2560 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y^-1 * z)^8, y^-1 * z^2 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * x * z ] T65.5 : Triangle type {2,4,6} Group order 1536 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, y * z^-1 * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^2 ] T65.6 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^2, y * z^-1 * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2, y^-1 * z^2 * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z^2 ] T65.7 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T65.8 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^2, y * z^-1 * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T65.9 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z * y^-1 * z, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T65.10 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^2, y * z^-1 * x * z^2 * y * x * y^2 * z^-1 * x * z * y^-1 * z^-2 ] T65.11 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, y * z^-1 * x * z^2 * y * x * y^2 * z^-1 * x * z * y^-1 * z^-2 ] T65.12 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, y * x * z * y * x * z * y * x * z * y^-2 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T65.13 : Triangle type {2,4,6} Group order 1536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2, x * z * y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T65.14 : Triangle type {2,4,8} Group order 1024 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2)^4, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2, y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T65.15 : Triangle type {2,4,8} Group order 1024 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.16 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-2 ] T65.17 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * y^-1 * z^2 * y * x * z * y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T65.18 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T65.19 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * y * z^-1 ] T65.20 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-2)^4, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2 ] T65.21 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T65.22 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T65.23 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, x * z * y * x * z * y * z^-1 * y * z^-2 * x * z * y^-1 * z^-1 * y ] T65.24 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T65.25 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^-2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T65.26 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-2)^4 ] T65.27 : Triangle type {2,4,8} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.28 : Triangle type {2,4,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y * z^-2 * y * x * y^-1 * z^-2 * x * y^-1 * z ] T65.29 : Triangle type {2,4,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, (y * z^-2)^4, (y * z^-5)^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T65.30 : Triangle type {2,4,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, (y * z^-5)^2, z^-4 * x * z^5 * y^-1 * z^-2, z^2 * y * z^-2 * x * z^2 * y^-1 * z^2 * y^-1 * z ] T65.31 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * z * y^2 * z^-2 * x * z * y^-1, z * y * z^-2 * y * x * y^-1 * z^-2 * x * y^-1 * z, (y * z^-2)^4, z^-4 * x * z^5 * y^-1 * z^-2 ] T65.32 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x, (y * z^-2)^4 ] T65.33 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2)^4, (y * z^-5)^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T65.34 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x, (y * z^-2)^4 ] T65.35 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * z * y^2 * z^-4 * y, (y * z^-2)^4, z^-4 * x * z^5 * y^-1 * z^-2 ] T65.36 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-2)^4, (y * z^-5)^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T65.37 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x, z^2 * y * z^-2 * x * z^2 * y^-1 * z^2 * y^-1 * z ] T65.38 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-5)^2, z^-4 * x * z^5 * y^-1 * z^-2, z^2 * y * z^-2 * x * z^2 * y^-1 * z^2 * y^-1 * z ] T65.39 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T65.40 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^-1 * z^-3 * y * z^-1, z^12 ] T65.41 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-2)^4, z^12, z^-3 * x * z * y^-2 * z^-3 * x * y^-1 * z^-1 * y ] T65.42 : Triangle type {2,4,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, y * z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T65.43 : Triangle type {2,4,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T65.44 : Triangle type {2,4,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^4 * y^-1 * z^-5, (y * z^-2)^4 ] T65.45 : Triangle type {2,4,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^-2 * x * z^10 * y * z^-7 ] T65.46 : Triangle type {2,4,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-1 * x * z * y^-1 * z * y^-1 * z^-3 * y * z^-1, x * z^4 * y^-1 * z^-5 ] T65.47 : Triangle type {2,4,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * z, z^7 * y * x * z^2 * y^-1 * z^-9 * x ] T65.48 : Triangle type {2,4,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-21 * x * z^11 * y^-1 * z^-3 ] T65.49 : Triangle type {2,4,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^6 * y * x * z^3 * y^-1 * x * z^3 * y^-1 * z^-1 * x * z^2 ] T65.50 : Triangle type {2,4,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-17 * x * z^11 * y^-1 * z^-7 ] T65.51 : Triangle type {2,4,68} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-53 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T65.52 : Triangle type {2,4,132} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-132 ] T65.53 : Triangle type {2,4,260} Group order 520 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-24 * x * y^-1 * z^-105 ] T65.54 : Triangle type {2,5,5} Group order 1280 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (z^-1 * y)^5, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-2 * y * x * z ] T65.55 : Triangle type {2,5,6} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z^6, (z^-1 * y)^5, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, (y * z^-2)^4 ] T65.56 : Triangle type {2,5,6} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, (z^-1 * y)^5, (y * z^-2)^4, y^-1 * z * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z ] T65.57 : Triangle type {2,6,6} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-2 * y * z^-1 * y)^2, x * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T65.58 : Triangle type {2,6,6} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-1 * z * y^2 * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x * z ] T65.59 : Triangle type {2,6,6} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1, (z^-1 * y^2 * z^-1)^3 ] T65.60 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z^-1 * x * y^-2 * z * y^2 * x * y^-1 * z * y^4 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y ] T65.61 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-1 * y)^4, (y * z^-2 * y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.62 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T65.63 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, (y * z^-1)^6 ] T65.64 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, (z^-1 * y^2 * z^-1)^3 ] T65.65 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y, z^-1 * y * x * z * y^-2 * z * y^-1 * z^-1 * y * z^-1, (y * z^-1 * y)^4 ] T65.66 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^-1 * y * x * z * y^-2 * z * y^-1 * z^-1 * y * z^-1 ] T65.67 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T65.68 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^-1 * z * y * z^-1 * y * x * z^2 * y^-2 * z^2 * y^-1 ] T65.69 : Triangle type {2,6,6} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.70 : Triangle type {2,6,7} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-3 * x * y * z^-3, (y * z^-1 * y * z^-1 * y)^2, z * y * x * z * y^-2 * z^-2 * x * y^-1 * z ] T65.71 : Triangle type {2,6,15} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-2 * y^2 * x * z^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T65.72 : Triangle type {2,6,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * z * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T65.73 : Triangle type {2,6,51} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^8 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y * x * z ] T65.74 : Triangle type {2,6,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^52 * y * x * y^-1 * z^-9 * x * z^2 ] T65.75 : Triangle type {2,8,8} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^8, y * z^-1 * x * z * y^2 * x * y^-1 * z^2, x * z * y^-4 * z^-2 * y^3 ] T65.76 : Triangle type {2,8,8} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1, x * z^2 * y^-2 * z^-1 * y * z^-2 ] T65.77 : Triangle type {2,8,8} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T65.78 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T65.79 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T65.80 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.81 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-4 * z^-2 * y^3 ] T65.82 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T65.83 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-2 * x * y^-2 * z^-3 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.84 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T65.85 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-2 * x * y^-2 * z^-3 * y, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z ] T65.86 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z ] T65.87 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T65.88 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T65.89 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T65.90 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z * y * z^-2 * x * y^-1 * z^-3 * x ] T65.91 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x ] T65.92 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z^2 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * x ] T65.93 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y ] T65.94 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, y^-1 * z * y * x * z * y * x * y^-1 * z^-2 * y * x * z ] T65.95 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, x * z^2 * y^-2 * z^-1 * y * z^-2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T65.96 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, z^8 ] T65.97 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1, x * z * y^-4 * z^-2 * y^3 ] T65.98 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, z^8, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T65.99 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T65.100 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, z^8, x * y^-1 * z * y^-3 * z^-2 * y * z^-2 ] T65.101 : Triangle type {2,8,8} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1)^4, z^8, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T65.102 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^4 * y * z^-2 * x * z^5 ] T65.103 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-5 * x * z * y * x * z^6 * y * z^-1 * x * y^-1 * z^-6 * x * y^-1 * z^-1 ] T65.104 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, (y * z^-1 * y^2)^2 ] T65.105 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z^2 * y^-2 * z^-3 * y, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T65.106 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-11 * x * z^6 * y * z^-6 ] T65.107 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, x * z * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T65.108 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z^2 * y^-2 * z^-3 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T65.109 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^-3 * z^-2 * x * z ] T65.110 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z * y^-1 * x * z^3 * y^-1 * z^-2 ] T65.111 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, x * z * y * x * z^3 * y * x * z^3 * y^-1 * z^-2 ] T65.112 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z^-2 * x * y^-1, z^-4 * x * z * y^-1 * x * z^3 * y^-1 * z^-2 ] T65.113 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, x * z^4 * y * z^-1 * x * z^3 * y^-1 * z^-2 ] T65.114 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, y * x * z * y * z^-3 * x * z^5 * y * z^-1 * x * z * y^-1 * z^-3 * x * z * y^-1 * z^-2 * x * z^2 ] T65.115 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z * y * x * z^9 * y * x * y * z^-5 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T65.116 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-5 * x ] T65.117 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-1 * x * z^3 * y * x * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T65.118 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^6 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T65.119 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, z^5 * y * x * z^4 * y^-1 * z^-1 * x ] T65.120 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T65.121 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-6 ] T65.122 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, x * z^5 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T65.123 : Triangle type {2,8,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, x * z^5 * y * x * y^-1 * z^-5 ] T65.124 : Triangle type {2,8,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^23 * y * x * z * y * x * y^-1 * z^-6 * x * z^11 ] T65.125 : Triangle type {2,8,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^32 * y * x * y^-1 * z^-9 * x * z ] T65.126 : Triangle type {2,12,12} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * x * z * y^2 * x * z * y^-1 * z, x * y^-5 * z^-5, y^12 ] T65.127 : Triangle type {2,12,12} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-5 * z^-5, z * y^-1 * z * y^-3 * z^-2 * x * z * y^-1 ] T65.128 : Triangle type {2,12,12} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, y^-1 * z * y^-3 * z^-1 * x * z^2, z^-1 * y * x * y^-2 * z * y^-1 * z^-2 ] T65.129 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-1 * z^-1 * x, z^3 * y^-2 * z^-1 * x * y^-1 * z, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T65.130 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^-1 * z * y^-3 * z^-1 * x * z^2, z * y * x * y^-2 * z * y^-1 * z^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T65.131 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^12 ] T65.132 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y * z^-2, z^-1 * y * x * y^-2 * z * y^-1 * z^-2, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^12 ] T65.133 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T65.134 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-5 * z^-5, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y ] T65.135 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-1 * z^-1 * x, z^3 * y^-2 * z^-1 * x * y^-1 * z, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T65.136 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-5, y^12 ] T65.137 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-2 * y * z^-1, y^12, (y * z^-1 * y)^4 ] T65.138 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * z^2 * y^-2 * z^-3 * y, y^12 ] T65.139 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^12 ] T65.140 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-1 * y * z^-2 * y, y^12 ] T65.141 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^2 * x * z * y^2 * x * z^3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.142 : Triangle type {2,12,12} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T65.143 : Triangle type {2,12,28} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^12 * y * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^3 ] T65.144 : Triangle type {2,12,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, x * z^7 * y^-1 * x * z^4 * y^-1 * z^-13 ] T65.145 : Triangle type {2,14,21} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, z^-2 * x * y^-2 * z * y^-1 * z^-2, y * z^-1 * y^4 * x * y^-1 * z^-1 * y ] T65.146 : Triangle type {2,20,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, z^-1 * y^5 * z^-4, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T65.147 : Triangle type {2,20,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-3 * y, z^-2 * x * y^-2 * z * y^-1 * z^-1 * y, z^-1 * y^5 * z^-4 ] T65.148 : Triangle type {2,20,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^-1 * z * y^-1 * z^2 * y^-1 * z^3 * y^-8 * z * y^-1 * z ] T65.149 : Triangle type {2,20,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * y^-1 * z * y^-2 * z^-2 * y * z^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T65.150 : Triangle type {2,20,20} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^-2 * z^3 * y^-12 * z * y^-2 ] T65.151 : Triangle type {2,22,143} Group order 286 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^7 * y^-1 * x * z^3 * y^-1 * z^-1 * x ] T65.152 : Triangle type {2,28,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-16 * z^3 * y^-5 * z^3 * y^-1 ] T65.153 : Triangle type {2,36,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-36 ] T65.154 : Triangle type {2,36,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-11 * z^2 * y^-1 ] T65.155 : Triangle type {2,36,36} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-19 * z^3 * y^-10 * z^2 ] T65.156 : Triangle type {2,54,135} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-15 * z^3 * y^-6 * z^2 * y^-1 ] T65.157 : Triangle type {2,68,68} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-38 * y^12 * z^-1 * y^16 * z^-1 ] T65.158 : Triangle type {2,131,262} Group order 262 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^111 * z^-20 ] T65.159 : Triangle type {2,132,132} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-111 ] T65.160 : Triangle type {2,260,260} Group order 260 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^19 * y^-110 ] T65.161 : Triangle type {3,3,4} Group order 1536 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, (z * y * x * z * y^-1 * z^-1 * x^-1)^2 ] T65.162 : Triangle type {3,3,5} Group order 960 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T65.163 : Triangle type {3,3,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * y * x * y^-1 * z^-1 * x * z * y^-1 * x * z * y, z^2 * y * x^-1 * y * x^-1 * z^2 * y * z^-1 * x^-1 ] T65.164 : Triangle type {3,4,4} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-2 * y * z^-1 * y * x^-1 * z * y * x^-1 * y^-1 ] T65.165 : Triangle type {3,4,4} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z * y * x^-1 * z * y * x^-1 * y * z^-1 * y * z^-1 * x^-1 ] T65.166 : Triangle type {3,4,4} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, x^-1 * y^-2 * z^-1 * y * x^-1 * z * y * x * y^-1 * z^-1 ] T65.167 : Triangle type {3,4,4} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, z * x^-1 * z * y * x^-1 * y * x^-1 * y * x * y^-1 * x * z * y * x ] T65.168 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2, y * z^-1 * x * z * y^-1 * x * z * y^-1 * z^2 ] T65.169 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, (x * y^-1 * z^-1)^4 ] T65.170 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z, x^-1 * z * y * x * y^-1 * x * z * y * x * z, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T65.171 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, (x * z * y^-1 * z^-1 * y)^2 ] T65.172 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T65.173 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T65.174 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, y * z^-1 * x^-1 * y * x^-1 * y * z^-1 * x^-1 * z, (z^-1 * x^-1 * y^-1)^3 ] T65.175 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T65.176 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, (x * z * y^-1 * z^-1 * y)^2 ] T65.177 : Triangle type {3,4,4} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, (y * z^-1)^6 ] T65.178 : Triangle type {3,4,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * y^-1 * x * y^-1 * z^-1 * y, z^-1 * x^-1 * y^-2 * x * z * y^2 ] T65.179 : Triangle type {3,4,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, z^3 * y^-1 * x * y^-1 * z^-1 * x ] T65.180 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T65.181 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * z^-1, z^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * z * x^-1 * z^-2 * x * z * y ] T65.182 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-3 ] T65.183 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * y^-1 * x * y^-1 * z^-1 * y, z^-1 * y * x * y^-1 * x * z * y * z^-1 ] T65.184 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2, y^-1 * z^-1 * x^-1 * y * x^-1 * z * y * z^-1 * x ] T65.185 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (y * z^-3)^2 ] T65.186 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y ] T65.187 : Triangle type {3,4,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y ] T65.188 : Triangle type {3,6,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T65.189 : Triangle type {3,6,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, (x^-1 * z * y^-2 * z^-1)^2 ] T65.190 : Triangle type {3,6,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z * y^-1 * z^-1 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * y * z^-1 * x * z ] T65.191 : Triangle type {3,6,6} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y ] T65.192 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * x * z * y * z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z ] T65.193 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (y * z^-1)^4, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T65.194 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T65.195 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z * y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-3 * z * y^-1 * z^2 ] T65.196 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, z^2 * y^2 * x^-1 * z * y^-1 * z * y^-1 ] T65.197 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, z^6, (y * x^-1 * z)^3 ] T65.198 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, x^-1 * z * y^2 * x * y^-1 * z^-2, (y * z^-1)^4, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T65.199 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T65.200 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y * x^-1 * y^-2 * x * y^-1 * z * y ] T65.201 : Triangle type {3,6,6} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, y * x^-1 * y^-2 * x * y^-1 * z * y ] T65.202 : Triangle type {3,7,7} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^-7, y^-1 * z^-1 * y^2 * x * y^-1 * z * y^-1 ] T65.203 : Triangle type {3,12,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3, z * y^2 * x^-1 * z^3 ] T65.204 : Triangle type {3,12,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, (x^-1 * z * y)^2 ] T65.205 : Triangle type {3,15,15} Group order 240 Chiral action Defining relators: [ x^3, x * y * z, z^2 * y^-1 * x * y^-2, (x * z * y)^2 ] T65.206 : Triangle type {3,15,15} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * y ] T65.207 : Triangle type {3,51,51} Group order 204 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y * z^-2 * y * z^-2 * y^5 * z^-1 * y^2 * z^-1 ] T65.208 : Triangle type {3,195,195} Group order 195 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-54 * z * y^-10 ] T65.209 : Triangle type {4,4,4} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2 ] T65.210 : Triangle type {4,4,4} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y^-1 * z^-2 * y * x * z^2 * x^-1, (y * z^-1)^4 ] T65.211 : Triangle type {4,4,4} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, (x * y^-1)^4, z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^2 * y ] T65.212 : Triangle type {4,4,4} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, z^-1 * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z * y^-2 ] T65.213 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-2 * x * z^-1 * x^-1 * y * x^-1 * y * x^-2 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T65.214 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x * z * y * x * z^-1 * y * x * z * x^-1 * y^-1 * z * y ] T65.215 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * z * y * x * z^-1 * y)^2 ] T65.216 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * y^-1)^4, y^-1 * z^-2 * y * x * z^2 * x^-1, (x * z^-1)^4, y * z^-1 * x * z^-1 * x^-1 * z * y^-1 * z ] T65.217 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1)^4, (y * z^-1)^4, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T65.218 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, (x * y^-1)^4, (x * z^-1)^4, (y * z^-1)^4 ] T65.219 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z^-2 * y * x * z^2 * x^-1, (x * z^-1)^4, y * z^-1 * x * z^-1 * x^-1 * z * y^-1 * z, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T65.220 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-2 * x * z^-1 * x^-1 * y * x^-1 * y * x^-2 * y^-1 * x * y^-1 * z^-1 * y * x^-1 ] T65.221 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, (x * z * y)^2 ] T65.222 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x^-1 * z * x^-1 * y * x^2 * y^-1 * x * z^-1 * x^-1, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T65.223 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T65.224 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T65.225 : Triangle type {4,4,4} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, x * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T65.226 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, x^-1 * z * y * x^2 * z * y * x^-1 ] T65.227 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1 ] T65.228 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * y * z^-1 ] T65.229 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T65.230 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T65.231 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * z^2 * y * x^-1 * z * y^-1 * z^-1 ] T65.232 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T65.233 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y * z^-2)^2, z^6, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T65.234 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z * x^-1 * y * x^-1 * y^2 * x, z^-3 * x^-1 * z^2 * y^-1, x * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T65.235 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z * x^-1 * y * x^-1 * y^2 * x, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4 ] T65.236 : Triangle type {4,4,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^6, z^-1 * y * z^-1 * y * x * z^-1 * x * z^-1, (x * z^2 * y)^2 ] T65.237 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, (x * z^-1)^4 ] T65.238 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1, (x * z^-1)^4 ] T65.239 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * y * z^-1 ] T65.240 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, x * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T65.241 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1, x * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T65.242 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4 ] T65.243 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4 ] T65.244 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z ] T65.245 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, y * x^-1 * y * x^2 * z^2 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, (x^-1 * z^2 * y)^2 ] T65.246 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, (x * z^2 * y^-1)^2 ] T65.247 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, (y * z^-1)^4, z * y * x^-1 * y * x^-1 * y^-1 * z^-2 * x ] T65.248 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^6, (y * z^-1)^4 ] T65.249 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, (y * z^-1)^4, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T65.250 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1, z^-1 * x^-1 * z * y * x^-1 * z * y * z^-1 ] T65.251 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T65.252 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1 ] T65.253 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T65.254 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^6 ] T65.255 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-2)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T65.256 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y, x^-1 * z * y * x^2 * z * y * x^-1 ] T65.257 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y, y * x^-1 * y * x^2 * z^2 * x^-1 ] T65.258 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, (x * z^2 * y^-1)^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1, x^-1 * y * x^-1 * y * x^-1 * z^2 * y^-1 * z^-1 ] T65.259 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-2)^2, z^6, x^-1 * z * y * x^2 * z * y * x^-1 ] T65.260 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T65.261 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, (y * z^-1)^4, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T65.262 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, (y * z^-1)^4, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T65.263 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T65.264 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T65.265 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, z^-1 * y * x^-1 * z * y * x^-1 * y^-1 * z^2 * y, x^-1 * z * y^-1 * z * y * x * y^-1 * z^-1 * y * z^-1 ] T65.266 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y * z^-1 * x^-2 * z^2 * x^-1, (x * z^2 * y)^2 ] T65.267 : Triangle type {4,4,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z^-1 * y * x * z^-1 * y * x * z * x^-1 * y^-1 * z^-1 * y ] T65.268 : Triangle type {4,4,10} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-3 * x^-1 * z * y^-1 * z^-1, (x * y^-1)^4 ] T65.269 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2, (x * z^-1)^4 ] T65.270 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T65.271 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, (y * z^-3)^2, z^10 ] T65.272 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z * y^-1 * z^-1 * x * z^2 ] T65.273 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z^-2)^2, (y * z^-2)^2, z^10 ] T65.274 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-2)^2, (y * z^-2)^2, z * y^-1 * z^-1 * x^-1 * z * y * x ] T65.275 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z^-2 * x * z^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T65.276 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-2 * x * z^2, y * x * z^-1 * x^-1 * z * x^-1 * z ] T65.277 : Triangle type {4,4,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^10 ] T65.278 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^10 * y * z^-1 * x * z^2 * y^-1 * z^-3 * x ] T65.279 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^6 * y^-1 * x * y^-1 * x * z^4 * y * x * z^5 ] T65.280 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z^-3 * x * z * y * x^-1 * y^-1 * z^-3 ] T65.281 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, z^3 * y^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-3 * x^-1 * z^6 ] T65.282 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^3 * y * x * z^2 * y^-1 * z^-1 * x^-1 * y^-1 * x^-1 * z^9 ] T65.283 : Triangle type {4,4,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^3 * y^-1 * z^-6 * x * y^-1 * x^-1 * y^-1 * z^-6 * x ] T65.284 : Triangle type {4,4,34} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T65.285 : Triangle type {4,4,34} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-22 * x * z^4 * y * z^-7 ] T65.286 : Triangle type {4,4,66} Group order 264 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-52 * x * y^-1 * x * y^-1 * z^-12 ] T65.287 : Triangle type {4,4,130} Group order 260 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-51 * x * y^-1 * z^-13 ] T65.288 : Triangle type {4,6,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^3 * y * x^-1 * y^-1 * x * z * y * z^-2 * x * z ] T65.289 : Triangle type {4,6,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, (x^-1 * z^3 * y)^2 ] T65.290 : Triangle type {4,6,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^9 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-6 * x^-1 * z ] T65.291 : Triangle type {4,7,28} Group order 224 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^-7, z * y^-3 * x^-1 * y^-1 * z^2 ] T65.292 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * z * y, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8 ] T65.293 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^8 ] T65.294 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8 ] T65.295 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8 ] T65.296 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y^8 ] T65.297 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^2 * z^-1 * x^-1 * y^-1 * z^2, y^8 ] T65.298 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3, y^-2 * z^-1 * x^-1 * y^-1 * z^2 ] T65.299 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2, z * y^-1 * z^-1 * x^-1 * z * y^-2 ] T65.300 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * y^-2 * x * z * x^-1, (x^-1 * z * y)^2, (x * z * y)^2 ] T65.301 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * y^-2 * x * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, y * z^-2 * x^-1 * y^-2 * z ] T65.302 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^8 ] T65.303 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T65.304 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^8, z^-1 * y^3 * x^-1 * y^4 ] T65.305 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^8, (y * z^-1)^4 ] T65.306 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^-2, x^-1 * y * x^-2 * z * y^2, z^8 ] T65.307 : Triangle type {4,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2 ] T65.308 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^8 ] T65.309 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^8 ] T65.310 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^8 ] T65.311 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^8 ] T65.312 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T65.313 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T65.314 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T65.315 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8 ] T65.316 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8 ] T65.317 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-1)^4 ] T65.318 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T65.319 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T65.320 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, (y * z^-1)^4, z^8 ] T65.321 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, (y * z^-1)^4 ] T65.322 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T65.323 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * y^3 * x^-1 * y^4 ] T65.324 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, (x^-1 * z * y)^2, (x * z * y)^2, y^8, (y * z^-1)^4 ] T65.325 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-2 * y)^2, z^8, y * z^-1 * y^2 * x^-1 * y^-1 * z * y * z^-1 ] T65.326 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, z^8, y * z^-1 * y^2 * x^-1 * z * y^-1 * z^-1 * y ] T65.327 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, (x^-1 * z * y)^2, (x * z * y)^2, y^8, z^-2 * y^2 * x^-1 * y^-2 * z * y^-1 ] T65.328 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1, y^8, y * z^-1 * y^2 * x^-1 * y^-1 * z * y * z^-1 ] T65.329 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, (y * z^-1)^4 ] T65.330 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y^8 ] T65.331 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3 ] T65.332 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3 ] T65.333 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T65.334 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T65.335 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T65.336 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T65.337 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * y * x^-1 * z * y^-2, y^8 ] T65.338 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^8 ] T65.339 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T65.340 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y^8 ] T65.341 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^3 * x^-1 * z^3, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T65.342 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * y^2 * x * z^-1 * x, (x * z * y)^2 ] T65.343 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-2 * x^-1 * y^-2 * z ] T65.344 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T65.345 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2 ] T65.346 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^8 ] T65.347 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T65.348 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x * z * y)^2, z^8, z^2 * y * x^-2 * z^3 * x^-1 ] T65.349 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T65.350 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * x * z^-1 * x^-1 * y * x * z^-1 ] T65.351 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, z^-1 * y^2 * x^2 * y^-1 * z^-1 * y, (x * y^-1)^4 ] T65.352 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y^8 ] T65.353 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, z^-1 * y^2 * x^-1 * z * y * z^-1 ] T65.354 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T65.355 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T65.356 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8 ] T65.357 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, (y * z^-1)^4, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T65.358 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T65.359 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, (x * y^-1)^4 ] T65.360 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z * y)^2, (x * y^-1)^4 ] T65.361 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, (x * y^-1)^4 ] T65.362 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, (x * y^-1)^4 ] T65.363 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1 ] T65.364 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8 ] T65.365 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y^3 * x^-1 * z^3 ] T65.366 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3 ] T65.367 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (x * y^-1)^4 ] T65.368 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x^-1 * z * y)^2, (x * y^-1)^4 ] T65.369 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T65.370 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-2 * z, z * y * x * y^-1 * x * z * y^-2 ] T65.371 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, z^8 ] T65.372 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-1 * y * x^-1 * z^2 * y, y^8 ] T65.373 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T65.374 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (y * z^-1 * y)^2, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^8 ] T65.375 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y * z^-1 * y * x^-1 * z^2 * y, y^8, y^3 * z^-1 * x^-1 * y^-1 * z * y * z^-1 ] T65.376 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 ] T65.377 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T65.378 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z^-1 * y * x^-1 * y^-1 * z^2, z^-2 * y * x^-1 * z * y^-2 ] T65.379 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x * z^-1 * x, x * z^-1 * y * x^-1 * y^-1 * z^-1, y^8 ] T65.380 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * y * x^-1 * z^2 * y ] T65.381 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * z^3 ] T65.382 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, z^8, z^3 * y^2 * x * z^-3 * x ] T65.383 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z^8, z^-3 * y * x^2 * z^3 * y ] T65.384 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^8 ] T65.385 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^8, z^8 ] T65.386 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, (y * z^-1)^4, z^8 ] T65.387 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T65.388 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^-2 ] T65.389 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.390 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T65.391 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, z^8 ] T65.392 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^8, z^-1 * y * z^-1 * y * x^-1 * z * y^-1 * z^-2 ] T65.393 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * z * y^-2, y^8, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T65.394 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-2 * y)^2, z^8, z^-1 * y^3 * x^-1 * y^4, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T65.395 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, (y * z^-1)^4 ] T65.396 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y * x^-1 * z * y^-2, y^8, (y * z^-3)^2 ] T65.397 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * z * y^-2, y^8, (y * z^-3)^2 ] T65.398 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.399 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.400 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1)^4, z^8, z^-1 * y^3 * x^-1 * y^4 ] T65.401 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, z^8, y * z^-1 * y^2 * x^-1 * y^-2 * z^2 ] T65.402 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^8, z^8, y * z^-1 * y^2 * x^-1 * y^-2 * z^-2 ] T65.403 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1)^4, z^8 ] T65.404 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.405 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, z^-1 * y^3 * x^-1 * y^4, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.406 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y ] T65.407 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T65.408 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T65.409 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, (y * z^-1 * y^2)^2, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T65.410 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T65.411 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * z * y, y^8 ] T65.412 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, y * z^-1 * y^2 * x^-1 * y^-2 * z^2 ] T65.413 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^8, z^8, y * z^-1 * y^2 * x^-1 * y^-1 * z * y * z^-1 ] T65.414 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, z^8, y * z^-1 * y^2 * x^-1 * y^-2 * z^2 ] T65.415 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-3)^2, z^8, z^-1 * y^3 * x^-1 * y^4 ] T65.416 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T65.417 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-2 * y)^2, (y * z^-3)^2, z^-1 * y^3 * x^-1 * y^4 ] T65.418 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T65.419 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1 * y^2)^2, z^8 ] T65.420 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, (y * z^-1 * y^2)^2, z^8 ] T65.421 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^8, z^8 ] T65.422 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y^8, z^8 ] T65.423 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * z^-2)^2, y * x^-1 * y * x^-1 * y^-1 * x * z, y^8 ] T65.424 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, (x * y^-2)^2, y^8 ] T65.425 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T65.426 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T65.427 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, (x * z * x^-1 * y^-1)^2, y^2 * x * y^-1 * x * z^2 * y ] T65.428 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x * z^-2)^2, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T65.429 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, (x * z * y)^2, (x * z * x^-1 * y^-1)^2 ] T65.430 : Triangle type {4,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z * y)^2, (x * z^-2)^2 ] T65.431 : Triangle type {4,8,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^10 * y^-1 * z^-5 * x * y * z^-1 * x * z^8 ] T65.432 : Triangle type {4,8,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^10 * y^-1 * z^-5 * x * z^10 ] T65.433 : Triangle type {4,16,48} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T65.434 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * x^-1 * y * z^-3 ] T65.435 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-3 * z^3 * y^-4 * z * y^-1 * z^4 ] T65.436 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, z^2 * y * x^-1 * z^3 ] T65.437 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, z^-3 * x^-1 * z * y * z^-1 ] T65.438 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * y^2 * z^-3 ] T65.439 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-3 * z^4 * y^-1 * z * y^-4 * z^3 ] T65.440 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, z^-1 * x^-1 * z^5 * y * x^-1 * z * y * z^-3 ] T65.441 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, (y * x^-1 * z^5)^2 ] T65.442 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^-1 * x^-1 * z^5 * y * x^-1 * z * y * z^-3 ] T65.443 : Triangle type {4,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, (y * x^-1 * z^5)^2 ] T65.444 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^7 * z^-3 * y^2 * z^-1 * y^6 * z^-2 * y^3 ] T65.445 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-6 * z * y^-2 ] T65.446 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^3 * z^-2 ] T65.447 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T65.448 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-7 * z^2 ] T65.449 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^-1 * z^2 * y^-5 * z * y^-1 * z * y^-1 ] T65.450 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * y^-2 * z, (y^-1 * z * y^-3 * z)^2 ] T65.451 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^3 * y^-2 * z * y^-3 * z^2 ] T65.452 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-4 * y^2 * z^-4 * y^2 ] T65.453 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-4 * z^5 ] T65.454 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y * z^-2 ] T65.455 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3 ] T65.456 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * x^-1 * y^-4, y^-1 * z^4 * y^-2 * z * y^-3 * z ] T65.457 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * x^-1 * y^-4, y^-1 * z^2 * y^-1 * z^2 * y^-6 ] T65.458 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y * z^-4 * y * z^-2 * y^4 * z^-1 * y * z^-2 * y^6 * z^-1 * y ] T65.459 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^4 * z^-5 * y^6 * z^-1 * y ] T65.460 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^4 * z^-1 * y^3 * z^-1 * y^3 * z^-1 * y * z^-2 * y^7 * z^-1 ] T65.461 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z^3 * y^-1 * z^-2, y^-1 * z * y^-3 * z * y^-2 * z^4 ] T65.462 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z^3 * y^-1 * z^-2, y^-3 * z * y^-3 * z^5 ] T65.463 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z^2 * y^-2 * z^4 ] T65.464 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-1 * z^2 * y^-1 * z^2 * y^-3 * z * y^-1 * z ] T65.465 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-1 * z^2 * y^-1 * z^2 * y^-1 * z * y^-3 * z ] T65.466 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z^2 * y^-6 ] T65.467 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-1 * z^2 * y^-1 * z^2 * y^-6 ] T65.468 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^-1 * z^2 * y^-1 * z^3 * x^-1 * y^-2 * z * y^-1 * z ] T65.469 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^-2 * z^2 * y^-6 * z^2 ] T65.470 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-2 * z * y^-2 * z * y^-3 * z^2 * y^-1 ] T65.471 : Triangle type {4,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^-3 * z^2 * y^-5 * z^2 ] T65.472 : Triangle type {4,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^-1 * z^2 * y^-2 * z^-3 * y, z^2 * y^-3 * x * y^-2 * z^2 ] T65.473 : Triangle type {4,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-20 * z^3 * y^-5 * z * y^-1 * z * y^-11 ] T65.474 : Triangle type {4,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^22 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y^2 ] T65.475 : Triangle type {5,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^2 * y^-1 * z^-1, z^-1 * x * y^-1 * x * z^-1 * y, y^6 ] T65.476 : Triangle type {5,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, y^6, y^-1 * z^-1 * x^-2 * z * y^-1 * x, z^-1 * x^-1 * y * x^-1 * y^-1 * x * z^-1 ] T65.477 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, y^8 ] T65.478 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, x^-1 * z * y^-1 * x * z^2 ] T65.479 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^-3 * x^-1 * z^2 * y^-1 ] T65.480 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, (x * z * y^-1)^2, (x * z^-2)^2, y * x^-3 * z * x^-2 ] T65.481 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * x^-2 * z * y^-1 * z ] T65.482 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^8 ] T65.483 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, (x * z * y^-1)^2, (x * z^-2)^2, x * z^-1 * x^-2 * z * y^-1 * z^-1 ] T65.484 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T65.485 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^8, z^-2 * y * z^-1 * y * z^-3 ] T65.486 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^8 ] T65.487 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y * x^-1 * z * y^2, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T65.488 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T65.489 : Triangle type {6,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^-4 * x^-1 * y * z^-3 ] T65.490 : Triangle type {6,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * y * x^-1 * y^-2 * z ] T65.491 : Triangle type {6,12,12} Group order 192 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * y * x^2 * y^-2 * z ] T65.492 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T65.493 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T65.494 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, (y * z^-1)^4 ] T65.495 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y * z^-1 * x^-1 * y^-3, (y * z^-1)^4 ] T65.496 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, (x * z * y)^2, y^3 * x^-1 * y^-1 * z * y ] T65.497 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * z * y)^2, y * x^-3 * z * x^-2, z^2 * y^-1 * x^2 * z^3 ] T65.498 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, z * y * x^-2 * z * y * x, y^3 * x^-1 * y^-1 * z * y ] T65.499 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, z^2 * y^-1 * x^2 * z^3 ] T65.500 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^-3 ] T65.501 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * z * y)^2, y^-1 * z^-1 * x^-2 * y * x * y^-1, x * z * x^-2 * y^-1 * z^-2 ] T65.502 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z * y * x^-1 * y^-3 ] T65.503 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z * y^-1 * z^-1 * x^-1 * y^-2 * z ] T65.504 : Triangle type {6,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, (y * z^-1)^4 ] T65.505 : Triangle type {6,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y^-4 * z * y^-1 * z ] T65.506 : Triangle type {6,28,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z * y^-5 * z * y^-1 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-11 ] T65.507 : Triangle type {6,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T65.508 : Triangle type {7,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * z, (x * z * y)^2, x^-7 ] T65.509 : Triangle type {7,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * z * y^-1, x * z^-1 * x^2 * z^-1 * y ] T65.510 : Triangle type {7,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, x * z^-1 * x^-1 * y^2, x^-1 * z * y^-1 * x * z^-1 * y, x^-7 ] T65.511 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T65.512 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, z^-2 * y * x^-1 * y * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^8 ] T65.513 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z^-1 * y)^2, (y * z^-2)^2, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T65.514 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z^-1 * y)^2, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T65.515 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^3 * x * z^2, z^-2 * y * x^-1 * y * z^-1 * y ] T65.516 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x^-1 * y * x^-1 * y^-2 * z, z^-2 * y * x^-1 * y * z^-1 * y, x^8 ] T65.517 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, x^-2 * z * x^2 * z^-1, x^8, y^8, y * z^-1 * y^2 * x^-1 * z * y^2 ] T65.518 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, (y^-1 * x)^3, y^8, y * z^-1 * y^2 * x * y^-1 * z^-1 * y ] T65.519 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, x * z * x^-2 * y^-1 * x * y^-1 ] T65.520 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, z * x^-3 * y^-3 ] T65.521 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z * y, x^-1 * y^-1 * x^2 * z^-2, y^-1 * z^-1 * x^2 * z * y^-1 ] T65.522 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, (y^-1 * x)^3, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3 ] T65.523 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z * y * x^-1 * y^-1 * x * z^3 ] T65.524 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, x^8, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T65.525 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, (x * z^-1 * y)^2, z * x^-3 * y^-3, z^-3 * x^-1 * z^2 * y^-1 ] T65.526 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, z * x^-3 * y^-3, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1 ] T65.527 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z * y * z^-1 * x^-1 * z^3 ] T65.528 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-2 * x^-1 * z^3 * y * x * y * x^-1 * y^-1 * z^-4 ] T65.529 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z * x^-3 * y^-3, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3 ] T65.530 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * x^-3 * y^2 * z^-1, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-3 * x^-1 * z^2 * y^-1 ] T65.531 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^-5 * x * y * z^-6 ] T65.532 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T65.533 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * x^-3 * y^2 * z^-1, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z * y * z^-1 * x^-1 * z^3 ] T65.534 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, z * x^-3 * y^-3, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * y * z^-1 * x^-1 * z^3 ] T65.535 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z * x^-3 * y^-3, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T65.536 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^-1 * y^-1 * z, z * y^-1 * x * z * y * x^-1 * z^8 ] T65.537 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z * x^-3 * y^-3, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3 ] T65.538 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-2)^2, y * x^-3 * y^-2 * z^-1, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z * y * x^-1 * y^-1 * x * z^3 ] T65.539 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x * z^5 * y * x^-1 * y * z^-4 * x * y^-1 ] T65.540 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^8, y^8, z^-1 * x^-1 * z * y * x * y^-1 * z^-2 ] T65.541 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T65.542 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y^-1 * z^-3 * x^-1 * z * y^-1 * z^-5 * x^-1 ] T65.543 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^-5 * x^-1 * z * y^-1 * z^-5 ] T65.544 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * x * y^-1 * x * z^3, y^8 ] T65.545 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^8, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T65.546 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, y^-1 * x * z * y^-1 * x * z^3 ] T65.547 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T65.548 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T65.549 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T65.550 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T65.551 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y^8, y * x * z * y * x * z^3 ] T65.552 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T65.553 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z * y^-1 * x * y^-1 * x * z^3 ] T65.554 : Triangle type {8,8,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, y^-1 * x * z * y^-1 * x * z^3 ] T65.555 : Triangle type {8,8,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^7 * y * x^-1 * y * x^-1 * z^13 ] T65.556 : Triangle type {8,8,44} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, x^-1 * z * y * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x^-1 * y^-1 * z^-6 * x^-1 * z * y * z^-1 ] T65.557 : Triangle type {8,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-6 * x * z * y * z^-2 ] T65.558 : Triangle type {8,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T65.559 : Triangle type {8,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z * y^-1 * z^-3 * x^-1 * y^-1 * x * z^4 ] T65.560 : Triangle type {8,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-3 * x ] T65.561 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-3 * y * x * y * z^-4 ] T65.562 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, z^-1 * y^5 * z^-1 * y * z^-2 ] T65.563 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^12 * y^-3 * z^4 ] T65.564 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T65.565 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 * z^-4 ] T65.566 : Triangle type {8,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^6 * z^-4 ] T65.567 : Triangle type {8,38,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-9 * z^4 * y^-6 ] T65.568 : Triangle type {10,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, z^-1 * x^4 * z^-3 ] T65.569 : Triangle type {10,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^10 ] T65.570 : Triangle type {11,14,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-2 * y * z^-5 * y^2 * z^-4 ] T65.571 : Triangle type {11,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, z^-1 * y * x^2 * z * y^-1, y * z^-2 * y * z^-4 * y^4 * z^-3 ] T65.572 : Triangle type {11,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x, z^-1 * y * x^-1 * z * y^-1, y * z^-3 * y * z^-3 * y^4 * z^-2 * y ] T65.573 : Triangle type {11,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^7, x^11 ] T65.574 : Triangle type {11,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x^11 ] T65.575 : Triangle type {11,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^3 * z^-4, x^11 ] T65.576 : Triangle type {11,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^5 * z^-2, x^11 ] T65.577 : Triangle type {11,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-8 * y * z^-4 ] T65.578 : Triangle type {12,12,14} Group order 168 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, z^-1 * y * x^2 * z * y, x^-12 ] T65.579 : Triangle type {12,12,14} Group order 168 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y^2 * x^2 * z^-2, x^-1 * y * x^-3 * y * x^-2 * y * x^-1 * y * x^-1 ] T65.580 : Triangle type {12,12,14} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z^9 * y * x * z^4 ] T65.581 : Triangle type {12,12,78} Group order 156 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, y * z^-1 * x * z^2 * y^-1 * z^-4 * x * z^4 ] T65.582 : Triangle type {12,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^4 * z^-4 * x^2 * y^-4 * x^2 ] T65.583 : Triangle type {12,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-2 * z^2 * y^-1 * z * y^-5 * z ] T65.584 : Triangle type {14,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-2 * x * z^-4 * x^2 * z^-4 ] T65.585 : Triangle type {14,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T65.586 : Triangle type {14,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^4 * z^-3 * x^4 * y^-3 * x^3 ] T65.587 : Triangle type {18,24,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, x^-2 * y^6 * x^-4 * y^2 ] T65.588 : Triangle type {18,24,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-4 * x * y^-1 * x^3 * y^-1 * x * y^-1 * x * y^-1 ] T65.589 : Triangle type {18,24,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, y^-1 * x^5 * y^-1 * x * y^-2 ] T65.590 : Triangle type {18,24,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^4 ] T65.591 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^-2 * x^2 * y^-1 * z ] T65.592 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2, x^-4 * y * x^-1 * y ] T65.593 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-4 * x^2 * y^-4 ] T65.594 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-5 * y * x^-1 * y * x^-11 ] T65.595 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, (x^3 * y^-1 * x)^2 ] T65.596 : Triangle type {18,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-4 * z * x^-2 * z * x^-2 * y^2 * x^-6 * z * y * x^-1 ] T65.597 : Triangle type {20,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^6 * z^-1 * x^10 * y^-1 * x^3 ] T65.598 : Triangle type {20,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^2, x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T65.599 : Triangle type {20,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-3 * y * x^-1 * y^6 * x^-8 ] T65.600 : Triangle type {27,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-6, z^-6 * x * z^-4 ] T65.601 : Triangle type {27,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y * z^-1 * y * z^-1 * y * z^-1 * y^9 ] T65.602 : Triangle type {27,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, z^5 * x^-4 * z * x^-1 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T65.603 : Triangle type {27,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 * x * z^-1 * x * z^-1 ] T65.604 : Triangle type {27,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^3 * z^-4 * x^7 * z^-1 * x ] T65.605 : Triangle type {28,28,70} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y^-1 * x * z^2, z^-2 * x^3 * z^-2 * x ] T65.606 : Triangle type {28,28,70} Group order 140 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^7 * z^-1 * x * z^-1 ] T65.607 : Triangle type {28,28,70} Group order 140 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^-2 * x * z^-1 * y * z^-1 * x * z^-3 * x^2 * y * z^-4 ] T65.608 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-4 * y * x^-1 * y^5 * x^-4 * z^2 * x^-3 ] T65.609 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^4 * z^-4, x^-1 * y * x^-1 * y^5 * x^-4 * y^2 ] T65.610 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T65.611 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^-9 * z^4 * x^-3 ] T65.612 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^11 * x^-2 * y^5 ] T65.613 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x^-7 * z^4 * x^-1 ] T65.614 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z * x^-1 * z^10 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T65.615 : Triangle type {34,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^19 * z^-1 * x^8 * y^-1 * x^6 ] T65.616 : Triangle type {66,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-5 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-2 ] T65.617 : Triangle type {66,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-2 * x^5 * y^-5 * x * y^-1 * x * y^-2 ] T65.618 : Triangle type {66,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^4 * z^-1 * y^9 ] T65.619 : Triangle type {66,132,132} Group order 132 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 * y^3 ] T65.620 : Triangle type {66,132,132} Group order 132 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-66, y * z^-1 ] T65.621 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x^-2 * y^-1, y^-56 * x * y^-9, x * z^-1 ] T65.622 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^36 * x^-1 * y^7 ] T65.623 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-14 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-3 * y^6 ] T65.624 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^10 * x^-1 * y * x^-1 * y^5 * x^-2 * y^7 ] T65.625 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^6 * x^-1 * y ] T65.626 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^7 * y^-5 * x * y^-1 * x * y^-3 ] T65.627 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T65.628 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y^5 * x^-1 * y^5 ] T65.629 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-3 * y^5 * x^-6 ] T65.630 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * x^-1 * y^5, z^-6 * x * z^-4 ] T65.631 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-5 ] T65.632 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-2, x^2 * z^-4 * x^7 ] T65.633 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-6 ] T65.634 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^5 * z^-4, x^2 * z^-4 * x^6 * z^-1 ] T65.635 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^5 * x^-6 * z^4 * x^-1 * z * x^-1 * z^3 ] T65.636 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^3 * z^-1 * y * z^-1 * y^9 ] T65.637 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^5 * z^-4, x^-2 * y * x^-1 * y^5 * x^-2 * z^4 * x^-2 ] T65.638 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-1 * y^5, z^-1 * x * z^-4 * x^5 * z^-2 ] T65.639 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^4 * z^-4, x^-3 * y^3 * x^-7 ] T65.640 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^5 * z^-3 * x^12 ] T65.641 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^2 * z^-3 * x^9 ] T65.642 : Triangle type {131,131,131} Group order 131 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-20 * z^2 * x^-5 ] Genus 66 T66.1 : Triangle type {2,3,26} Group order 1014 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-25 * x ] T66.2 : Triangle type {2,4,30} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y^-1 * z^-1 * y * z^-2 * y * x * z^6 ] T66.3 : Triangle type {2,4,69} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-53 * x * z^8 * y^-1 * z^-7 ] T66.4 : Triangle type {2,4,134} Group order 536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-134 ] T66.5 : Triangle type {2,4,264} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-25 * x * y^-1 * z^-106 ] T66.6 : Triangle type {2,6,68} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^54 * y * x * z * y^-1 * z^-5 * x * z^6 ] T66.7 : Triangle type {2,8,20} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^-5 * x * y^-3 * z^-4 ] T66.8 : Triangle type {2,8,46} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-23 * x * z^3 * y * x * z * y^-1 * z^-5 * x * y^-1 * z^-11 ] T66.9 : Triangle type {2,9,10} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, z^10 ] T66.10 : Triangle type {2,10,35} Group order 350 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^22 * y * z^-1 * x * y * z^-7 * x * z^3 ] T66.11 : Triangle type {2,10,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-5 * x * z^20 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T66.12 : Triangle type {2,13,26} Group order 338 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-13 ] T66.13 : Triangle type {2,14,24} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^6 * y * x * z * y * z^-5 * x * y^-1 * z^-3 * x * z^6 ] T66.14 : Triangle type {2,14,154} Group order 308 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-2 * y^9 * z^-2, z^-1 * x * z^9 * y * z^-4 * x * z * y^-1 * z^-5 ] T66.15 : Triangle type {2,26,143} Group order 286 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^6 * y^-3 * x * z^4 ] T66.16 : Triangle type {2,30,30} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^-8 * z^-1 * y * x, z^-3 * x * z * y^-1 * z^-5 ] T66.17 : Triangle type {2,30,30} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-16 * z^4 * y^-5 * z^4 * y^-1 ] T66.18 : Triangle type {2,46,138} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-14 * y^11 * z^-3 * y^15 * z^-1 * y ] T66.19 : Triangle type {2,68,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-1 * y^12 * z^-3 * y^18 ] T66.20 : Triangle type {2,69,69} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-55 * y^11 * z^-1 ] T66.21 : Triangle type {2,133,266} Group order 266 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^112 * z^-20 * y ] T66.22 : Triangle type {2,134,134} Group order 268 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^21 * y^-111 * z ] T66.23 : Triangle type {2,264,264} Group order 264 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-110 * z ] T66.24 : Triangle type {3,3,13} Group order 507 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-13 ] T66.25 : Triangle type {3,3,133} Group order 399 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^7 * y * x^-2 * z^4 ] T66.26 : Triangle type {3,3,133} Group order 399 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x * z^3 * y^-1 * x * z^-5 ] T66.27 : Triangle type {3,10,40} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y, y^10 ] T66.28 : Triangle type {3,12,76} Group order 228 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y * z^-1 ] T66.29 : Triangle type {3,30,70} Group order 210 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^2 * z^-1 * x^-1 * z^3, z^-1 * y^5 * z^-1 * y * z^-2 ] T66.30 : Triangle type {3,67,201} Group order 201 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-56 * z * y^-8 * z^2 ] T66.31 : Triangle type {3,68,68} Group order 204 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^55 * y^-10 * z * y^-1 ] T66.32 : Triangle type {3,198,198} Group order 198 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-55 * z * y^-9 * z ] T66.33 : Triangle type {4,4,15} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^4 * y * z^-5 * x^-1 * y^-1 * z^-1 * x * z^3 ] T66.34 : Triangle type {4,4,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * x^-1 * y * x^2 * z^3 ] T66.35 : Triangle type {4,4,67} Group order 268 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^56 * y * x^-1 * y * x^-1 * z^9 ] T66.36 : Triangle type {4,4,132} Group order 264 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-52 * x * y^-1 * z^-13 ] T66.37 : Triangle type {4,6,6} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, y * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z^2 ] T66.38 : Triangle type {4,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, z^-3 * x^-1 * y * z^-2 ] T66.39 : Triangle type {4,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-3 * x^-1 * y * z^-2 ] T66.40 : Triangle type {4,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * y^7 * z^-1, z^4 * y^-1 * x * z^5 ] T66.41 : Triangle type {4,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^5 * x^-1 * y^-3 * z * y, z^3 * y * z^-1 * x^-1 * z^5 ] T66.42 : Triangle type {4,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^19 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y^2 ] T66.43 : Triangle type {4,46,46} Group order 184 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^16 * z^-2 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y^5 * z^-3 * y^4 ] T66.44 : Triangle type {4,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^15 * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 ] T66.45 : Triangle type {5,8,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^2 * z^2, x^-1 * z * y * x * y^-1 * z^-1, y^8 ] T66.46 : Triangle type {5,8,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T66.47 : Triangle type {5,9,9} Group order 225 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^9 ] T66.48 : Triangle type {5,34,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T66.49 : Triangle type {5,35,35} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T66.50 : Triangle type {5,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T66.51 : Triangle type {5,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T66.52 : Triangle type {6,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, x * z^-1 * x^2 * y^-2 ] T66.53 : Triangle type {6,6,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, (x * z^-1 * x)^2, y^6, z * y^2 * x^-1 * z^2, y * z^-1 * y * x^-1 * y * x * z ] T66.54 : Triangle type {6,6,34} Group order 204 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^20 * y * x * z^13 ] T66.55 : Triangle type {6,24,56} Group order 168 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^2, x^6, y^-1 * z^-1 * y * x * z * x^-1 ] T66.56 : Triangle type {6,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, z * y^-1 * z * y^-1 * x * z * y^-1 * z ] T66.57 : Triangle type {6,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-1 * z * y^-4 * z * y^-1 * z^2 * y^-1 ] T66.58 : Triangle type {7,23,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-5 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T66.59 : Triangle type {7,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 * y^6 * z^-2 * y^2 ] T66.60 : Triangle type {7,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, z * x^-2 * y * x, z * y^-2 * z * y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-5 * z * y^-4 ] T66.61 : Triangle type {7,24,24} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-3 * z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-9 * z ] T66.62 : Triangle type {7,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-3 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-3 ] T66.63 : Triangle type {7,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T66.64 : Triangle type {7,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T66.65 : Triangle type {8,8,10} Group order 200 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T66.66 : Triangle type {8,8,10} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z * y^-1 * x^3 * z^3 ] T66.67 : Triangle type {8,8,23} Group order 184 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^8 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z^5 ] T66.68 : Triangle type {8,76,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^2 * x^-1 * y^6 ] T66.69 : Triangle type {8,76,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-2 * y * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-1 * y * z^-1 ] T66.70 : Triangle type {9,9,57} Group order 171 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, y * z^-1 * x^-2 * z^3 ] T66.71 : Triangle type {10,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x * z^2, x^10 ] T66.72 : Triangle type {10,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^10 ] T66.73 : Triangle type {10,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * z * x^-1 * z^3, x * y^-1 * x * y^-1 * x * y^-3 ] T66.74 : Triangle type {10,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, x^-1 * z * x^-3 * z^4 ] T66.75 : Triangle type {12,13,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * y * z^-4, x^12 ] T66.76 : Triangle type {12,14,14} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, (y^4 * z^-1 * y * z^-1)^2, x^-12 ] T66.77 : Triangle type {12,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-3, x^4 * z^-4 * x^2 * y^-4 * x^2 ] T66.78 : Triangle type {12,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, z^-3 * x * z^-4 * x * y * z^-4 ] T66.79 : Triangle type {13,13,13} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * x * y * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T66.80 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^2 * z^-4, x^4 * z^-3 * x^4 * y^-3 * x^2 ] T66.81 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^2 ] T66.82 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^4 * z^-3, x^4 * z^-3 * x^4 * y^-3 * x^2 ] T66.83 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^5 * z^-1 * y, x^4 * z^-3 * x^4 * y^-3 * x^2 ] T66.84 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^3 * z^-4, x^4 * z^-3 * x^4 * y^-3 * x^2 ] T66.85 : Triangle type {13,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^-1 * y^11 ] T66.86 : Triangle type {14,14,77} Group order 154 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^4 * y^-1 * z^-1 * x^-1 * y * x * z^4 ] T66.87 : Triangle type {14,14,77} Group order 154 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^4 * y^-1 * z^-2 * x^-1 * z^4 ] T66.88 : Triangle type {14,14,77} Group order 154 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, y * z^-1 * x * z * y^-1 * z^-3 * x * z^4 ] T66.89 : Triangle type {15,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * y^-1 * z^-1 * x^7 * z^-1 ] T66.90 : Triangle type {15,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^3 ] T66.91 : Triangle type {15,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, z^-1 * y * x^4 * z^-4 ] T66.92 : Triangle type {15,30,30} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, y^8 * z^-2 ] T66.93 : Triangle type {16,36,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^6 * z^-4 * x^2 * y^-4 * x^4 ] T66.94 : Triangle type {16,36,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^-2 * x^4 * y^-7 ] T66.95 : Triangle type {18,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-4 * x^2 * y^-4 ] T66.96 : Triangle type {18,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-4 * x^2 * z^-4 ] T66.97 : Triangle type {18,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x * z^-3 * x^5 * y^-1 * x ] T66.98 : Triangle type {20,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-3 * y^4 * z^-4, x^-2 * y^6 * x^-4 * y ] T66.99 : Triangle type {20,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^-4 * y * x^-1 * y^6 * x^-9 ] T66.100 : Triangle type {20,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 ] T66.101 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, z * x^-6 * z^5 ] T66.102 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-2 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T66.103 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-3 * x^5 * y^-5 * x * y^-1 * x * y^-3 ] T66.104 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-3 * x * z^-4 * x^2 * z^-5 ] T66.105 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x^6 * y^-5 * x * y^-1 * x * y^-1 * x * y^-2 ] T66.106 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z * x^-1 * z * x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T66.107 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T66.108 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-4 * y^2, z^-7 * y * x^2 * z^-4 ] T66.109 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, x^2 * z^-4 * x^5 * z^-2 ] T66.110 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^5 * z^-4, x^-1 * y * x^-1 * y^5 * x^-6 ] T66.111 : Triangle type {23,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^8 * y^-1 * x^8 * z^-1 * x^6 ] T66.112 : Triangle type {24,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T66.113 : Triangle type {28,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-4 ] T66.114 : Triangle type {28,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^8 * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x^3 ] T66.115 : Triangle type {28,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T66.116 : Triangle type {28,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-6 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T66.117 : Triangle type {28,35,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^-2 * y^6 * x^-4 * z * x^-1 ] T66.118 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-14 * x^4 * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T66.119 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-3 * y * x^-1 * y * x^-1 * z^3 * x^-4 * z^3 * x^-4 ] T66.120 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^5 * z^-4, x^2 * z^-4 * x^7 ] T66.121 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-6, z^-7 * y * x^2 * z^-4 ] T66.122 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^3, z^-7 * y * z^-4 ] T66.123 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^8 * z^-1 * y^11 ] T66.124 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^2 * y^-9 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T66.125 : Triangle type {34,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^3 * y^-1 * z * y^-7 * z * y^-1 * z * y^-2 * z^3 ] T66.126 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-31 * y * x^-8 * z * x^-5 ] T66.127 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^3 * x^-7, y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 ] T66.128 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-5 * y, z^-1 * x * z^-4 * x^2 * z^-4 ] T66.129 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^3 * z^-3 * x^10 ] T66.130 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-7 * x * y^-5 * x * y^-1 * x * y^-5 ] T66.131 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, z^-1 * x * z^-4 * x^2 * z^-4 ] T66.132 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^2 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T66.133 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] T66.134 : Triangle type {45,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^13 * y^-7 * x^3 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T66.135 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^4 * z^-1 * x^-1 * y * x^-1 * y^5 ] T66.136 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^2 * x^-1 * y * x^-1 * y^3 * z^-1 ] T66.137 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, z^-3 * x^2 * z^-3 ] T66.138 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * y^-1 * z^-2, y^-4 * z^3 ] T66.139 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, z * x^-1 * z^2 * x^-3 * z * x^-1 * z^3 * x^-1 ] T66.140 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, y * z^-1 * y^4 * z^-1 * y * z^-2 ] T66.141 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * x^-3 * z^4 ] T66.142 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1, x * y^-1 * x * y^-1 * x * y^-3 ] T66.143 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^8 * y^-2 ] T66.144 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^9 * z^-1 * x * z^-1 * x^4 ] T66.145 : Triangle type {46,46,69} Group order 138 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^5 * x^-1 * z^2 * x^-1 * z^3 * x^-2 * z^4 * x^-1 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z ] T66.146 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-14 * z * y^-19 ] T66.147 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-32 * x * y^-12 ] T66.148 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-2 * x^6 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T66.149 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^5 * y^-9 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T66.150 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, z^-6 * x^2 * z^-4 ] T66.151 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-3 * y * x^-1 * y * x^-1 * y^5 * x^-7 * y * x^-1 ] T66.152 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^3 * y^-1 * z * y^-6 * z^7 ] T66.153 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^7 * y^-5 * x * y^-1 * x^2 ] T66.154 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * y^-2 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T66.155 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^4 * x^-6, z^-6 * x * z^-4 ] T66.156 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^5 * z^-4, x^-2 * y^2 * x^-8 ] T66.157 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^2 * x^-8, y^2 * z^-1 * y * z^-1 * y^7 * z^-2 ] T66.158 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^7 * y^-1 * z^8 * x^-3 * z^10 ] T66.159 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-5 * y, y^2 * z^-1 * y * z^-1 * y^5 * z^-4 ] T66.160 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^2 * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T66.161 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^3 * x^-7 * z^4 * x^-1 * z^3 ] T66.162 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-4 * y^5 * x^-3 * z^3 * x^-2 ] T66.163 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-2 * z^13 * x^-3 * z * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 ] T66.164 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^9 * y^-3 * x^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T66.165 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-6, z^-5 * y^5 * z^-4 ] T66.166 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-1 * y^5, x * z^-4 * x^2 * z^-4 ] T66.167 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, x^-1 * y * x^-1 * y^5 * x^-2 * y^4 ] T66.168 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 ] T66.169 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^-4 * y^5 * x^-5 * z * x^-1 ] T66.170 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-16 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T66.171 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^4 * z^-1 * y^9 ] T66.172 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 * y^2 * z^-1 ] T66.173 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T66.174 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-4 * y * x^-1 * y^5 * x^-8 ] T66.175 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T66.176 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, z^-2 * x * z^-4 * x^6 * z^-2 ] T66.177 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-8 * z^6 ] T66.178 : Triangle type {67,134,134} Group order 134 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-67, y * z^-1 ] T66.179 : Triangle type {68,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-1 * x, y * x^4 * z^-4 * y * x^2 * z^-4 ] T66.180 : Triangle type {68,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^7 * y^-1 * x * y^-1 ] T66.181 : Triangle type {68,68,68} Group order 136 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-12 * z * x^-1 * z * x^-1 * z * x^-1 * y ] T66.182 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x^-2 * y^-1, y^-56 * x * y^-10, x * z^-1 ] T66.183 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, z * x^-7 * z^6 ] T66.184 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-2, z * x^-7 * z^6 ] T66.185 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^2 * z^-1 * x * z^-4 * x^9 ] T66.186 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^31 * x^-1 * y^5 * x^-1 * y^7 ] T66.187 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 ] T66.188 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, y^-2 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T66.189 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * x^-1 * y^5, x^-10 * z ] T66.190 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 * y^2 * z^-1 ] T66.191 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^3 * x^-1 * z^5 * x^-1 * z^5 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T66.192 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-12 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-3 * y^6 ] T66.193 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * y, z^3 * x^-4 * y^-4 * z * y^-1 * z * y^-1 * z^2 ] T66.194 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-1 * y, x^2 * z^-4 * x^6 * z^-1 ] T66.195 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-4 * y * x^-1 * y * x^-3 * y * x^-1 * y * x^-1 * y * x^-9 * y * x^-4 ] T66.196 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * x^-1 * y^5, x^2 * z^-4 * x^3 * y^-3 * x^3 ] T66.197 : Triangle type {133,133,133} Group order 133 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-1 * y^7 * z^-2, x^-3 * y^4 * x^-6 ] Genus 67 T67.1 : Triangle type {2,4,48} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y * z^-1)^6, z^-3 * x * z^2 * y * x * z^2 * y * x * y * z^-6 ] T67.2 : Triangle type {2,4,48} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^2 * y * z^-3 * x * y^-1 * z * y^-1 * z^3 ] T67.3 : Triangle type {2,4,136} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-136 ] T67.4 : Triangle type {2,4,136} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-53 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T67.5 : Triangle type {2,4,268} Group order 536 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-26 * x * y^-1 * z^-107 ] T67.6 : Triangle type {2,6,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^2 * y * x * z * y * z^-2 * x * z^2 * y * x * y^-1 * z^-7 * x ] T67.7 : Triangle type {2,6,69} Group order 414 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-36 * x * z^18 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T67.8 : Triangle type {2,6,201} Group order 402 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-35 * x * z^17 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T67.9 : Triangle type {2,8,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-4)^2, z^10 ] T67.10 : Triangle type {2,8,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1, z^10, z^-2 * y * x * y^-2 * z^-2 * y * z^-1 * y ] T67.11 : Triangle type {2,9,12} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z^2 * y * x * y^-1 * z^-3 * y * z^-1 ] T67.12 : Triangle type {2,9,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T67.13 : Triangle type {2,12,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * z * y * x * y^-1 * z^-4 ] T67.14 : Triangle type {2,15,30} Group order 330 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^-15 ] T67.15 : Triangle type {2,15,30} Group order 330 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * z^2 * y^-2 * z^-1 * y * z^-2, y^-15 ] T67.16 : Triangle type {2,16,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, x * z^2 * y * x * z^3 * y * x * z * y * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T67.17 : Triangle type {2,16,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * z * y^10 * x * y^-1 * z^-1 * y, x * z^3 * y * x * z^3 * y^5 * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-5 ] T67.18 : Triangle type {2,36,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-3 * y^11 * z^-3 * y^19 ] T67.19 : Triangle type {2,36,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^2 * z^-3 * y * z^-1 * y^10 * z^-3 * y * z^-13 * y^2 ] T67.20 : Triangle type {2,48,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^-19 * y^9 * z^-1 * y * z^-2 * y * z^-14 * y ] T67.21 : Triangle type {2,48,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-1 * z * y^6 * x * y^-4, y^-3 * z^5 * y^-1 * z^2 * y^-4 * z * y^-8 ] T67.22 : Triangle type {2,48,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y^2 * z^-3 * y^3)^2 ] T67.23 : Triangle type {2,48,48} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z * y^-5 * z^-1 * x * z^3 ] T67.24 : Triangle type {2,135,270} Group order 270 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^113 * z^-22 ] T67.25 : Triangle type {2,136,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-37 * y^12 * z^-1 * y^17 ] T67.26 : Triangle type {2,136,136} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-113 ] T67.27 : Triangle type {2,268,268} Group order 268 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^21 * y^-112 ] T67.28 : Triangle type {3,6,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y * x^-1 * z^4, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T67.29 : Triangle type {3,6,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^2 * y * x^-1 * y * x^-1 * z^4 ] T67.30 : Triangle type {3,8,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T67.31 : Triangle type {3,8,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T67.32 : Triangle type {3,8,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T67.33 : Triangle type {3,10,60} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^10 ] T67.34 : Triangle type {3,15,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * z^-1 * x * z^2 * y^-1 ] T67.35 : Triangle type {3,36,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-2)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2 ] T67.36 : Triangle type {3,36,36} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, z^-2 * y * z^-1 * y * z^-2 * y^7 * z^-1 * y^3 ] T67.37 : Triangle type {3,68,204} Group order 204 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-57 * z * y^-8 * z^2 ] T67.38 : Triangle type {3,69,69} Group order 207 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-58 * z * y^-8 * z^2 ] T67.39 : Triangle type {3,201,201} Group order 201 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-56 * z * y^-9 * z ] T67.40 : Triangle type {4,4,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T67.41 : Triangle type {4,4,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^-1 * z^3 * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 * z ] T67.42 : Triangle type {4,4,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, y * z^-2 * x^-1 * y^-1 * x * z^4 ] T67.43 : Triangle type {4,4,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x^2 * z^2 * y ] T67.44 : Triangle type {4,4,68} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^4 * x^-1 * z^2 * y^-1 * z ] T67.45 : Triangle type {4,4,68} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-4 * x^-1 * z^2 * y^-1 * z^-1 ] T67.46 : Triangle type {4,4,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-23 * x^-1 * z^3 * y * z^-7 ] T67.47 : Triangle type {4,4,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-23 * x^-1 * z^3 * y * z^-1 * x * z * y^-1 * z^-4 ] T67.48 : Triangle type {4,4,68} Group order 272 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^54 * y * x * z^13 ] T67.49 : Triangle type {4,4,134} Group order 268 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^56 * y * x^-1 * z^10 ] T67.50 : Triangle type {4,6,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, y * x * y^-2 * x * z * y^-1 * z, (y * z^-1)^4, z^8 ] T67.51 : Triangle type {4,6,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^-2, y^6, z^8 ] T67.52 : Triangle type {4,6,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x * z^-1 * y)^2, (y * z^-2)^2, x^-1 * y * x^-2 * z * y^2, z^8 ] T67.53 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^2, z^8 ] T67.54 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, x^-1 * z * y * x * y^-1 * z^-1 ] T67.55 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, (y * z^-2)^2, z^8 ] T67.56 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y, y^6, (x * z^-1 * y)^2 ] T67.57 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y)^2, z^8 ] T67.58 : Triangle type {4,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y)^2 ] T67.59 : Triangle type {4,6,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, z * y * z^-1 * y^2 * z^-1 * x^-1 * z ] T67.60 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z^4 * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * z ] T67.61 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^5 * y * z^-2 * x^-1 * z * y * x^-1 * z^4 ] T67.62 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-14 * x^-1 * z * y^-1 * z^-1 * x * z^3 * y * x * y^-1 * z^-6 ] T67.63 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-7 * x * z^5 * y^-1 * x * z * y^-1 * z^-13 ] T67.64 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 * x * z ] T67.65 : Triangle type {4,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z^4 * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 * x * z ] T67.66 : Triangle type {4,9,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-3 * x * y^-4 ] T67.67 : Triangle type {4,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1, x^-1 * z * y^2 * x * z * y^2 ] T67.68 : Triangle type {4,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (z^-1 * y)^3, x^-1 * z * y^2 * x * z * y^2 ] T67.69 : Triangle type {4,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, z * y^3 * x * y^-1 * z * y^-1 ] T67.70 : Triangle type {4,10,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T67.71 : Triangle type {4,10,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1 ] T67.72 : Triangle type {4,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T67.73 : Triangle type {4,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^9 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x * z ] T67.74 : Triangle type {4,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z * y * x * z^5 * y * x * y^-1 * z^-1 * x^-1 * z^8 ] T67.75 : Triangle type {4,12,51} Group order 204 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z * y^-1 * z^-1 * x^-1 * z^2 ] T67.76 : Triangle type {4,12,51} Group order 204 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, y * x^-1 * z^7 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x^-1 * z ] T67.77 : Triangle type {4,24,48} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y^2 * x^-1 * y * z^-2 ] T67.78 : Triangle type {4,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z^4 * y * z^-1, y^-1 * z * y^-1 * z * y^-8 ] T67.79 : Triangle type {4,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z^4 * y * z^-1, y^-1 * z * y^-1 * z * y^-3 * z * y^-3 * z ] T67.80 : Triangle type {4,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-22 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T67.81 : Triangle type {4,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^16 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 ] T67.82 : Triangle type {5,8,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y * x^-2 * y^-2 * z, z^-2 * x^-2 * z * x^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x ] T67.83 : Triangle type {5,8,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, (z^-1 * y)^3, y^3 * x^-1 * z^3 ] T67.84 : Triangle type {6,6,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-2 * x^-2 * y^-2 * z^-1 ] T67.85 : Triangle type {6,6,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, x^-1 * z^3 * y * x * z * y^-1 * z^-3 ] T67.86 : Triangle type {6,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, z * y * x^-1 * z * y * x * z^4 ] T67.87 : Triangle type {6,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T67.88 : Triangle type {6,9,9} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, x * z * y * x^-1 * y * z^-1 * y ] T67.89 : Triangle type {6,9,9} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y^-1 * z * y^-3 * z^2 * y^-2 ] T67.90 : Triangle type {6,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^-2 * x^2 * y^-2, z^-2 * y * x^-1 * z * y^-2, z * y^-1 * z^-2 * x^-1 * z^4 ] T67.91 : Triangle type {6,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^9 * y^-1 * x^-1 * y * z^-5 * x ] T67.92 : Triangle type {6,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T67.93 : Triangle type {6,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y^-4 * z * y^-1 * z ] T67.94 : Triangle type {6,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^5 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T67.95 : Triangle type {6,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^4 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T67.96 : Triangle type {8,21,24} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x^8, y^4 * x * y^-1 * z * y ] T67.97 : Triangle type {8,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^5 * z^-1 * y * z^-2 ] T67.98 : Triangle type {8,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^2 * z^-1 * y^3 * z^-1 * y * z^-2 ] T67.99 : Triangle type {8,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y * z^-7 * y * z^-1 * y^2 * z^-1 * y^5 * z^-1 * y ] T67.100 : Triangle type {8,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z * y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-6 * z * y^-1 ] T67.101 : Triangle type {9,51,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T67.102 : Triangle type {9,51,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-7 * z^5 * y^-1 * z * y^-3 ] T67.103 : Triangle type {10,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * x^-1 * y^3 * z^-1, x^10 ] T67.104 : Triangle type {10,16,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y * z^-5 * y^3 * z^-3 ] T67.105 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, (x * z^-1)^4 ] T67.106 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x^3 * z^-2 * x, z^-4 * x^-1 * y * z^-3 ] T67.107 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-1 * x^4 * y^-3, z^2 * y * z^-1 * x^-1 * z^4 ] T67.108 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, y^-1 * x^4 * y^-3 ] T67.109 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^10 ] T67.110 : Triangle type {10,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, x^10 ] T67.111 : Triangle type {10,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^2 * z^-1 * y * z^-4 * y^5 * z^-1 * y ] T67.112 : Triangle type {10,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^2 * z^-1 * y * z^-4 * y^4 * z^-3 ] T67.113 : Triangle type {10,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-8 * y^3 * z^-4 ] T67.114 : Triangle type {10,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^4 * z^-4 * y^7 ] T67.115 : Triangle type {15,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, y * x * y^-1 * x * z^-2, z^-1 * y^2 * x^-2 * y^4 ] T67.116 : Triangle type {15,15,15} Group order 165 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x^2 * z^-1 * y, x^-1 * y * x^2 * y^-1 * z^-1, y^3 * x^-2 * y^2 * x^-1 * y ] T67.117 : Triangle type {16,16,20} Group order 160 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, y^2 * x^2 * z^2, x^5 * y^-1 * x * y^-1 ] T67.118 : Triangle type {16,16,20} Group order 160 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y * z^-1 * x^2 * z * y, x^5 * y^-1 * x * y^-1 ] T67.119 : Triangle type {16,16,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T67.120 : Triangle type {16,16,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * z * y * z^-4 * x^-1 * y * x^-1 * y * x^-1 * y * z^-1 ] T67.121 : Triangle type {16,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T67.122 : Triangle type {16,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-2 * x^5 * y^-6 * x * y^-1 ] T67.123 : Triangle type {16,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^2 * z^-1 * x * z^-4 * x^2 * z^-4 ] T67.124 : Triangle type {16,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T67.125 : Triangle type {18,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T67.126 : Triangle type {18,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T67.127 : Triangle type {18,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-4 * x^2 * y^-4 ] T67.128 : Triangle type {18,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^-7 * z^4 * x^-1 * z^4 ] T67.129 : Triangle type {18,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^7 * y^-4 * x^2 * y^-4 * x^5 ] T67.130 : Triangle type {18,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * y^2 * x^-10 * z * x^-1 * z * x^-1 * z * x^-1 * y ] T67.131 : Triangle type {24,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T67.132 : Triangle type {24,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3, y^-2 * x^4 * y^-4 ] T67.133 : Triangle type {24,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-2 * y * x^-1 * y * x^-5 * z * x^-1 * z * x^-1 ] T67.134 : Triangle type {24,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^4 * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x ] T67.135 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y * x^-8 * z * x^-6 ] T67.136 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-2, x^7 * y^-6 * x^2 ] T67.137 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-4 * x * z^-1 * x * z^-4 * x^4 * z^-3 ] T67.138 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-12 * y^2 * x^-8 * z * y * x^-2 ] T67.139 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x * z^-1 * x * z^-1 * x^9 ] T67.140 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-4 * z * x^-1 * z, z^-1 * y^4 * z^-3 ] T67.141 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-7 * z * y ] T67.142 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y^-3 * x^2 * y^-2 * z, z^-2 * y * x^2 * z^-3 ] T67.143 : Triangle type {24,48,48} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z * y^-1 * z * x^-1 * y^-1 * z^2, x^-7 * z * y ] T67.144 : Triangle type {28,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^5 * z^-2 * y^8 ] T67.145 : Triangle type {28,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^-3 * y^6 * x^-4 * z * x^-2 ] T67.146 : Triangle type {28,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-13 * z^2 * x^-6 * y^2 * x^-7 ] T67.147 : Triangle type {28,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5, z^-3 * y * z^-3 * y^4 * z^-4 ] T67.148 : Triangle type {28,70,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-5 ] T67.149 : Triangle type {36,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^7 * z^-1 * y * z^-1 ] T67.150 : Triangle type {36,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z * y^-1 * z * y^-11 * x * y^-1 * x * y^-1 ] T67.151 : Triangle type {36,36,36} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * z * y^-5 * z^3 * y^-7 ] T67.152 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-10 * x^3 * y^-5 * x * y^-6 ] T67.153 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^3 * z^-3 * x^10 ] T67.154 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^14 * y^-7 * x^3 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T67.155 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^12 * x^-1 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T67.156 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z^2 ] T67.157 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^3 * x^-7, y * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-3 ] T67.158 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T67.159 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x * z^-3 * x^8 ] T67.160 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^2 * x^-1 * y^5 * x^-1 * y^5 ] T67.161 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-5 * z * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T67.162 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-2 * x * z^-4 * x^4 * z^-3 ] T67.163 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-2 ] T67.164 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^3 * z^-1 * y * z^-1 * y^9 ] T67.165 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^7 * y^-5 * x * y^-1 * x^2 ] T67.166 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T67.167 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^8 * x^-4 * z^10 ] T67.168 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-2 * y^4, z^-6 * y^2 * z^-4 ] T67.169 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-1 * y^5, x^-8 * z^6 ] T67.170 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^4 * z^-1 * y * z^-1 * y * z^-1 * y^4 * x^-1 * y^5 ] T67.171 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^38 * z^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T67.172 : Triangle type {46,69,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y^5 * z^-4, x^-3 * y^3 * x^-7 ] T67.173 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^-68, y * z^-1 ] T67.174 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^3 * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T67.175 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-4 * y^2, z^2 * x^-7 * z^4 * x^-1 * z^2 ] T67.176 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-7 * y^2 ] T67.177 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y ] T67.178 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-1 * y, x^-2 * y * x^-1 * y^5 * x^-2 * z^4 * x^-2 ] T67.179 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-19 * z * y^-1 * z * y^-6 ] T67.180 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-8 * z^4 * x^-2 ] T67.181 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-40 * x^2 * z^-4 ] T67.182 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-5 * y^2 * z^-1 ] T67.183 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^2 * x^-8, y^2 * z^-1 * y * z^-1 * y^6 * z^-3 ] T67.184 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, z^2 * x^-7 * z^4 * x^-1 * z^2 ] T67.185 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^5 * z^-1 * x^5 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T67.186 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-5 * y, z^-6 * x * z^-4 ] T67.187 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^4 * z^-1 * y^9 ] T67.188 : Triangle type {68,136,136} Group order 136 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^19 * z^-1 * x^8 * z^-1 * x^6 ] T67.189 : Triangle type {135,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-2 * x * y^-7 * x^3 * y^-5 * x * y^-6 ] T67.190 : Triangle type {135,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^6 * z^-3, x^-3 * y^2 * x^-4 * z^4 * x^-2 ] T67.191 : Triangle type {135,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-3 ] T67.192 : Triangle type {135,135,135} Group order 135 Reflexible action Defining relators: [ x^-2 * y^-1, y^-57 * x * y^-10, x * z^-1 ] T67.193 : Triangle type {135,135,135} Group order 135 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^4 * z^-1 * y^9 ] Genus 68 T68.1 : Triangle type {2,4,138} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-138 ] T68.2 : Triangle type {2,4,272} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-27 * x * y^-1 * z^-108 ] T68.3 : Triangle type {2,6,6} Group order 804 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z^2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2 * y * z^-1 ] T68.4 : Triangle type {2,6,70} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^56 * y * x * z * y^-1 * z^-5 * x * z^6 ] T68.5 : Triangle type {2,6,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-33 * x * z * y * x * z^18 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T68.6 : Triangle type {2,8,92} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-23 * x * z^3 * y * x * z * y^-1 * z^-6 * x * y^-1 * z^-10 ] T68.7 : Triangle type {2,10,36} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-6 * x * z^12 * y * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-4 ] T68.8 : Triangle type {2,10,170} Group order 340 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-4 * x * z^19 * y * z^-7 * x * z^2 * y^-1 ] T68.9 : Triangle type {2,12,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^18 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^4 ] T68.10 : Triangle type {2,18,153} Group order 306 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-5 * z^4)^2, z^-1 * x * z^4 * y * z^-4 * x * y * z^-6 ] T68.11 : Triangle type {2,20,32} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z * y * x * z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-5 ] T68.12 : Triangle type {2,36,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * z^6 * y * x * z * y^-1 * z^-4, y^-6 * z^3 * y^-4 * z^5 ] T68.13 : Triangle type {2,70,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-39 * y^12 * z^-1 * y^17 ] T68.14 : Triangle type {2,137,274} Group order 274 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^114 * z^-22 * y ] T68.15 : Triangle type {2,138,138} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^23 * y^-113 * z ] T68.16 : Triangle type {2,272,272} Group order 272 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-112 * z ] T68.17 : Triangle type {3,6,6} Group order 402 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z * y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T68.18 : Triangle type {3,6,6} Group order 402 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z * y^-1 * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x^-1 * y * x ] T68.19 : Triangle type {3,7,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, y^-7, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T68.20 : Triangle type {3,7,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * z^2 * y, z * y^-1 * z^-1 * x^-1 * y * x * z ] T68.21 : Triangle type {3,70,70} Group order 210 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^57 * y^-10 * z * y^-1 ] T68.22 : Triangle type {3,204,204} Group order 204 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-57 * z * y^-10 ] T68.23 : Triangle type {4,4,69} Group order 276 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^69 ] T68.24 : Triangle type {4,4,136} Group order 272 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^54 * y * x^-1 * z^13 ] T68.25 : Triangle type {4,6,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^9 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-6 * x * z ] T68.26 : Triangle type {4,8,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-5 * x^-1 * z ] T68.27 : Triangle type {4,12,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, y * x^-1 * z^7 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x * z ] T68.28 : Triangle type {4,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-1 * y^14 * z^-2 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y^5 * z^-3 * y^3 * z^-1 ] T68.29 : Triangle type {5,36,36} Group order 180 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y * z^-27 * y^6 * z^-2 ] T68.30 : Triangle type {5,36,36} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y * z^-4 * y^16 * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 * y^3 * z^-1 ] T68.31 : Triangle type {5,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T68.32 : Triangle type {5,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T68.33 : Triangle type {6,6,35} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y * x * z^2 ] T68.34 : Triangle type {6,6,35} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z * y * z^-1 * x * z^2 ] T68.35 : Triangle type {6,6,35} Group order 210 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^21 * y * x * z^13 ] T68.36 : Triangle type {6,6,102} Group order 204 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^20 * y * x * z^4 * y * x * z^8 ] T68.37 : Triangle type {6,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-1 * z * y^-8 * z ] T68.38 : Triangle type {6,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-11 ] T68.39 : Triangle type {8,8,46} Group order 184 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^8 * y * x^-1 * y * x^-1 * z^13 ] T68.40 : Triangle type {9,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-7 * z^5 * y^-1 * z * y^-1 * z * y^-1 ] T68.41 : Triangle type {9,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-6 * x * y^-1 * z^5 * y^-5 ] T68.42 : Triangle type {10,10,18} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^4 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z^4 ] T68.43 : Triangle type {10,10,85} Group order 170 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-2 * x * z^8 * y * z^-1 * x^-1 * z^2 * y^-1 * z^-2 ] T68.44 : Triangle type {10,10,85} Group order 170 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * x * z^3 * y * z^-1 * x^-1 * y * x * z^3 ] T68.45 : Triangle type {10,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x^3 * z^-2 * x, z * y * z^-2 * x^-1 * z^4 ] T68.46 : Triangle type {10,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-1 * x^4 * y^-3, z^-4 * x^-1 * z * y * z^-2 ] T68.47 : Triangle type {10,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * y * x^-1 * z^4 ] T68.48 : Triangle type {10,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, z^-1 * y * z^-4 * y * z^-2 * y^7 ] T68.49 : Triangle type {10,32,32} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z^-1 * y^5 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T68.50 : Triangle type {12,12,28} Group order 168 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^2, y * x^-3 * z * x^-2 ] T68.51 : Triangle type {12,12,28} Group order 168 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y * x^-3 * y * z^-1 * y ] T68.52 : Triangle type {12,12,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^4 * y * x^-1 * z^4 ] T68.53 : Triangle type {14,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-3, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T68.54 : Triangle type {15,50,50} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T68.55 : Triangle type {15,50,50} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, y^6 * z^-4 ] T68.56 : Triangle type {16,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^2 * z^-1 * y * z^-1 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 * y ] T68.57 : Triangle type {18,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T68.58 : Triangle type {18,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^7 * x^-5 * y ] T68.59 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^18 * z^-1 * x * z^-1 * x^11 * z^-1 * x * z^-1 * x ] T68.60 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-4 * x * y^-1 * x * y^-11 * x * y^-1 * x * y^-1 * x * y^-2 ] T68.61 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^5 * y^-5 * z^10 ] T68.62 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^4 * z^-4, x^2 * z^-2 * x^3 * y^-6 * x^2 ] T68.63 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, z^-3 * x * z^-4 * x * y * z^-4 ] T68.64 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 ] T68.65 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^4 * y^-5 * x^2, z^-7 * y * z^-4 ] T68.66 : Triangle type {35,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-35 ] T68.67 : Triangle type {36,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^7 * z^-1 * y * z^-1 ] T68.68 : Triangle type {36,36,72} Group order 144 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, z^-2 * y * z^-2 * x^2 * z^-3 * x ] T68.69 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-22 * x * y^-12 ] T68.70 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^4 * x^-1 * y^5 * x^-1 * y^5 ] T68.71 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^2 * y^-1 * z^5 * x^-1 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T68.72 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^5 * y^-9 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T68.73 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^4 * z^-1 * y^9 ] T68.74 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-6, z^4 * x^-2 * y^-4 * z * y^-1 * z * y^-1 * z^2 ] T68.75 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * y^3, z^-6 * x * z^-4 ] T68.76 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-2 ] T68.77 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^7 * z^-2, x^-2 * y * x^-1 * y^5 * x^-2 * z^4 * x^-2 ] T68.78 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x * z^-1 * x * z^-4 * x^7 * z^-1 ] T68.79 : Triangle type {69,138,138} Group order 138 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^69, y * z^-1 ] T68.80 : Triangle type {70,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T68.81 : Triangle type {70,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-7 * x^4 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T68.82 : Triangle type {70,70,70} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-16 * x * z^-11 * x^2 * y * z^-6 ] T68.83 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x^-2 * y^-1, y^-57 * x * y^-11, x * z^-1 ] T68.84 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-32 * x * y^-13 ] T68.85 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^15 * y^-7 * x^3 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T68.86 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^6 * y^-8 * x^2 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T68.87 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-1 * y^6 * x^-1 * y^2 ] T68.88 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-1 * y * x^-1 * y * x^-1 * y^5 * x^-7 * y^2 ] T68.89 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-3 * x^4 * y^-5 * x * y^-1 * x * y^-1 * x * y^-1 ] T68.90 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-1 * x^6 * y^-5 * x * y^-3 ] T68.91 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-1 * y * x^-1 * y^5 * x^-1 * y^5 ] T68.92 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-4 * y^2, z^-6 * x * z^-4 ] T68.93 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-6, z^-2 * x * z^-4 * x * y * z^-4 ] T68.94 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * y, z^-7 * y * x^2 * z^-4 ] T68.95 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^2 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T68.96 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^7 * z^-1 * y, x^2 * z^-4 * x^5 * y^-1 * x^2 ] T68.97 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * x * z^-4 * y ] T68.98 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^6 * z^-3, x * z^-1 * x * z^-4 * x^6 * z^-2 ] T68.99 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^7 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T68.100 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^5 * z^-3 * x^8 * z^-1 * x * z^-1 * x^2 ] T68.101 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^16 * y^-1 * x^-2 * z^10 ] T68.102 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-5 * x^3 * y^-11 ] T68.103 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-1 * y^7 * z^-2, x^-3 * y^5 * x^-6 ] T68.104 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * x^-3 * y^-4 * z * y^-1 * z * y^-2 * z^3 ] T68.105 : Triangle type {137,137,137} Group order 137 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^3 * z^-4, x^-2 * y * x^-1 * y^5 * x^-2 * z^4 * x^-2 ] Genus 69 T69.1 : Triangle type {2,3,9} Group order 2448 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^-1 * x * z * y * z^-1 * x * z * y * z^-3 * y^-1 * z^-3 * x * y^-1 * z^-1 ] T69.2 : Triangle type {2,3,9} Group order 2448 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, y * z^-1 * x * z * y * z^-1 * x * z^2 * y * z^-3 * y^-1 * z^-3 * x * z^2 ] T69.3 : Triangle type {2,3,9} Group order 2448 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^3 * y * z^-1 * x * z^3 * y * z^-3 * y * x * y^-1 * z^-3 * x, x * z * y * z^-1 * x * z * y * z^-1 * x * z * y * x * z * y * z^-3 * y^-1 * z^-3 * x * y^-1 * z^-1 ] T69.4 : Triangle type {2,4,8} Group order 1088 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^2 * y * x * y^-1 * z^2 * y * x * z * y * z^-1 * y * x * z * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-2 * y * z^-1 * x ] T69.5 : Triangle type {2,4,8} Group order 1088 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y * x * z * y * z^-1 * y * x * z * y * z^-1 * y * z^-1 * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-2 * y * z^-1 * y ] T69.6 : Triangle type {2,4,12} Group order 816 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, y * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T69.7 : Triangle type {2,4,20} Group order 680 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T69.8 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-56 * x * z^8 * y^-1 * z^-7 ] T69.9 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-20 * x * z^8 * y^-1 * z^-7 ] T69.10 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-5 * x * z * y * z^-3 * x * z * y * x * y^-1 * z^-5 ] T69.11 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z * y * x * z * y * z^-3 * x * z^6 * y^-1 * z^-1 ] T69.12 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-57 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T69.13 : Triangle type {2,4,72} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-17 * x * z^10 * y * x * z * y^-1 * z^-6 ] T69.14 : Triangle type {2,4,140} Group order 560 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-140 ] T69.15 : Triangle type {2,4,276} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-28 * x * y^-1 * z^-109 ] T69.16 : Triangle type {2,6,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^4 * y^-1 * z^-5, x * z * y * x * z * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T69.17 : Triangle type {2,6,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T69.18 : Triangle type {2,6,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-1 * x * z^3 * y * x * z^5 * y^-1 * z^-3 * x * y^-1 * z^-5 ] T69.19 : Triangle type {2,6,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4 ] T69.20 : Triangle type {2,6,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3 * y)^2, (y * z^-4)^2, z * y^-1 * z * y^-3 * z^-1 * x * z^2 * y^-1 ] T69.21 : Triangle type {2,8,8} Group order 544 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T69.22 : Triangle type {2,8,8} Group order 544 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * x * z * y^-2 * z^-1 * y ] T69.23 : Triangle type {2,8,8} Group order 544 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T69.24 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-11 * x * z^6 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T69.25 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-3 * x * z^10 * y * z^-1 * x * y^-1 * z^-8 ] T69.26 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^33 * y * z^-2 * x * y^-1 * z^-9 * x * z^2 ] T69.27 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-17 * x * z^16 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-5 ] T69.28 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, x * z^2 * y * z^-1 * x * z * y * x * z^5 * y^-1 * x * y^-1 * z^-11 ] T69.29 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^10 * y * x * z^2 * y^-1 * z^-5 * x * z^5 ] T69.30 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, x * z^9 * y * x * z^2 * y^-1 * z^-5 * x * z^3 * y^-1 * z^-2 ] T69.31 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-3 * x * z^5 * y * z^-1 * x * z * y^-1 * z^-3 * x * z * y^-1 * z^-4 ] T69.32 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, z^4 * y * z^-1 * x * z^6 ] T69.33 : Triangle type {2,8,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T69.34 : Triangle type {2,8,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-16 * x * z^17 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-3 ] T69.35 : Triangle type {2,8,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-15 * x * z^18 * y * x * y * z^-7 * x * z^2 * y^-1 * z^-1 ] T69.36 : Triangle type {2,12,12} Group order 408 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, x * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-2 * y ] T69.37 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, (y * z^-3)^2, x * z * y^-3 * z * y^-1 * z^-1 * y, y^12, z * y * x * z * y^3 * z^-2 * x * z^2 ] T69.38 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T69.39 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-2 * y * z^-1, y^12, y^-1 * z * y * x * y^-1 * z * y * z^-4 * x ] T69.40 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, (z * y^-1 * z)^3, y^12, y^-1 * z * y * x * y^-1 * z * y * z^-4 * x ] T69.41 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-6 ] T69.42 : Triangle type {2,12,16} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, y^12 ] T69.43 : Triangle type {2,12,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^9 * y * x * z^4 * y^-1 * z^-13 * x ] T69.44 : Triangle type {2,14,161} Group order 322 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^7 * z^-3, z^-1 * x * z^10 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T69.45 : Triangle type {2,16,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^4 * y^-5 * z^4, z^-1 * x * z^7 * y * z^-4 * x * z^2 * y^-1 * z^-4 ] T69.46 : Triangle type {2,16,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z * y * x * z * y * x * z^2 * y * z^-2 * x * z^3 * y^-1 * z^-4 * x * y^-1 * z^-1 * x * z ] T69.47 : Triangle type {2,16,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^4 * y^-5 * z^4, z^9 * y * z^-4 * x * z^4 * y^-1 * z^-1 * x ] T69.48 : Triangle type {2,16,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-1 * x * z * y * x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T69.49 : Triangle type {2,20,20} Group order 340 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-2 * y^2 * z^-1 * y * z^-1 * y ] T69.50 : Triangle type {2,20,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z * y^-1 * z^4 * y^-11 * z^3 ] T69.51 : Triangle type {2,20,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z * y^-15 * z * y^-3 ] T69.52 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-1 * z * y^-13 * z * y^-1 * z ] T69.53 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, z^2 * y^-15 * z ] T69.54 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-33 * z^3 ] T69.55 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-58 * y^11 * z^-1 ] T69.56 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-40 * y^12 * z^-1 * y^17 * z^-1 ] T69.57 : Triangle type {2,72,72} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-19 * z^3 * y^-9 * z^2 * y^-1 ] T69.58 : Triangle type {2,94,141} Group order 282 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-16 * y^11 * z^-3 * y^15 * z^-2 ] T69.59 : Triangle type {2,139,278} Group order 278 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^115 * z^-24 ] T69.60 : Triangle type {2,140,140} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-115 ] T69.61 : Triangle type {2,276,276} Group order 276 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^23 * y^-114 ] T69.62 : Triangle type {3,3,139} Group order 417 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * x^-1 * z^5 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 ] T69.63 : Triangle type {3,4,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * x^-1 * z * y * x * z^2 * y^-1, y * z^-1 * x^-1 * y * x^-1 * y^-1 * x * z^2 ] T69.64 : Triangle type {3,4,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * z^2 * y^-1 * x * z^3 ] T69.65 : Triangle type {3,4,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T69.66 : Triangle type {3,4,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^4, x^-1 * y^-1 * z^-3 * x^-1 * y^-1 * x * z^3 * y^-1 * z^-1 ] T69.67 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-2 * y^6 * z^-3 * y^2 ] T69.68 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^2 * z^-6 * y^5 * z^-1 * y * z^-2 * y * z^-1 * y ] T69.69 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^3 * y^-5 * z^2, (y * z^-1 * y * z^-1 * y)^2 ] T69.70 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (y * z^-1 * y^2)^2 ] T69.71 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z^2, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T69.72 : Triangle type {3,20,20} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x^-1 * z * y)^2 ] T69.73 : Triangle type {3,70,210} Group order 210 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-59 * z * y^-8 * z^2 ] T69.74 : Triangle type {3,207,207} Group order 207 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-58 * z * y^-9 * z ] T69.75 : Triangle type {4,4,4} Group order 544 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * z ] T69.76 : Triangle type {4,4,4} Group order 544 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * z ] T69.77 : Triangle type {4,4,6} Group order 408 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^-2 * y^-1 * z^-1 * y * x^2 * y^-1 * z * x^-1 * y^-1 * z ] T69.78 : Triangle type {4,4,10} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * y * x * z * y ] T69.79 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^-3 * x * z^8 * y * x * z * y^-1 * z^-4 ] T69.80 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-3 * x^-1 * z^7 * y^-1 * z^-1 * x * z * y^-1 * z^-4 ] T69.81 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^29 * y^-1 * x * z * y * z^-4 * x ] T69.82 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^4 * y * x * z^5 ] T69.83 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^6 * y * z^-5 * x^-1 * y^-1 * x * y^-1 * z^-3 * x * z ] T69.84 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^3 * y * z^-1 * x^-1 * z^4 ] T69.85 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, y * z^-4 * x^-1 * z^4 ] T69.86 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-24 * x * z^4 * y * z^-7 ] T69.87 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^10 * y^-1 * x * y^-1 * z^-6 * x ] T69.88 : Triangle type {4,4,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^28 * y * z^-7 * x ] T69.89 : Triangle type {4,4,70} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^3 * y * z^-5 * x * z^5 ] T69.90 : Triangle type {4,4,70} Group order 280 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-70 ] T69.91 : Triangle type {4,4,138} Group order 276 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^60 * y * x^-1 * z^8 ] T69.92 : Triangle type {4,5,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^-5, y^2 * x * y^-1 * x * y^-1 * z^2 ] T69.93 : Triangle type {4,5,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-5, (y * z^-2)^2, z * y^2 * x^-1 * z * x^-1 * y^-1 ] T69.94 : Triangle type {4,5,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-5, (x^-1 * z * y)^2, z^-1 * x^-1 * y * x^-1 * y^2 * z^-1, (x * y^-1 * z * y^-1)^2 ] T69.95 : Triangle type {4,5,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-5, y^2 * x^-2 * z * y * x^-1, z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 ] T69.96 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-5, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T69.97 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-5, (y * z^-1)^4 ] T69.98 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^-5, (x * z * y^-1)^2, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T69.99 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^-5, z^8, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T69.100 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^-5, y^-1 * z * y * x^-1 * y^-1 * z * x^-1 ] T69.101 : Triangle type {4,5,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^-5, (x * z^-2)^2 ] T69.102 : Triangle type {4,6,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, y * x^-1 * z^9 * y * x^-1 * y * z^-7 * x * z ] T69.103 : Triangle type {4,8,8} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z^2 * y * x^-1 * y^-1 * z * y^-1 * z^-1 * x * z ] T69.104 : Triangle type {4,8,8} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T69.105 : Triangle type {4,8,8} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-1 * z * y^-2 * z^-1 * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T69.106 : Triangle type {4,8,8} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, (x * z * x^-1 * y^-1)^2, z^-1 * y^3 * x * z^-1 * x^-1 * y^-1 ] T69.107 : Triangle type {4,8,8} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T69.108 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^3 * y * z^-1 * x * z^4 * y^-1 * z^-3 * x^-1 * z ] T69.109 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z * y * z^-1 * x * z^4 * y^-1 * z^-4 * x * z ] T69.110 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z * y * z^-1 * x * z^4 * y^-1 * z^-4 * x^-1 * z ] T69.111 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^3 * y * z^-1 * x * z^4 * y^-1 * z^-3 * x * z ] T69.112 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-7 * x * z^5 * y^-1 * z^-1 * x * z^4 * y * z^-9 ] T69.113 : Triangle type {4,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-14 * x^-1 * z * y^-1 * z^-1 * x * z^3 * y * x * z^2 * y^-1 * z^-4 ] T69.114 : Triangle type {4,10,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^-2 * z^-1, z^-12 ] T69.115 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, (y * z^-2)^2 ] T69.116 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, x^-1 * z^6 * y * x^-1 * y^-1 * x * y^-1 * z^-3 ] T69.117 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^3 * x^-1 * y^-1 * z, (x * z * y)^2 ] T69.118 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^3 * x * y^-1 * z^-1, (y * z^-2)^2 ] T69.119 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^-1 * y * z^-2 ] T69.120 : Triangle type {4,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2 ] T69.121 : Triangle type {4,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-3 * z^3 * y^-7 * z^3 ] T69.122 : Triangle type {4,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-3 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z^4 ] T69.123 : Triangle type {4,47,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-23 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T69.124 : Triangle type {4,48,48} Group order 192 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-2 * y * z^-3 * y * z^-1 * y * z^-2 * y ] T69.125 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^7 * z^-3 * y^2 * z^-1 * y^8 * z^-1 * y^2 ] T69.126 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-4 * y^5 * z^-1 * y^2 ] T69.127 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^3 * y^-2 * z * y^-2 * z * y^-2 ] T69.128 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^5 * z^-1 * y * z^-2 * y^6 * z^-1 * y ] T69.129 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^4 * z^-1 * y^3 * z^-1 * y * z^-1 * y^3 * z^-2 * y^7 * z^-1 ] T69.130 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, y^2 * z^-1 * y^9 * z^-1 * y * z^-2 * y^6 * z^-2 ] T69.131 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-19 * z * y^-4 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T69.132 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^17 * z^-2 * y * z^-1 * y^6 * z^-1 * y^5 * z^-1 * y * z^-1 * y^9 * z^-1 * y ] T69.133 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^4 * z^-5 * y^7 * z^-1 ] T69.134 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^5 * z^-1 * y * z^-2 * y^7 * z^-1 ] T69.135 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z^2 * y^-4 * z^4 ] T69.136 : Triangle type {4,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z^2 * y^-8 ] T69.137 : Triangle type {4,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-22 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T69.138 : Triangle type {4,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-21 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T69.139 : Triangle type {5,6,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^2 * y * x^-1 * z^2 ] T69.140 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^10 ] T69.141 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, (x * z * y^-1)^2, y^6, (x^-1 * z * y)^2, (x * z^-2)^2, (y * z^-2)^2, y * x^-3 * z * x^-2 ] T69.142 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * z * y^-1 * x * z^2, y^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x ] T69.143 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, y^-1 * z^-2 * x * z^2, z * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x ] T69.144 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, (x * z^-1 * y)^2 ] T69.145 : Triangle type {6,6,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x * z^-2)^2, (y * z^-2)^2, z^-1 * y * x^-2 * z * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T69.146 : Triangle type {6,12,12} Group order 204 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T69.147 : Triangle type {6,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^-1 * z^-1 * x^-2 * y * x * y^-1, x * z * x^-2 * z^2 * y ] T69.148 : Triangle type {6,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (x * z * y)^2, y^3 * x^-1 * y^-1 * z * y ] T69.149 : Triangle type {6,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^6, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^-4 * x^-1 * z^3 * y^-1 ] T69.150 : Triangle type {6,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T69.151 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, y^-3 * z * x^-1 * y^-3 * z ] T69.152 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, (y * z^-2 * y)^2 ] T69.153 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T69.154 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x * z^-1 * x^-1, z^-1 * y^4 * z^-3 ] T69.155 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^4 * z^-3 ] T69.156 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^2 * z^-1 * y * z^-1 * y^2 * x^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T69.157 : Triangle type {6,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, z^-2 * y^3 * z^-2 * y ] T69.158 : Triangle type {6,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^3 * y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T69.159 : Triangle type {6,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T69.160 : Triangle type {7,24,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^4 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T69.161 : Triangle type {7,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T69.162 : Triangle type {7,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T69.163 : Triangle type {7,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-3 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-4 ] T69.164 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^-1 * y^-1 * z, z^-1 * x * z * y * x^-1 * z^6 * y^-1 * z^-2 ] T69.165 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^-4 * x^-1 * z * y * z^-6 ] T69.166 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-5 * x^-1 * y * x^-1 * y * x^-1 * y * z^-4 ] T69.167 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, z * y^2 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1 ] T69.168 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, (y * z^-2)^2, z^-3 * x^2 * z^-3 ] T69.169 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, z * y^2 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y * z^-2 ] T69.170 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2 ] T69.171 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z^5 ] T69.172 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x * z^5 * y * z^-6 ] T69.173 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3, x^8 ] T69.174 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^8 ] T69.175 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-2 * x^-1 * z^2 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^4 * y * z^-7 * x^-1 * z * y * z^-1 ] T69.176 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * x^-1 * y * z^-6 ] T69.177 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, y^8 ] T69.178 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^6 * y * z^-1 * x * z^4 ] T69.179 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^5 * y^-1 * x * z * y^-1 * z^-4 * x ] T69.180 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^6 * y^-1 * x * y^-1 * x * z^4 ] T69.181 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, x^8 ] T69.182 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y^-1 * z^-1 * x^-1 * y^-1 * x * z^3 ] T69.183 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, x^8, y^8 ] T69.184 : Triangle type {8,8,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, y^8 ] T69.185 : Triangle type {8,8,92} Group order 184 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^9 * y * z^-6 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T69.186 : Triangle type {8,8,92} Group order 184 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^8 * y * z^-7 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T69.187 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y^-1 * x)^3, z^-1 * y^3 * z^-2, z * y^-1 * z^-1 * x * z * y^-1, z^-1 * x^-3 * y^-2 * z^-1 ] T69.188 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * z^-1 * y * x * y^-1 * z^-1, x * z^-1 * x^-2 * y * x * z^-1 ] T69.189 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, (y^-1 * x)^3, y * x * z^-1 * x^-1 * y^-1 * x * z ] T69.190 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, x^8, y^-1 * z * x^-1 * y^-1 * x * y^-2 * z ] T69.191 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, (x * z * y)^2, (y * z^-2)^2 ] T69.192 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z * y^-1 * z * y^-4 * z * y^-1 * z ] T69.193 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^3 * y^-2 * z * y^-1 * x^-1 * y^-2 * z^3 ] T69.194 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z * y^-1 * z^3 * y^-1 * x * z * y^-4 ] T69.195 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T69.196 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (y * z^-1 * y)^2, x^8 ] T69.197 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T69.198 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, y * z^-1 * y * x^2 * z^-3 ] T69.199 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^-1 * x^-3 * z^2 * y ] T69.200 : Triangle type {8,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, (x * z * y)^2, z^-1 * x^-3 * z^2 * y, y^2 * x^-2 * y^-1 * z * x^-1, z * y * x^-2 * y * x^-1 * y^-1, y * z^-1 * y * x^-1 * y * z^-2 ] T69.201 : Triangle type {8,21,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-4 * x * y^-1 * z * y^-1 ] T69.202 : Triangle type {8,24,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x^8, z * y * x^-1 * y * x^-1 * z^4 ] T69.203 : Triangle type {8,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^12 * y^-4 * z * y^-1 * z ] T69.204 : Triangle type {8,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T69.205 : Triangle type {8,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^12 * y^-5 * z^2 ] T69.206 : Triangle type {8,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-6 * z^5 * y^-6 ] T69.207 : Triangle type {10,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * x^3 * z^-2 * x ] T69.208 : Triangle type {10,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, x^10 ] T69.209 : Triangle type {10,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^10 ] T69.210 : Triangle type {10,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^10 ] T69.211 : Triangle type {12,12,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, x^-1 * z * y^-1 * z^-1 * x * z^4 * y^-1 * z^-1 * x^-1 * y * z^-4 ] T69.212 : Triangle type {12,14,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^2 * z^-1 * y^4 * z^-1 * y * z^-2 * y^3 ] T69.213 : Triangle type {12,26,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^12 ] T69.214 : Triangle type {12,39,52} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-4 * y^6, x^12 ] T69.215 : Triangle type {15,50,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, y^-2 * x^6 * y^-8 ] T69.216 : Triangle type {15,50,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^3 * z^-1 * y^4 * x^-4 * y^2 ] T69.217 : Triangle type {15,50,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^5 * z^-3 * x^4 * y^-3 * x^3 ] T69.218 : Triangle type {15,50,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^3 ] T69.219 : Triangle type {16,16,40} Group order 160 Chiral action Defining relators: [ x * y * z, (x * z^-1 * x)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T69.220 : Triangle type {16,16,40} Group order 160 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-1 * z * x^-1 * z^4 ] T69.221 : Triangle type {16,16,40} Group order 160 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * x^-1 * y^-1 * z ] T69.222 : Triangle type {16,16,40} Group order 160 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, (x * z^-1 * x)^2 ] T69.223 : Triangle type {16,16,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^5 * y * x * z^4 ] T69.224 : Triangle type {16,16,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^3 * y * z^-1 * x^-1 * z * y * z^-3 * x^-1 ] T69.225 : Triangle type {16,16,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T69.226 : Triangle type {16,16,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^2 * y^-1 * z^-3 * x^-1 * z^4 ] T69.227 : Triangle type {20,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, x^-2 * y^3 * x^-1 * y^2 * x^-1 * y^3 ] T69.228 : Triangle type {20,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^4 * y^-5 ] T69.229 : Triangle type {20,20,20} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^4 * z^-3 ] T69.230 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^3 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T69.231 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^3 * z^-4, x^-1 * y^6 * x^-5 * y ] T69.232 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 ] T69.233 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, y^6 * z^-3 * y^2 * x^-6 * y^3 ] T69.234 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^4 * z^-3 * y^7 ] T69.235 : Triangle type {21,49,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-6 * z^2 * x^-5 * y^3 * x^-1 * z * x^-6 ] T69.236 : Triangle type {24,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T69.237 : Triangle type {24,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^-4 * x^2 * y^-8 ] T69.238 : Triangle type {24,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^12 * y^-1 * x * y^-1 * x * y^-1 * x ] T69.239 : Triangle type {24,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^-1 * y^6 * x^-6 ] T69.240 : Triangle type {36,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-6 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T69.241 : Triangle type {36,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^3 * z^-4, x^-2 * y^6 * x^-4 * y^2 ] T69.242 : Triangle type {36,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-16 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T69.243 : Triangle type {36,48,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, y^2 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^2 ] T69.244 : Triangle type {36,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-3 * x * y^-1 * x * y^-4 ] T69.245 : Triangle type {36,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-2, x^3 * z^-2 * x^3 * y^-6 * x^2 ] T69.246 : Triangle type {36,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-21 * y * x^-8 * z * x^-6 ] T69.247 : Triangle type {36,72,72} Group order 144 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-4 * z * x^-2 * z * x^-2 * y^2 * x^-8 ] T69.248 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-16 * z * y^-7 ] T69.249 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^6 * z^-2 * y^3 * x^-3 * y^4 ] T69.250 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^16 * y^-2 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T69.251 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * z^2 * x^-1, y^2 * z^-1 * y * z^-3 * y^5 * z^-3 ] T69.252 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^6 * z^-2, x^-1 * y * x^-5 * z^4 * x^-3 ] T69.253 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-4 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 ] T69.254 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y, z^-7 * y^4 * z^-4 ] T69.255 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-1 * y * x^-1 * y^6 * x^-4 * z * x^-2 ] T69.256 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^7 * z^-2 * y^3 * x^-1 * y^6 ] T69.257 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-3 * x * z^-4 * x * y * z^-4 ] T69.258 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-13 * y^2 * z^-6 ] T69.259 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, x^-2 * y^6 * x^-5 ] T69.260 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-3 * x^7 ] T69.261 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-4 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T69.262 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^3 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T69.263 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-31 * z * x^-8 * z^2 * x^-6 ] T69.264 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^-9 * z^3 * y^-1 * z * y^-1 * z^3 ] T69.265 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^-13 * z * y^-3 * x^3 * y^-10 ] T69.266 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^10 ] T69.267 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^8, x^2 * z^-1 * x * z^-4 * x^2 * z^-4 ] T69.268 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^4 * z^-3 * y^8 ] T69.269 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, y^5 * z^-1 * y^4 * x^-6 * y^2 ] T69.270 : Triangle type {47,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * z * x^-7 * y^2 * x^-6 * y^2 * x^-6 ] T69.271 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y * z^-1 * y * z^-3 * y^5 * z^-3 ] T69.272 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^4 * y^-5 * x^2, y * z^-1 * y * z^-3 * y^5 * z^-3 ] T69.273 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x * y^-1 * x^12 * y^-1 * x^56, y * z^-1 ] T69.274 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^4 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T69.275 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-34 * x * y^-12 ] T69.276 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^5 * y^-3 * x^-1 * z^4 * x^-1 * z^6 ] T69.277 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^4 * z^-4, x^3 * z^-3 * x^6 * y^-1 * x ] T69.278 : Triangle type {70,140,140} Group order 140 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^3 * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T69.279 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x^-2 * y^-1, y^-58 * x * y^-11, x * z^-1 ] T69.280 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-33 * x^2 * y^-12 ] T69.281 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-21 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T69.282 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^5 * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T69.283 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-2 ] T69.284 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-4 * x^5 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T69.285 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^10 * x^-5 * y^3 ] T69.286 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^9 * x^-5 * y^2 ] T69.287 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^2 * x^-1 * y^11 ] T69.288 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^6 * x^-2 * y^3 ] T69.289 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-4 * y, z^-2 * x * z^-4 * x * y * z^-4 ] T69.290 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^2, z^-3 * x * z^-4 * x * y * z^-4 ] T69.291 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^2 * y^-1 * z * y^-6 * z^3 * y^-1 * z^5 ] T69.292 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^6 * z^-1 * y, x^2 * z^-1 * x * z^-4 * x^6 ] T69.293 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^4 * y^-6 * z^3 * y^-1 * z^6 ] T69.294 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^5 * z^-3, x * z^-1 * x * z^-4 * x^6 ] T69.295 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^3 * z^-3 * y^8 ] T69.296 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^7 * z^-3 * x^5 * z^-2 * x^5 ] T69.297 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-1 * z^5 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T69.298 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-3 * y^6 * z^-2 ] T69.299 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^2 * x^-5 * z^4 * x^-1 * z * x^-1 * z^2 ] T69.300 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^3 * z^-4, x^-2 * y^6 * x^-1 * y^4 ] T69.301 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-10 * z * y^-8 * z^2 * y^-8 ] T69.302 : Triangle type {139,139,139} Group order 139 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^3 * z^-2 * y^8 ] Genus 70 T70.1 : Triangle type {2,4,142} Group order 568 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-142 ] T70.2 : Triangle type {2,4,280} Group order 560 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-29 * x * y^-1 * z^-110 ] T70.3 : Triangle type {2,5,11} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^-5 * x * y * z^-5, (y * z^-1)^6 ] T70.4 : Triangle type {2,5,11} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (z * y^-1 * z)^3, (z^-1 * y)^5 ] T70.5 : Triangle type {2,6,72} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^8 * y * z^-1 * x * y^-1 * x * y^-1 * z^-6 * x * z * y^-1 * z^-2 ] T70.6 : Triangle type {2,6,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^57 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-3 * x * z ] T70.7 : Triangle type {2,6,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^52 * y^-1 * x * z^19 ] T70.8 : Triangle type {2,6,210} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^56 * y * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-3 * x * z ] T70.9 : Triangle type {2,12,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z^-3 * x * z * y^-1 * z^-5, y^12 ] T70.10 : Triangle type {2,12,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^15 * y * z^-4 * x * z^4 * y^-1 * z^-1 * x * z^4 ] T70.11 : Triangle type {2,12,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-11 * x * z * y * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-9 ] T70.12 : Triangle type {2,12,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-9 * x * z^4 * y^-1 * z^-14 ] T70.13 : Triangle type {2,16,22} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-5 * z^-1 * x * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1, z^3 * y * x * z * y * x * z * y * z^-5 * x * y^-1 * z^-3 * x * y^-1 * z^-3 * x * z ] T70.14 : Triangle type {2,22,154} Group order 308 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^3 * y^-1 * z^-2 * x, y^-8 * z^4 * y^-5 * z^4 * y^-1 ] T70.15 : Triangle type {2,58,145} Group order 290 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-12 * z^4 * y^-12 * z ] T70.16 : Triangle type {2,141,282} Group order 282 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^116 * z^-24 * y ] T70.17 : Triangle type {2,142,142} Group order 284 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^25 * y^-115 * z ] T70.18 : Triangle type {2,280,280} Group order 280 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-114 * z ] T70.19 : Triangle type {3,4,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z^3 * y * x * z^-4, x^-1 * z * y * z^-1 * x^-1 * z * x^-1 * z^-1 * x * z^2 * y^-1 * z^-1 ] T70.20 : Triangle type {3,5,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^-5, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^2 * z^-1 * y * x ] T70.21 : Triangle type {3,12,28} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y^-1 * z * y * x^-1 * z^2 * y^-1, z * y^-1 * z^-1 * x^-1 * y^-3 ] T70.22 : Triangle type {3,71,213} Group order 213 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-60 * z * y^-8 * z^2 ] T70.23 : Triangle type {3,72,72} Group order 216 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-6 * y * z^-2 * y^2 * z^-1 * y * z^-2 * y^6 * z^-1 * y ] T70.24 : Triangle type {3,72,72} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-61 * z * y^-8 * z^2 ] T70.25 : Triangle type {3,72,72} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-11 * y^6 * z^-4 * y^2 * z^-1 ] T70.26 : Triangle type {3,72,72} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^59 * y^-10 * z * y^-1 ] T70.27 : Triangle type {3,210,210} Group order 210 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-59 * z * y^-9 * z ] T70.28 : Triangle type {4,4,71} Group order 284 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-71 ] T70.29 : Triangle type {4,4,140} Group order 280 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-55 * x * y^-1 * z^-14 ] T70.30 : Triangle type {4,6,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, y * x^-1 * z^9 * y * x^-1 * y * z^-7 * x^-1 * z ] T70.31 : Triangle type {4,12,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, z^-1 * x^-1 * z * y * x * z^2 * y ] T70.32 : Triangle type {4,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z * y * x * z^5 * y * x * y^-1 * z^-1 * x * z^8 ] T70.33 : Triangle type {4,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^9 * y * z^-1 * x^-1 * z * y^-1 * z^-4 * x^-1 * z ] T70.34 : Triangle type {4,14,16} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y * z^-1 * x^-1 * z^4, y^-14 ] T70.35 : Triangle type {4,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y^-1 * z^3 * y^-1 * z^2 * y^-5 * z * y^-5 ] T70.36 : Triangle type {4,94,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-19 * z^3 * y^-1 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T70.37 : Triangle type {5,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^5 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T70.38 : Triangle type {5,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^12 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T70.39 : Triangle type {5,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T70.40 : Triangle type {6,6,36} Group order 216 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^5 * y * x * y^-1 * x * z^5 ] T70.41 : Triangle type {6,6,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^3 * y^-1 * z^-4 * x^-1 * z^4 ] T70.42 : Triangle type {6,6,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^22 * y^-1 * x^-1 * z^13 ] T70.43 : Triangle type {6,6,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-15 * x * z^7 * y^-1 * z^-6 * x^-1 * z * y * z^-5 ] T70.44 : Triangle type {6,6,105} Group order 210 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-27 * x * z * y * z^-6 ] T70.45 : Triangle type {6,9,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y^-1 * x^2 * y^-1 * z, y^-1 * x * y^-1 * x * z^2 ] T70.46 : Triangle type {6,9,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z^2 ] T70.47 : Triangle type {6,9,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, z^-1 * y^2 * x^-1 * y^3, y^-9 ] T70.48 : Triangle type {6,9,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, z^-1 * y^2 * x^-1 * y^3, y^-9 ] T70.49 : Triangle type {6,12,32} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^9 * y^-1 * z^-5 * x^-1 * z ] T70.50 : Triangle type {6,18,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^3 * y^-1 * z^-2 * x * z^4 ] T70.51 : Triangle type {6,18,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^2 * y^-1 * z^-2 * x * y^-1 * x * z^4 ] T70.52 : Triangle type {6,20,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T70.53 : Triangle type {6,29,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T70.54 : Triangle type {6,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y^5 * z^-2 * y * z^-1 ] T70.55 : Triangle type {6,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^7 * z^-1 * y * z^-1 ] T70.56 : Triangle type {6,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^8 * z^-2 ] T70.57 : Triangle type {6,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^15 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^3 * z^-1 ] T70.58 : Triangle type {6,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T70.59 : Triangle type {6,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T70.60 : Triangle type {7,7,29} Group order 203 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * x, z * y * x^2 * z * x^-1, x^-7 ] T70.61 : Triangle type {7,7,29} Group order 203 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2, x^-7 ] T70.62 : Triangle type {7,7,29} Group order 203 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^2, x^-7, z * y * x^-2 * y^-2 * x ] T70.63 : Triangle type {8,21,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-3 ] T70.64 : Triangle type {8,22,22} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^9 * z^-1 * y * z^-1 * y^2 * x * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 ] T70.65 : Triangle type {8,24,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z * y^-1 * z^-2 * x * z^3 ] T70.66 : Triangle type {8,24,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z^2 * y * z^-1 * x^-1 * z^3 ] T70.67 : Triangle type {8,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T70.68 : Triangle type {8,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^3 * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T70.69 : Triangle type {9,9,21} Group order 189 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^-3 * x^-1 * y^2 * z^-1 ] T70.70 : Triangle type {9,9,21} Group order 189 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * x * z^2, x^-9 ] T70.71 : Triangle type {9,10,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y^-1 * x^2, y^2 * x^-2 * y * z^-2, x^-9 ] T70.72 : Triangle type {9,54,54} Group order 162 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, z^-5 * y^12 * z^-1 ] T70.73 : Triangle type {9,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^2 * y^-6 * z^10 ] T70.74 : Triangle type {9,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-2 * y * x^2 * z^-3, y^-2 * x * y^-1 * x * y^-3 ] T70.75 : Triangle type {9,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-9 ] T70.76 : Triangle type {9,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^2 * x^-1 * y * z^-1 * y, x^-9 ] T70.77 : Triangle type {10,32,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T70.78 : Triangle type {11,15,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T70.79 : Triangle type {11,16,16} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-11, y^6 * z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-1 ] T70.80 : Triangle type {11,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-5 * y^6 ] T70.81 : Triangle type {11,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-5 * y^2 * z^-4 ] T70.82 : Triangle type {11,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-8 * y^2 * z^-4 ] T70.83 : Triangle type {11,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-5 * y^3 * z^-3 ] T70.84 : Triangle type {11,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T70.85 : Triangle type {12,12,15} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * y^-1 * z^-1, y^-3 * x * z^2, y^-1 * z * y^-1 * x * z^-1 * x ] T70.86 : Triangle type {12,12,15} Group order 180 Chiral action Defining relators: [ x * y * z, z * y * x * z, z * x^-3 * y^-3, x^-4 * y * x^-1 * y * x^-2 * y * x^-1 * y ] T70.87 : Triangle type {12,12,15} Group order 180 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, x^-1 * y^2 * x^-7 * y * x^-1 ] T70.88 : Triangle type {12,12,15} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x * z^2, y^-1 * x * y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 * x * y^-1 ] T70.89 : Triangle type {12,12,15} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-2 * x * z * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x^-1 * y * z^-4 ] T70.90 : Triangle type {12,12,15} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z^10 * y * x * z^4 ] T70.91 : Triangle type {12,12,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-2 * x * z * y^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * y * z^-4 ] T70.92 : Triangle type {12,14,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-1 * z * y^-5 * z^2 * y^-1 * z ] T70.93 : Triangle type {12,39,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^12 ] T70.94 : Triangle type {12,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x^12 ] T70.95 : Triangle type {15,15,33} Group order 165 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, y^-1 * x * y^-1 * x * y^-1 * z ] T70.96 : Triangle type {15,15,33} Group order 165 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * y^-2, y^-2 * x^2 * z * y^-1 ] T70.97 : Triangle type {15,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, y^2 * x^-1 * y^6 * x^-6 * y^2 ] T70.98 : Triangle type {15,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T70.99 : Triangle type {21,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^6 * z^-2 * y^3 * x^-6 * y * x^-1 * y^2 ] T70.100 : Triangle type {21,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^2, z^-9 * y * z^-4 ] T70.101 : Triangle type {21,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-10 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T70.102 : Triangle type {22,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-2 * x^-1 * y * x^-1 * y * z^-3 ] T70.103 : Triangle type {22,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-3 * x^2 * y^-3, z^3 * y^-1 * x * z^3 ] T70.104 : Triangle type {22,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^2 * y^-1 * z^-1 * x * z^3 ] T70.105 : Triangle type {22,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1, z * y^-1 * z^-2 * x * z^3 ] T70.106 : Triangle type {22,22,77} Group order 154 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, (y * z^-5)^2 ] T70.107 : Triangle type {25,30,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^9 * x^-5 * y^3 ] T70.108 : Triangle type {25,30,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y, z^-4 * x * z^-4 * x^2 * z^-4 ] T70.109 : Triangle type {25,30,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T70.110 : Triangle type {25,30,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-3 * y * x^-1 * y * x^-1 * y * x^-12 * y * x^-1 * y * x^-1 * y * x^-1 ] T70.111 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^5 * z^-2 * y^3 * x^-1 * y^5 ] T70.112 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5 * x, y^2 * z^-1 * y * z^-4 * y^4 * z^-3 ] T70.113 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^-2 * z^4 * y^-2 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T70.114 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T70.115 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-1 * z^6 * x^-4 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T70.116 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x^2 * z^-1 * x * z^-4 * x^6 ] T70.117 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-14 * y^2 * x^-6 * z^2 * x^-7 ] T70.118 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-7 * z^4 * x^-1 * z * x^-3 ] T70.119 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, x^-2 * y^5 * x^-6 ] T70.120 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-1 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T70.121 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^-6 * z * y^-9 * x * y^-1 * x * y^-3 ] T70.122 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5, z^-3 * y * z^-4 * y^3 * z^-4 ] T70.123 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-4 ] T70.124 : Triangle type {29,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-2 * y * x^-1 * z^4 * x^-4 * z^2 * x^-4 ] T70.125 : Triangle type {36,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-4 * x * z^-4 * x^2 * z^-4 ] T70.126 : Triangle type {36,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-10 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-7 ] T70.127 : Triangle type {36,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-2 ] T70.128 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T70.129 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-8 * x^2 * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T70.130 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-4 * y^6 * x^-2 * z^3 * x^-5 ] T70.131 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-5 * x * y^-2 * z^3 * y^-5 ] T70.132 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-28 * y * x^-1 * y * x^-1 * y * x^-16 ] T70.133 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x ] T70.134 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-4, x^-2 * y^6 * x^-2 * z^3 * x^-3 ] T70.135 : Triangle type {48,72,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-4, y^-2 * x^5 * y^-6 * x * y^-1 ] T70.136 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-21 * z * y^-14 ] T70.137 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-35 * x^2 * y^-11 ] T70.138 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^6 * z^-2 * y^3 * x^-6 * y * x^-1 * y^2 ] T70.139 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^7 * y^-4 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T70.140 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^-1 * y^6 * x^-6 ] T70.141 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 ] T70.142 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^7 ] T70.143 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^2 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T70.144 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y * x^-1 * y^11 ] T70.145 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^5 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T70.146 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-1 * y ] T70.147 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^4 * z^-1 * y * z^-4 * y^8 ] T70.148 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y * z^-1 * y * z^-4 * y^5 * z^-1 * y ] T70.149 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^4 * y^-5 * x, z^-7 * y^3 * z^-4 ] T70.150 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^2 * y^-1 * z^4 * x^-2 * y^-2 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T70.151 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^5 * z^-1 * x^7 * z^-2 * x * y^-1 * x^3 ] T70.152 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^5 * z^-4 * x^4 * y^-2 * x^2 ] T70.153 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T70.154 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-9 * x^4 * y^-9 ] T70.155 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-3, x^4 * z^-4 * x^4 * y^-2 * x ] T70.156 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, y^3 * z^-4 * y^7 ] T70.157 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-22 * x * z^-6 ] T70.158 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T70.159 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y * z^-1 * y * z^-4 * y^7 ] T70.160 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-3 * z^2 * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T70.161 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-6 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-4 ] T70.162 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^2 * x^-1 * y^6 * x^-6 * y^2 ] T70.163 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T70.164 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^17 * x^-3 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T70.165 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^6 * z^-3 * y^2 * x^-2 * y^5 ] T70.166 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^3 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T70.167 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-2 * x^8 ] T70.168 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^4 * z^-2 * y^8 ] T70.169 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, y^-1 * x^6 * y^-6 * x * y^-1 ] T70.170 : Triangle type {71,142,142} Group order 142 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^71, y * z^-1 ] T70.171 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x^-2 * y^-1, y^-58 * x * y^-12, x * z^-1 ] T70.172 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-4 * x^3 * y^-6 * x * y^-3 ] T70.173 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, x^-2 * y^6 * x^-3 * y^2 ] T70.174 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^9 * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T70.175 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z ] T70.176 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-4 ] T70.177 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^4 * z^-4, x^-1 * y * x^-1 * y^6 * x^-4 * z * x^-2 ] T70.178 : Triangle type {141,141,141} Group order 141 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^11 ] Genus 71 T71.1 : Triangle type {2,4,32} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-9 * x * z^11 * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-2 ] T71.2 : Triangle type {2,4,32} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2, y * z^-1 * x * z^3 * y * x * z * y * z^-1 * x * y^-1 * z^-5 * x * z ] T71.3 : Triangle type {2,4,60} Group order 600 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-9 * x * z * y * x * z^6 * y * z^-2 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-2 ] T71.4 : Triangle type {2,4,144} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-144 ] T71.5 : Triangle type {2,4,144} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-57 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T71.6 : Triangle type {2,4,284} Group order 568 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-30 * x * y^-1 * z^-111 ] T71.7 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^8, (y * z^-2 * y * z^-1)^2 ] T71.8 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T71.9 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T71.10 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, z * y^2 * z^-1 * y^2 * z^-1 * y * x * z ] T71.11 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, (y^-2 * z)^3 ] T71.12 : Triangle type {2,6,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-3 * y)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T71.13 : Triangle type {2,6,33} Group order 462 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z^4 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T71.14 : Triangle type {2,6,213} Group order 426 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^57 * y * x * y^-1 * z^-9 * x * z^3 ] T71.15 : Triangle type {2,8,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z^-12 ] T71.16 : Triangle type {2,8,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-12 ] T71.17 : Triangle type {2,8,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, z^2 * y^-1 * z * y^-2 * z^-2 * y * x * y^-1 ] T71.18 : Triangle type {2,8,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * x * y^-3 * z^-4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T71.19 : Triangle type {2,8,40} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z^3 * y * x * y * x * z * y^-1 * z^-3 ] T71.20 : Triangle type {2,8,40} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^2 * y * z^-1 * x * z * y * x * z^4 ] T71.21 : Triangle type {2,8,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-17 * x * z^16 * y * x * z * y * x * y^-1 * z^-11 ] T71.22 : Triangle type {2,8,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^35 * y * x * y^-1 * z^-9 * x * z^2 ] T71.23 : Triangle type {2,9,9} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, (y * z^-1 * y * z^-1 * y)^2, (y * z^-3 * y)^2, y * x * y^-1 * z * y^2 * z^-4, z^-2 * x * z * y^2 * x * y^-1 * z^-2 ] T71.24 : Triangle type {2,20,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-6 * z^4 * y^-5 * z^4 * y^-1 ] T71.25 : Triangle type {2,20,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, z * y^-1 * z^4 * y^-11 * z^3 ] T71.26 : Triangle type {2,24,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y * x * y^-1 * z^-2 * x, z^2 * y^-1 * z * y^-5 * z * y^-1 * z * y^-9 * z^3 ] T71.27 : Triangle type {2,24,24} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y^-2 * z^-1 * y * z^-2, y^8 * z^-1 * y^2 * z^-1 ] T71.28 : Triangle type {2,32,32} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^11 * y^-5 * z * y^-1 * z * y^-10 * z^3 ] T71.29 : Triangle type {2,32,32} Group order 320 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, y^-2 * z * y^-1 * z * y^-1 * z * y^-6 * z * y^-2 ] T71.30 : Triangle type {2,60,60} Group order 300 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^9 * y^-4 * z^2 * y^-10 * z * y^-1 * z^3 ] T71.31 : Triangle type {2,143,286} Group order 286 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^117 * z^-26 ] T71.32 : Triangle type {2,144,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-41 * y^12 * z^-1 * y^18 ] T71.33 : Triangle type {2,144,144} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^26 * y^-117 ] T71.34 : Triangle type {2,284,284} Group order 284 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^25 * y^-116 ] T71.35 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-2 * z, y^3 * x^-1 * z^3 ] T71.36 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^3 * x^-1 * z^3, y^8 ] T71.37 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^8, y * z^-1 * y^2 * z^-2 * x * y^3 * z^-1 * y^2 ] T71.38 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^8, (x^-1 * z * y^2)^2, (x^-1 * z^2 * y)^2 ] T71.39 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^8, (y * z^-1)^4 ] T71.40 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2 ] T71.41 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, (z^-1 * y)^3, x^-1 * y^-3 * x * y^-2 * z, y^8 ] T71.42 : Triangle type {3,8,8} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, (y * z^-1 * y)^2, y^8 ] T71.43 : Triangle type {3,20,30} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y^4 * z^-4 ] T71.44 : Triangle type {3,33,33} Group order 231 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^2 * z^-1 * y * z^-2 * y^2 * z^-1 * y^2 ] T71.45 : Triangle type {3,213,213} Group order 213 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-60 * z * y^-10 ] T71.46 : Triangle type {4,4,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4, x^-1 * z * y * z^-1 * y * x * y^-1 * z^-2 * y ] T71.47 : Triangle type {4,4,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4, x^-1 * z * y * z^-1 * y * x * z * y * z^-1 * y ] T71.48 : Triangle type {4,4,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x^-1 * y * x^2 * y^-1 * z * x^-1 * y^-1, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-4 ] T71.49 : Triangle type {4,4,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-6 * x^-1 * y * z^-1 * x * z * y^-1 * z^-6 ] T71.50 : Triangle type {4,4,30} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-5 * x^-1 * z * y * z^-1 * x^-1 * z^2 * y^-1 * z^-4 ] T71.51 : Triangle type {4,4,72} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-72 ] T71.52 : Triangle type {4,4,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-23 * x * z^6 * y^-1 * x * z * y^-1 * z^-4 ] T71.53 : Triangle type {4,4,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^28 * y^-1 * z^-7 * x ] T71.54 : Triangle type {4,4,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-23 * x * z^6 * y^-1 * z^-6 ] T71.55 : Triangle type {4,4,142} Group order 284 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-56 * x * y^-1 * z^-14 ] T71.56 : Triangle type {4,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^6, z * y * x^-1 * z * y * x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x ] T71.57 : Triangle type {4,6,6} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, (x * y^-1)^4 ] T71.58 : Triangle type {4,6,6} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, z^6, y * x^-1 * y * x^-1 * z * x^-1 * z ] T71.59 : Triangle type {4,6,6} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * y)^3, z^6, y^2 * x^-2 * z^2 * x^-1, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T71.60 : Triangle type {4,6,6} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, (x * z * x^-1 * y^-1)^2 ] T71.61 : Triangle type {4,8,24} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T71.62 : Triangle type {4,8,24} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y ] T71.63 : Triangle type {4,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, z^2 * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T71.64 : Triangle type {4,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, (y^-3 * z * y^-1 * z)^2 ] T71.65 : Triangle type {4,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T71.66 : Triangle type {4,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^-1 * z * y^-2 * z * y^-3 * z^2 * y^-2 ] T71.67 : Triangle type {4,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * y * z^-2, y^-2 * z * x^-1 * y^-3, x^-1 * z * y^2 * x * z * y * z^-1 ] T71.68 : Triangle type {4,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * y * z^-2, y^-2 * z * x^-1 * y^-3, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T71.69 : Triangle type {4,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^2 * z^-1 * y^4 * z^-1 * y * z^-1 ] T71.70 : Triangle type {4,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * y^3 * z^-2 * y * z^-1 ] T71.71 : Triangle type {4,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^18 * z^-2 * y * z^-1 * y^6 * z^-1 * y^5 * z^-1 * y * z^-1 * y^11 ] T71.72 : Triangle type {4,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-18 * z * y^-4 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T71.73 : Triangle type {6,8,8} Group order 240 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8 ] T71.74 : Triangle type {6,8,8} Group order 240 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^3 * x^-1 * z^3, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T71.75 : Triangle type {6,8,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, z * y * x^-2 * z * y * x, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T71.76 : Triangle type {6,8,8} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, z * y * x^-2 * z * y * x, z^-1 * y * x^-1 * y^-1 * x * z * y^-2 ] T71.77 : Triangle type {6,10,15} Group order 210 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x^2 * z * x^-1 * y ] T71.78 : Triangle type {6,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * z^5 * y^-1 * z^-1 * x^-1 * z^6 * y * z^-1 ] T71.79 : Triangle type {6,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^6, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^-4 * x^-1 * z^2 * y * z^-1 ] T71.80 : Triangle type {6,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, z^2 * y * z^-1 * x^-1 * z^4, x^-1 * z * y^3 * x * y^-3 * z^-1 ] T71.81 : Triangle type {6,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y * z^-1 * y * z^-3, y^4 * x^-1 * y^-2 * z^-1 * y ] T71.82 : Triangle type {6,36,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, y * z^-2 * x^-1 * y^-2 * z, z * y^-1 * z * x^-1 * z^2 * y^-1 ] T71.83 : Triangle type {6,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^2 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T71.84 : Triangle type {8,8,20} Group order 200 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-2 ] T71.85 : Triangle type {8,8,20} Group order 200 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, z * x^-1 * y * x^-1 * y^2 * x, x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 ] T71.86 : Triangle type {8,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-3 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^4 * y * z^-7 * x^-1 * z * y * z^-1 ] T71.87 : Triangle type {8,8,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 * y * x^-1 * y * x^-1 * z^13 ] T71.88 : Triangle type {8,12,16} Group order 192 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * y^-1 * x^2 * z * y^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, z * y^3 * x * y^-1 * z^-1 * x ] T71.89 : Triangle type {8,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^8, y^4 * x * z^-1 * x * z^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T71.90 : Triangle type {8,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, z^-1 * y^3 * x * z * x^-1 * y^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T71.91 : Triangle type {8,42,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-4 * x^-1 * z^3 ] T71.92 : Triangle type {10,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3, x^10 ] T71.93 : Triangle type {10,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T71.94 : Triangle type {10,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T71.95 : Triangle type {10,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x^10 ] T71.96 : Triangle type {12,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, z^-8 * y^2 * z^-4 ] T71.97 : Triangle type {12,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z * x^-1 * y^-1 * x * z * y^-1, z^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T71.98 : Triangle type {12,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * z, y^2 * x^2 * z^2, x^-12 ] T71.99 : Triangle type {12,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-4 * y * x^-1 * y, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T71.100 : Triangle type {12,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-2 * y^2 * z^-1 * y, x^12 ] T71.101 : Triangle type {12,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^3 * z^-2 * y^8 ] T71.102 : Triangle type {14,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-2, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T71.103 : Triangle type {14,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^-4 * x^2 * y^-7 ] T71.104 : Triangle type {14,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, y^-4 * x^3 * y^-6 * x * y^-1 ] T71.105 : Triangle type {14,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T71.106 : Triangle type {14,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^2 * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T71.107 : Triangle type {16,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^-1 * y * x^-1 * y^6 * x^-6 * y^3 ] T71.108 : Triangle type {16,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, z^-4 * y^2 * z^-4 ] T71.109 : Triangle type {16,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y * x^-1 * y * x^-1 * y^2 * x^-5 * y^2 ] T71.110 : Triangle type {16,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, z^-1 * y^2 * x^-1 * y * z^-1 * y ] T71.111 : Triangle type {16,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x * y^-2 * x * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T71.112 : Triangle type {16,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z, y^-1 * x^5 * y^-1 * z^-1 * x * y^-1 ] T71.113 : Triangle type {16,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^-5 * y^2 * x^-8 * z * x^-1 * z ] T71.114 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^6 * y^-2, z^-4 * x^-1 * z^3 * y^-1 ] T71.115 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-5 * y^-1 * x^2 * z, y^-4 * x * y^-1 * x^4 * z * y^-2 ] T71.116 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^4 * x^-1 * y * x^-2 * y * x^-1 * y^2 ] T71.117 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2, z^-2 * x^3 * z^-2 * x ] T71.118 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (x * y^-2)^2, (x * z^-1)^4 ] T71.119 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, z^-2 * x^3 * z^-2 * x ] T71.120 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-1 * y * z^-1 * y * z^-3 * x * z^-1 * x * z^-2 ] T71.121 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, y * x * z^-3 * x^3 * z^-3 * x * z^-1 ] T71.122 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-1 * x^4 * y^-3 ] T71.123 : Triangle type {20,20,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, y^-1 * x^4 * y^-3 ] T71.124 : Triangle type {30,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^-2 * y^6 * x^-4 * z * x^-2 ] T71.125 : Triangle type {30,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^6 * z^-2 * y^3 * x^-5 * y^4 ] T71.126 : Triangle type {30,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-11 * y * x^-1 * y * x^-1 * y^2 * x^-8 * y * x^-6 ] T71.127 : Triangle type {30,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-5 ] T71.128 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y * x^-8 * y * x^-6 ] T71.129 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-2, x^4 * z^-4 * x^4 * y^-2 * x ] T71.130 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^3 * z^-2 * x^3 * y^-6 * x^2 ] T71.131 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-4 * y * z^-1 * y * z^-1 * y * z^-4 * y^2 * x^2 * z^-4 * y * z^-1 * y ] T71.132 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^2 * y^-1 * x^12 * y^-1 * x^57, y * z^-1 ] T71.133 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-21 * y * x^-8 * y * x^-6 ] T71.134 : Triangle type {72,144,144} Group order 144 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^7 * y^-4 * x^4 * y^-2 * x^4 ] T71.135 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x^-2 * y^-1, y^-59 * x * y^-12, x * z^-1 ] T71.136 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-11 * x^2 * z^-4 ] T71.137 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, y^2 * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-2 ] T71.138 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-4 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T71.139 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T71.140 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^-2 * y * x^-1 * y^6 * x^-3 * z^2 * x^-4 ] T71.141 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-36 * x * y^-11 ] T71.142 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-1 * y, x^2 * z^-1 * x * z^-4 * x^6 ] T71.143 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T71.144 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-8 * z^3 * x^-7 ] T71.145 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-8 * x^2 * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-6 ] T71.146 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z^4 * x^-4 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T71.147 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-1 * y * z^-1 ] T71.148 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y^-1 * z^9 * x^-1 * y^-2 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T71.149 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^7 * y^-6 * x * y^-1 ] T71.150 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-4 * y * x^-1 * z * x^-10 * y * x^-1 * y * x^-2 ] T71.151 : Triangle type {143,143,143} Group order 143 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^17 * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] Genus 72 T72.1 : Triangle type {2,4,75} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-58 * x * z^8 * y * x * z * y^-1 * z^-6 ] T72.2 : Triangle type {2,4,146} Group order 584 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-146 ] T72.3 : Triangle type {2,4,288} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y^-1 * z^-112 ] T72.4 : Triangle type {2,5,10} Group order 710 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z^2 * y * z^-1 * y * x * y^-1 * z^4 * y^-1 ] T72.5 : Triangle type {2,5,10} Group order 710 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * z * y^-1 ] T72.6 : Triangle type {2,6,74} Group order 444 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^54 * y^-1 * x * z^19 ] T72.7 : Triangle type {2,8,50} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-26 * x * z^5 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-11 ] T72.8 : Triangle type {2,10,38} Group order 380 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-7 * x * z^16 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-5 ] T72.9 : Triangle type {2,10,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-6 * x * z^16 * y * z^-1 * x * z^3 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-3 ] T72.10 : Triangle type {2,14,26} Group order 364 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^8 * y * x * z * y * z^-5 * x * y^-1 * z^-1 * x * z^8 ] T72.11 : Triangle type {2,14,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^7 * z^-3, y * x * z^11 * y * z^-4 * x * y * z^-5 * x * z ] T72.12 : Triangle type {2,18,20} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * y^-1 * z^-1 * x * y^-1 * z * y * x * z * y^10, z^3 * y * x * z * y * x * z * y * z^-5 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z ] T72.13 : Triangle type {2,20,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * z^-2 * x * z^5 ] T72.14 : Triangle type {2,24,28} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z^3 * y * x * z^5 * y^5 * x * y^-1 * z^-1 * x ] T72.15 : Triangle type {2,26,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-12 * z^4 * y^-5 * z^4 * y^-1 ] T72.16 : Triangle type {2,34,153} Group order 306 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-2 * z^4 * y^-6 * z^3 ] T72.17 : Triangle type {2,38,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-3 * y * z^-2 * y * z^-2 * y^7 * z^-4 * y^17 * z^-1 ] T72.18 : Triangle type {2,39,52} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^-9 * z^4 ] T72.19 : Triangle type {2,50,150} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-18 * y * z^-2 * y^9 * z^-2 * y^18 ] T72.20 : Triangle type {2,74,148} Group order 296 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-1 * y * z^-39 * y * z^-2 * y^30 ] T72.21 : Triangle type {2,75,75} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-71 * z * y^-1 ] T72.22 : Triangle type {2,98,147} Group order 294 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-17 * y * z^-2 * y^10 * z^-2 * y^15 * z^-2 ] T72.23 : Triangle type {2,145,290} Group order 290 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^118 * z^-26 * y ] T72.24 : Triangle type {2,146,146} Group order 292 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^27 * y^-117 * z ] T72.25 : Triangle type {2,288,288} Group order 288 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^26 * y^-116 * z ] T72.26 : Triangle type {3,3,74} Group order 444 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 * x^-1 * z^3 * y^-1 * z^-2 ] T72.27 : Triangle type {3,20,40} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y, y^6 * z^-4 ] T72.28 : Triangle type {3,38,57} Group order 228 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^3 * z^-2 * y * z^-1 * y^8 * z^-1 * y * z^-2 ] T72.29 : Triangle type {3,73,219} Group order 219 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-62 * z * y^-8 * z^2 ] T72.30 : Triangle type {3,74,74} Group order 222 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^61 * y^-10 * z * y^-1 ] T72.31 : Triangle type {3,216,216} Group order 216 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-61 * z * y^-10 ] T72.32 : Triangle type {4,4,73} Group order 292 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6 * x^-1 * z^2 * y^-1 * z^2 ] T72.33 : Triangle type {4,4,73} Group order 292 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-64 * x^-1 * y^-1 * z^-8 ] T72.34 : Triangle type {4,4,144} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-57 * x * y^-1 * z^-14 ] T72.35 : Triangle type {4,6,22} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-3 * x^-1 * z^7 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-8 ] T72.36 : Triangle type {4,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-5 * x * z ] T72.37 : Triangle type {4,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^8 * y * x * z^6 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-8 * x ] T72.38 : Triangle type {4,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^24 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 * y ] T72.39 : Triangle type {4,50,50} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-17 * z^3 * y^-1 * z * y^-10 * z * y^-1 * z * y^-5 * z * y^-7 ] T72.40 : Triangle type {4,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-24 * z * y^-1 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T72.41 : Triangle type {5,5,5} Group order 355 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, x^-1 * y^-1 * z^-1 * x^2 * z * y * z^-1 ] T72.42 : Triangle type {5,5,5} Group order 355 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z^-1 * x * y^-1 ] T72.43 : Triangle type {5,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-2, y * x * z^-1 * x^-1 * y * z^-1 * x^-1, z^-3 * x^-1 * z^2 * y ] T72.44 : Triangle type {5,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, (z^-1 * y)^3, y^2 * x^-2 * z * x^-1 * y, z * y * x^-2 * y * z^-1 * x ] T72.45 : Triangle type {5,37,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-7 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T72.46 : Triangle type {5,38,38} Group order 190 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z^-1 * y * z^-6 * y^3 * z^-1 * y^6 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^9 * z^-1 * y ] T72.47 : Triangle type {5,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^5 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T72.48 : Triangle type {5,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^7 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T72.49 : Triangle type {6,6,37} Group order 222 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, x * z^-3 * y * z^-3 ] T72.50 : Triangle type {6,6,37} Group order 222 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z * y * z^-2 * x * z^3 ] T72.51 : Triangle type {6,6,37} Group order 222 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-29 * x * y * z^-7 ] T72.52 : Triangle type {6,12,96} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-8 * x * z^6 * y^-1 * z^-1 ] T72.53 : Triangle type {6,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-5 * z * y^-7 ] T72.54 : Triangle type {6,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T72.55 : Triangle type {7,25,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-4 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T72.56 : Triangle type {7,26,26} Group order 182 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^11 * z^-1 * y * z^-1 * y^2 * x * z^-1 * y * z^-1 * y * z^-2 * y^3 * z^-1 ] T72.57 : Triangle type {7,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y ] T72.58 : Triangle type {7,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-6 ] T72.59 : Triangle type {7,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T72.60 : Triangle type {8,8,25} Group order 200 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^-1 * y * z^-2 * x * z^-3 ] T72.61 : Triangle type {8,8,25} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^10 * y * x^-1 * y * x * z^5 * y^-1 * z^-1 * x * z^6 ] T72.62 : Triangle type {8,22,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y * z^-9 * y * z^-1 * y^2 * z^-1 * y^5 * z^-1 * y ] T72.63 : Triangle type {8,42,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-4 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T72.64 : Triangle type {8,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^-1 * z * y^-2 * x^-1 * z^3 ] T72.65 : Triangle type {8,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^-4 * x * z^2 * y^-1 ] T72.66 : Triangle type {9,19,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T72.67 : Triangle type {9,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^-1 * z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-7 * z ] T72.68 : Triangle type {9,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T72.69 : Triangle type {9,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T72.70 : Triangle type {9,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-8 * z^4 * y^-6 ] T72.71 : Triangle type {10,10,19} Group order 190 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-4 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T72.72 : Triangle type {10,10,90} Group order 180 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-3 * x * z^7 * y^-1 * z^-7 ] T72.73 : Triangle type {10,10,90} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, x^-1 * z^3 * y * z^-1 * x * z * y^-1 * z^-3 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T72.74 : Triangle type {10,17,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-4 * y * z^-5 * y^6 * z^-1 ] T72.75 : Triangle type {10,18,18} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * z * y^-1 * z * y^-5 * z * y^-1 ] T72.76 : Triangle type {10,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T72.77 : Triangle type {10,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-4 * y * z^-5 * y^2 * z^-4 ] T72.78 : Triangle type {12,28,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T72.79 : Triangle type {13,14,14} Group order 182 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, (y^4 * z^-1 * y * z^-1)^2, x^-5 * y * z^-1 * y * z^-1 * x^-2 * y^-1 * z * y^-1 * z * x^-2 ] T72.80 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T72.81 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T72.82 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T72.83 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, z^-4 * x * z^-4 * x^2 * z^-4 ] T72.84 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T72.85 : Triangle type {13,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T72.86 : Triangle type {14,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^-2 * x * z^3 * y^-1 * x * z * y * z^-4 ] T72.87 : Triangle type {14,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^-1 * x * z^5 * y * x * z * y * z^-3 ] T72.88 : Triangle type {14,14,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (z^2 * x^-1 * z)^2, z^-1 * x * z^5 * y * x^-1 * y^-1 * z^-4 ] T72.89 : Triangle type {14,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x * z^2, (z^-1 * x)^3, y^-3 * x^2 * y^-3 ] T72.90 : Triangle type {14,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, (y * z^-1 * y)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y ] T72.91 : Triangle type {14,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, y * z^-1 * y * x^-1 * z^2 * y, (x * y^-1)^4 ] T72.92 : Triangle type {14,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, (x^-1 * z^2 * y)^2 ] T72.93 : Triangle type {14,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * y * z^-1, (y * z^-1)^4 ] T72.94 : Triangle type {14,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x^-1, y * z^-1 * x^2 * y^-1 * z, z^-4 * y^2 * z^-1 * y^2 * z^-2 * y ] T72.95 : Triangle type {14,24,24} Group order 168 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x, y^2 * x^2 * z^2, y * z^-3 * y * z^-1 * y * z^-1 * y^2 * z^-2 ] T72.96 : Triangle type {14,24,24} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 * y ] T72.97 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T72.98 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^7 * z^-4 * x^2 * y^-4 * x^4 ] T72.99 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^7 * x^-5 * y^2 ] T72.100 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x ] T72.101 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T72.102 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y * x^-1 * y^6 * x^-6 * y^2 ] T72.103 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T72.104 : Triangle type {17,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, y^-2 * x^5 * y^-4 * z * y^-2 ] T72.105 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, x^-7 * z^4 * x^-1 * z^4 ] T72.106 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^-1 * x^6 * y^-6 * x * y^-1 ] T72.107 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T72.108 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T72.109 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^9 ] T72.110 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T72.111 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y^6 * x^-6 * y * x^-1 ] T72.112 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, x^-2 * y^6 * x^-4 * y^2 ] T72.113 : Triangle type {19,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^7 * z^-3 * x^4 * y^-3 * x^5 ] T72.114 : Triangle type {20,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^6 * y^-2, z * y * z^-2 * x^-1 * z^4 ] T72.115 : Triangle type {20,20,80} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y * z^-1 * x^-1 * z^4 ] T72.116 : Triangle type {20,32,32} Group order 160 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-3 * y^2 * z^-2 * y ] T72.117 : Triangle type {20,32,32} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z ] T72.118 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-11 * y^3 * x^-4 * y^3 * x^-7 ] T72.119 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^-1 * y^6 * x^-6 ] T72.120 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^3 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T72.121 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y * x^-1 * y^11 ] T72.122 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^3 * x^-5 * z^4 * x^-1 * z * x^-1 * z^4 ] T72.123 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^3 * z^-4, x^-2 * y^6 * x^-6 ] T72.124 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, z^4 * x^-6 * y * x^-7 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T72.125 : Triangle type {25,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T72.126 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^4 * x^-1 * y^2 * x^-1 * y^6 ] T72.127 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-2 * x^4 * y^-4 ] T72.128 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^6 * y^-2, z^-3 * x^2 * z^-3 ] T72.129 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y^4 * z^-4 ] T72.130 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^8 * y^-2 ] T72.131 : Triangle type {26,26,78} Group order 156 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * x * z^-1 * x * z^-4 * y * x^2 * z^-4 ] T72.132 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3, y^-2 * x * y^-1 * x * z * y^-2 ] T72.133 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z^4 ] T72.134 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-3 * y * x^-1 * y^3 ] T72.135 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * z^3, y^3 * x^-1 * y * z^-2 ] T72.136 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x * z^-1 * x * y^-1 * z^-1 * x^4 * z^-1 * x * z^-1 * x^3 ] T72.137 : Triangle type {26,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * x * y^-1 ] T72.138 : Triangle type {30,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^5 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^4 ] T72.139 : Triangle type {30,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-6, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T72.140 : Triangle type {30,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-7 * z^4 * x^-1 * z * x^-3 ] T72.141 : Triangle type {30,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^5 * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-10 * y * x^-1 * y * x^-1 * y^2 ] T72.142 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^7 * z^-2 * y^6 * z^-1 * y^4 ] T72.143 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^11 * x^-1 * y * x^-1 * y^2 ] T72.144 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^4 * y^-5 * x, y * z^-1 * y * z^-1 * y * z^-4 * y^4 * z^-3 ] T72.145 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^7 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^2 ] T72.146 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-3, x^3 * z^-2 * x^3 * y^-6 * x^2 ] T72.147 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T72.148 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-9 * y^3 * z^-4 ] T72.149 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^9 * x^-5 * y^3 ] T72.150 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^2 * z^-1 * y^9 ] T72.151 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-8 * x * z^-1 * x * z^-4 * x * y * z^-6 ] T72.152 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^18 * x^-3 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T72.153 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * x, z^-3 * x * z^-4 * x * y * z^-4 ] T72.154 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^2 * y^-1 * z * y^-5 * z^4 * y^-1 * z * y^-1 * z^4 ] T72.155 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^7, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T72.156 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^6 * z^-3 * x^8 * z^-1 * x ] T72.157 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^3 * z^-4 * x^6 ] T72.158 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^6 * y^-4 * x^4 * z^-2 * x * y^-1 * x * y^-1 * x^2 ] T72.159 : Triangle type {37,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-22 * z * x^-8 * y * x^-6 ] T72.160 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^5 * z^-1 * y^4 * x^-2 * y * x^-1 * y^7 ] T72.161 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-5 * x * y^-3 * z * y^-1 * x^4 ] T72.162 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, y^-4 * x^2 * y^-4 ] T72.163 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, z^-4 * x^2 * z^-4 ] T72.164 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^7 * z^-1 * x * z^-1 ] T72.165 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, z * x^-1 * z^2 * y^-1 * z * x^-2 * z * x^-1 * z^4 * x^-5 ] T72.166 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * z^-4, y^-2 * x^4 * y^-4 ] T72.167 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^2 * z^-4 * x * z^-1 * x^4 * y^-1 * x^2 ] T72.168 : Triangle type {38,38,76} Group order 152 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^7 * y^-1 * x^-1 * y^-1 * z^3 * x^-1 * z * y^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T72.169 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^14 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^2 ] T72.170 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^11 * z^-3 * x^4 ] T72.171 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^2 * z^-1 * y * z^-4 * y^5 * z^-1 * y ] T72.172 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^3 * z^-4, x^-2 * y^6 * x^-2 * z^3 * x^-3 ] T72.173 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T72.174 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-5 * x^2 * z^-12 * y * z^-6 ] T72.175 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^6 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 ] T72.176 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-33 * y * x^-8 * z * x^-7 ] T72.177 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-11 * y^5 * z^-2 ] T72.178 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^5 * z^-3 * y^2 * x^-6 * y^2 ] T72.179 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-6 * x * y^-6 * x * y^-3 ] T72.180 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y, z^-8 * y^3 * z^-4 ] T72.181 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, y^-2 * x^4 * y^-7 ] T72.182 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^9 ] T72.183 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^20 * x^-4 * y^7 ] T72.184 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^8 * y^-6 * x^3 ] T72.185 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-3 * x^7, y * x^-1 * y^11 ] T72.186 : Triangle type {49,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 * y^2 * x^-7 * y * x^-6 ] T72.187 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^-3 * z * y^-1 * z * y^-4 * z * y^-1 * z * y^-5 ] T72.188 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, y^-4 * x * z^2 * y^-1 ] T72.189 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, x^-2 * z * y^-1 * z^2 * x^-2 * z^2 * x^-1 * z^2 * x^-2 ] T72.190 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^-4 * y^2 * x^-5 * z^3 * x^-1 ] T72.191 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-2 * x^-1 * z^4 ] T72.192 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^9 * x^-1 * z^3 * x^-2 * z^4 * x^-1 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T72.193 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1, y^-4 * z^3 ] T72.194 : Triangle type {50,50,75} Group order 150 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^7 * y^-1 * z^-2 ] T72.195 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-18 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T72.196 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x ] T72.197 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-1 * y * x^-1 * z^2 * x^-9 * y * x^-1 * y * x^-1 ] T72.198 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^8 * y^-6 * x^3 ] T72.199 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-3, x^4 * z^-4 * x * y^-6 * x^2 ] T72.200 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^4 * z^-3, x^-1 * y^6 * x^-6 ] T72.201 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y * z^-1 * y * z^-1 * y * z^-4 * y^4 * z^-3 ] T72.202 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z * y^-1 * z * y^-5 * z^4 * y^-1 * z * y^-1 * z^3 ] T72.203 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-5 * x * z^-4 * x * y * z^-4 ] T72.204 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, x * y^-1 * x^6 * y^-5 * x^3 ] T72.205 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y * z^-7 * y * z^-4 * y^2 * x^2 * z^-4 * y * z^-1 * y ] T72.206 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^6 * x^-6 ] T72.207 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T72.208 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-6 * z^2 * y^-14 ] T72.209 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^4 * y^-5 * x, z^-8 * y^2 * z^-4 ] T72.210 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^3 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T72.211 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-23 * y^2 * z^-5 ] T72.212 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-5 * x^5 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T72.213 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^8, z^-7 * y^3 * z^-4 ] T72.214 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-3 ] T72.215 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^3 * z^-4 * y^7 ] T72.216 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^3 * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T72.217 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-30 * x * z^-6 ] T72.218 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^7 * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T72.219 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^5 * z^-4 * x * y^-6 * x^3 ] T72.220 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y, z^-2 * y * z^-1 * y * z^-4 * y^3 * z^-4 ] T72.221 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, y^2 * z^-1 * y^9 ] T72.222 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^2 * x * z^-4 * y * z^-1 * y ] T72.223 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^2 * x^-1 * y^6 * x^-6 * y^2 ] T72.224 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-5 * x * z^-1 * x * z^-4 * x^3 * z^-4 ] T72.225 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^7 * x^-5 * y ] T72.226 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^7, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T72.227 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T72.228 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^6 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T72.229 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-44 * x * z^-4 ] T72.230 : Triangle type {73,146,146} Group order 146 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^73, y * z^-1 ] T72.231 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^28 * x^-2 * y^8 ] T72.232 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y * x^-2 * y^18 * x^-1 * y * x^-1 * y^2 ] T72.233 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-5 * x^4 * y^-6 * x * y^-1 * x * y^-2 ] T72.234 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-2 * x^6 * y^-8 ] T72.235 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^3 * z^-2 * x^3 * y^-6 * x^2 ] T72.236 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z * y^-1 * z * y^-5 * z^4 * y^-1 * z * y^-1 * z^3 ] T72.237 : Triangle type {74,74,74} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^4 * z^-3, x^2 * z^-1 * x * z^-4 * x^5 * z^-1 ] T72.238 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x^-2 * y^-1, y^-59 * x * y^-13, x * z^-1 ] T72.239 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^5 * z^-2 * y^3 * x^-5 * y^3 ] T72.240 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T72.241 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-36 * x^2 * y^-11 ] T72.242 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-3 * y^2, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T72.243 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T72.244 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-5 * y * z^-4 * y^3 * z^-4 ] T72.245 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^19 * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T72.246 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^4 * z^-3 * y^7 ] T72.247 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y, z^-5 * y * z^-1 * y * z^-4 * y^7 * z^-3 ] T72.248 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-4 * y^3 * z^-4, x^-1 * y^6 * x^-6 ] T72.249 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y^2 * z^-4, x^2 * z^-1 * x^9 ] T72.250 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-2 * z * y^-1 * z * y^-9 * z * y^-7 ] T72.251 : Triangle type {145,145,145} Group order 145 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-1 * y * x^-1 * y^6 * x^-6 * y^2 ] Genus 73 T73.1 : Triangle type {2,3,10} Group order 2160 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^10, z^3 * y * x * z^2 * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-4 * x, z * y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-1 * x * z * y^-1 * z^-3 * x ] T73.2 : Triangle type {2,3,10} Group order 2160 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * z^-1 * x * z * y * z^-3 * x * z * y * z^-1 * x * y^-1 * z^-4 * x ] T73.3 : Triangle type {2,3,10} Group order 2160 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T73.4 : Triangle type {2,3,12} Group order 1728 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^5 * y * x * z * y * x * y * z^-3 * x * y^-1 * z^-1, x * z * y * x * z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T73.5 : Triangle type {2,3,12} Group order 1728 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y * x * z * y * x * z * y * z^-1 * x * z^2 * y * x * z^2 * y * z^-1 * x * z * y * x * z^2 * y * x * z * y * x * y * z^-2 * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T73.6 : Triangle type {2,3,15} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * z^-1 * x * z * y * x * z * y^2 * z^-2 * x * y^-1 * z^-1 * x, z * y * z^-1 * x * z^2 * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x, z^-7 * x * z^2 * y * x^2 * y^-1 * z^-1 * x * y^-1 * z^-7 ] T73.7 : Triangle type {2,3,24} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * z^2 * y^-1 * x * z^2 * y^-1 * z^-2, z^2 * y * x * z^3 * y * x * z^2 * y^-1 * z^3 * y^-1 * z^-1 * x, z * y * z^-1 * x * z * y * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z ] T73.8 : Triangle type {2,3,24} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, y * x * z * y * x * z * y * x * z * y * x * z^2 * x * z * y^-1 * z^-1 * x * z, x * z^4 * y * z^-3 * x * z^2 * y^-1 * x * y^-1 * z^-4 ] T73.9 : Triangle type {2,3,24} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z^2 * y * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-2 ] T73.10 : Triangle type {2,3,30} Group order 1080 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z^4 * y * x * z * y^-2 * z^-3 * x * z, x * z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 ] T73.11 : Triangle type {2,3,42} Group order 1008 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z^2 * y * z^-3 * x * z * y * z^-1 * y * x * z^2 * y^-1 * z^-2 ] T73.12 : Triangle type {2,4,6} Group order 1728 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * z^-1 * x * z * y * x * y^-1 * z^2 * y^-1 * z^-1 * x * z ] T73.13 : Triangle type {2,4,7} Group order 1344 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-1)^6, z^2 * y * z^-1 * y * x * z * y^2 * z^-3 * y * z^-1 * x ] T73.14 : Triangle type {2,4,8} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, y * z^-2 * x * z * y^2 * z^-1 * x * z^3 ] T73.15 : Triangle type {2,4,8} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y^-1 * z * y * x * z * y^-2 * z^-2 * y * z^-1 * y ] T73.16 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z^2 * y^-1 * z * y * z^-1 * x * z^2 * y^-2 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T73.17 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^8 ] T73.18 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z^2 * y^-1 * z * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T73.19 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-1)^6 ] T73.20 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T73.21 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, x * y^-1 * z^2 * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 ] T73.22 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y * x * z * y^-1 * z * y * x * z * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * x * y^-1 * z^-2 * y * z^-1 * y ] T73.23 : Triangle type {2,4,8} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y * x * z * y^-1 * z * y * x * z * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * x * y^-1 * z^-2 * y * z^-1 * x ] T73.24 : Triangle type {2,4,10} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^10, (y * z^-1)^6, x * z^2 * y^-1 * z * y^-2 * z^-3 * y * z^-1 * y, z^2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z ] T73.25 : Triangle type {2,4,12} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2)^4, z^12, z^-3 * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T73.26 : Triangle type {2,4,12} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T73.27 : Triangle type {2,4,12} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^12, x * z * y * x * z^3 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T73.28 : Triangle type {2,4,12} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, y * x * y^-1 * z^2 * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 ] T73.29 : Triangle type {2,4,12} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^-1 * z^2 * y^-1 * z * y^-1 * z^-3 * x * z, z^12 ] T73.30 : Triangle type {2,4,20} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y * z^-1)^6, z^-1 * x * z * y * z^-1 * x * z^4 * y * z^-1 * x * z^2 * y^-1 * z^-7 ] T73.31 : Triangle type {2,4,28} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-4 * y * z^-4 * x ] T73.32 : Triangle type {2,4,28} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T73.33 : Triangle type {2,4,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y * z^-1)^6, z^7 * y * z^-1 * x * z * y * x * y^-1 * z^-6 * x ] T73.34 : Triangle type {2,4,40} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-21 * x * z^11 * y^-1 * z^-7 ] T73.35 : Triangle type {2,4,40} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z^-1 * x * z^2 * y * x * z^2 * y * z^-4 * x * y^-1 * x * z^2 * y^-1 * z^-5 ] T73.36 : Triangle type {2,4,40} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z^4 * y * x * z^2 * y * z^-4 * x * y^-1 * x * z^4 * y^-1 * z^-2 * x ] T73.37 : Triangle type {2,4,40} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * z, z^6 * y * z^-1 * x * z^2 * y^-1 * z^-7 * x * y^-1 * z^-1 * x ] T73.38 : Triangle type {2,4,76} Group order 608 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-60 * x * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T73.39 : Triangle type {2,4,148} Group order 592 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-148 ] T73.40 : Triangle type {2,4,292} Group order 584 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-32 * x * y^-1 * z^-113 ] T73.41 : Triangle type {2,5,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, (y * z^-1)^4, (y * z^-4)^2 ] T73.42 : Triangle type {2,5,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1, z^10, z * y * z^-3 * y^2 * z^-3 * x * y^-1 ] T73.43 : Triangle type {2,6,6} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-3 * z^-2 * y^2, z^2 * y * x * z^2 * y * z^-2 * y * x * y * x * y^-1 * z^-2 * y * z^-2 * x ] T73.44 : Triangle type {2,6,6} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3, (y * z^-1 * y)^4 ] T73.45 : Triangle type {2,6,6} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 ] T73.46 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-4 * x * y * z^-4 ] T73.47 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-4 * x * y * z^-4, z^-1 * y * z^-2 * x * z^2 * y^-1 * z^2 * y^-1 * z^-2 ] T73.48 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y * x * y^-1 * z^2 * y * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 * z^-1 * y * z^-1 ] T73.49 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y * x * y^-1 * z^2 * y * z^-1 * y^2 * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T73.50 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y * x * y^-1 * z^2 * y * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 * z^-1 * x * z ] T73.51 : Triangle type {2,6,9} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, y^-1 * z^2 * y^-2 * z^2 * y^-1 * z, y * x * y^-1 * z * y^-1 * z * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 ] T73.52 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, z^2 * y^-1 * z^2 * y^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T73.53 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-1 * x * z^2 * y^-2 * z^-1 * x * z * y^-1 * z^-1, z^12 ] T73.54 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^12 ] T73.55 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T73.56 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-3 * y^2 ] T73.57 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^-1 * z^-4, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T73.58 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y^-2 * z)^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T73.59 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y^2 * z^-1 * x * y^-2 * z^-3 * x * z ] T73.60 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T73.61 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y^2 * z^-1)^3 ] T73.62 : Triangle type {2,6,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, z^-12 ] T73.63 : Triangle type {2,6,21} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-1 * x * z^6 * y * z^-1 * x * y * z^-11 ] T73.64 : Triangle type {2,6,27} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^8 * y * z^-7 * x * z * y^-1 * z^-6 * x * y^-1 * z^-1 * x * z ] T73.65 : Triangle type {2,6,27} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^2 * y * z^-1 * y^2 * z^-1 * x * z * y^-1 * z^-2 * x ] T73.66 : Triangle type {2,6,27} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * z^3 ] T73.67 : Triangle type {2,6,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^2 * y * x * z * y * x * y * z^-2 * x * z^2 ] T73.68 : Triangle type {2,6,57} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-1 * x * z^4 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T73.69 : Triangle type {2,6,75} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-41 * x * z^18 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T73.70 : Triangle type {2,6,219} Group order 438 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-40 * x * z^17 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T73.71 : Triangle type {2,8,8} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, y^-2 * z * y^3 * x * y^-1 * z^-1 * x ] T73.72 : Triangle type {2,8,8} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y * z^-1 * x * z * y^2 * x * y^-1 * z^2 ] T73.73 : Triangle type {2,8,8} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^3 * y * x * y^-1 * z^-3 * x ] T73.74 : Triangle type {2,8,8} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T73.75 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T73.76 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^-1 * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^6 ] T73.77 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T73.78 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z ] T73.79 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z^2 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * x ] T73.80 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, (y * z^-1)^6 ] T73.81 : Triangle type {2,8,8} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y * x * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y ] T73.82 : Triangle type {2,8,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^-2 * x * y^-2 * z * y^-1 * z^-2 ] T73.83 : Triangle type {2,8,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T73.84 : Triangle type {2,8,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z^3 * y^-1 * z^-4, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T73.85 : Triangle type {2,8,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T73.86 : Triangle type {2,8,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T73.87 : Triangle type {2,10,10} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^10, z^-1 * x * z * y^3 * x * y^-1 * z^-2, z^10, y^-1 * z * y^-4 * z^-1 * y^2 * z^-1 * x ] T73.88 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, (y * z^-3)^2, y * x * z * y^3 * x * y^-1 * z^-1 * y, y^12, (y * z^-1 * y^4)^2 ] T73.89 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^12, (y * z^-1 * y^4)^2, z^-12 ] T73.90 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-3)^2, z^-1 * y * x * y^-3 * z^-1 * y * z^-1 * y^2, y^12, (y * z^-1 * y^4)^2 ] T73.91 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12, (y * z^-1 * y^4)^2 ] T73.92 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, (y * z^-1)^6 ] T73.93 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y^-1 * z * y^-3 * z^-2 * x * y^-1, (y * z^-1)^6 ] T73.94 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12, z^-4 * x * z^5 * y^-1 * z^-2 ] T73.95 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^12, (y * z^-1 * y^4)^2, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T73.96 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z * y^-3 * z * y^-1 * z^-1 * y, y^12, z^-4 * x * z^5 * y^-1 * z^-2 ] T73.97 : Triangle type {2,12,12} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y^-5 * z * y^-1 * z^-2 * x ] T73.98 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * z^2 * y^-2 * z^-3 * y, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^12 ] T73.99 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-4, y^12 ] T73.100 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, y^12 ] T73.101 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y^12 ] T73.102 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-3 * z^-1 * x * y^-2, z * y^-1 * z * y^-2 * z^-1 * x * z^2 ] T73.103 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-1 * z^-1 * x, x * z^2 * y^-2 * z^-3 * y ] T73.104 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T73.105 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y^-3 * z^4, x * z^3 * y^2 * z^-1 * y * z^-1 * y, y * z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T73.106 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^3 * y^2 * x * z^2, y^12, y * z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T73.107 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T73.108 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z^2 * y^-2 * z^-5, y^12 ] T73.109 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^2 * y^-2 * z^-1 * y * z^-2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, y^12 ] T73.110 : Triangle type {2,12,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * y^-1 * z * y^2 * z^-1 * x * z^2, y^12 ] T73.111 : Triangle type {2,12,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^2 * y * z^-2 * x * z * y * z^-4 * x * z^4 * y^-1 * z^-13 * x * z ] T73.112 : Triangle type {2,12,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, x * z^12 * y * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-5 ] T73.113 : Triangle type {2,12,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^12, (y * z^-1 * y^4)^2, x * z * y * x * z * y * x * z^2 * y^-1 * z^-3 ] T73.114 : Triangle type {2,15,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, z * y * z^-1 * y^2 * z^-1 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T73.115 : Triangle type {2,15,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^-1 * z^2 * y^-1 * z^2 * y^-3 * z * y^-1 * z^2 * y^-1 * z ] T73.116 : Triangle type {2,20,20} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z^2 * y^-12 * z * y^-1 * z^3 ] T73.117 : Triangle type {2,21,42} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-3 * y, y^-3 * z * y^-2 * z^4 * y^-7 * z * y^-1 * z^2 ] T73.118 : Triangle type {2,36,36} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z^2 * y^-3 * z^-1 * x * z * y^-1 ] T73.119 : Triangle type {2,36,36} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-2 * z^2 * y^-9 * z * y^-1 * z^2 * y^-1 ] T73.120 : Triangle type {2,39,78} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-39 ] T73.121 : Triangle type {2,40,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^3 * y^-1 * z^3 * y^-10 * z * y^-1 * z ] T73.122 : Triangle type {2,40,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y * z^-6 * y * z^-1 * y^11 * z^-3 * y * z^-16 ] T73.123 : Triangle type {2,40,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-23 * z^3 * y^-10 * z^2 ] T73.124 : Triangle type {2,40,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^-2 * z^3 * y^-11 * z * y^-1 * z^2 ] T73.125 : Triangle type {2,40,40} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^6 * y^-11 * z^2 * y^-1 ] T73.126 : Triangle type {2,51,102} Group order 306 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^-20 * y^10 * z^-1 * y * z^-2 * y * z^-15 * y ] T73.127 : Triangle type {2,76,76} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-43 * y^2 * z^-1 * y^30 ] T73.128 : Triangle type {2,147,294} Group order 294 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^106 * y^-40 ] T73.129 : Triangle type {2,148,148} Group order 296 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^41 * z^-106 * y ] T73.130 : Triangle type {2,292,292} Group order 292 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^27 * y^-118 ] T73.131 : Triangle type {3,3,5} Group order 1080 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, z * y^-1 * z^-2 * x^-1 * y * x * y^-1 * z^-1 * x^-1 * y^-1 * x, x^-1 * z * y * x * z * y^-1 * x * z * y * x * z^2 ] T73.132 : Triangle type {3,3,5} Group order 1080 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (x * z^2 * y * z^-1)^2 ] T73.133 : Triangle type {3,3,5} Group order 1080 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T73.134 : Triangle type {3,3,6} Group order 864 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-2 * x * z * y^-1 * x * z^2 * y^-1 * z^-1 * x ] T73.135 : Triangle type {3,3,6} Group order 864 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y * x ] T73.136 : Triangle type {3,3,6} Group order 864 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z * y * x * z)^3, x^-1 * z * y * z^-1 * x * z * y^2 * z^-2 * x^-1 * z * y ] T73.137 : Triangle type {3,3,6} Group order 864 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z^-1 * x * z * y^-1 * z * y * x * z * y * x * z * y^-1 * z^-1 * x * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 ] T73.138 : Triangle type {3,3,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, z^2 * x^-1 * z * y * x^-1 * z * y * x^-1 * y^-1 * x, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 ] T73.139 : Triangle type {3,3,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x, (x * z^2 * y * z^-1)^2 ] T73.140 : Triangle type {3,3,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z ] T73.141 : Triangle type {3,3,15} Group order 540 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * y * x^-1 * z * y^-1 * x * y^-1, (z^-1 * x^-1 * y^-1)^3 ] T73.142 : Triangle type {3,3,21} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1, z^2 * y * z^-1 * x^-1 * z^2 * y^-1 * x ] T73.143 : Triangle type {3,3,21} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z^2 * y^-1 * x * z^3, z^-1 * x^-1 * z * y * x^-1 * z * y * x * y^-1 ] T73.144 : Triangle type {3,3,21} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-3 * x * z^3 ] T73.145 : Triangle type {3,3,39} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 ] T73.146 : Triangle type {3,3,147} Group order 441 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^6 * y * z^-1 * x^-2 * z^5 ] T73.147 : Triangle type {3,4,4} Group order 864 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y^-2 * x * z * y^-1 * z * y^-1 ] T73.148 : Triangle type {3,4,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 ] T73.149 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^6 ] T73.150 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z * y^-1 ] T73.151 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, z * y * x * z^2 * y * z^-2 * x^-1 * y^-1 * x * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y * z^-1 * x ] T73.152 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, (x^-1 * z^2 * y)^2, (x * z^2 * y * z^-1)^2 ] T73.153 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2, (x * z^2 * y^-1 * z^-1)^2 ] T73.154 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, y^-1 * z^-2 * x^-1 * y * x^-1 * y * z^-1 * x * z^2 ] T73.155 : Triangle type {3,4,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, y^-1 * z^-2 * x^-1 * y * x^-1 * y^-1 * z^-2 * x^-1 * z ] T73.156 : Triangle type {3,4,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T73.157 : Triangle type {3,4,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, (z^-1 * x^-1 * y^-1)^3, z^-4 * x^-1 * y^-1 * z * y * z^-1 ] T73.158 : Triangle type {3,4,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^12 ] T73.159 : Triangle type {3,4,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, (z^-1 * x^-1 * y^-1)^3, y * z^-1 * y * z^-1 * x^-1 * z^4 ] T73.160 : Triangle type {3,4,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 * x^-1 ] T73.161 : Triangle type {3,4,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1 ] T73.162 : Triangle type {3,4,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 ] T73.163 : Triangle type {3,4,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y * z^-1 * x^-1 * z * x^-1 * z^-2 * x * z * y^-1 ] T73.164 : Triangle type {3,5,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z^2 ] T73.165 : Triangle type {3,6,6} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T73.166 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y^2 * x^-1 * z * y^3 ] T73.167 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, x * y^-1 * z * y^-1 * z^2 * y * x^-1 * z^-2 * y * z^-1 * y * z^-1 ] T73.168 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * y * z^-2, y * x^-1 * y * x * z * y * x^-1 * y^-1 * z * y^-1 * z^-1 * x^-1 ] T73.169 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, z^6, z * y^-1 * z^-1 * y * x * z * y^-2 ] T73.170 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1, y^-1 * z^-1 * y^2 * x * y^-1 * z^-1 * x ] T73.171 : Triangle type {3,6,6} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1, y * x^-1 * y^-2 * x * y^-1 * z * y ] T73.172 : Triangle type {3,6,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, z^-1 * x^-1 * y^-2 * x * z^2 * y^-1 ] T73.173 : Triangle type {3,6,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z * y * z^-1 * y * x * y^-1 * z^2 ] T73.174 : Triangle type {3,6,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z, z^8, y * z^-3 * x^-1 * y * z^-3 ] T73.175 : Triangle type {3,6,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T73.176 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^8 ] T73.177 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^8 ] T73.178 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, x * z * y * x^-1 * y^-1 * z^-2 ] T73.179 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y^-2 * x * z * y^-1 * z^-1, z^8, y * z^-3 * x^-1 * y * z^-3 ] T73.180 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, z^-1 * x * y^-2 * x * y^-2 * z^-1 ] T73.181 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, y * z^-1 * y * z^-1 * y * z^-3, x * z * y * x^-1 * y^2 * x^-1 * y * x^-1 * y^-1 * z^-1 * y ] T73.182 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, (z^-1 * y)^3, (x^-1 * z * y^2)^2 ] T73.183 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, y^6, x * z^2 * y * x^-1 * z * y^-1 * z^-1 ] T73.184 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T73.185 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, y * z^-1 * y * x^-1 * y^-1 * z * y, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T73.186 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, y * z^-1 * y * x^-1 * y^-1 * z * y ] T73.187 : Triangle type {3,6,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, y * z^-1 * y * x^-1 * y^-1 * z * y, z^2 * x^-1 * y^-1 * x * z * y^-2 ] T73.188 : Triangle type {3,6,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, (x^-1 * z^2 * y^-1 * z^-1)^2 ] T73.189 : Triangle type {3,6,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, (x * z * y^2)^2 ] T73.190 : Triangle type {3,6,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z * y^2 * x^-1 * z^3, (x * z^2 * y)^2 ] T73.191 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z * y ] T73.192 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z * y * z^-1 * x^-1 * y^-2 * z ] T73.193 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, y * x * z * y^-1 * x * z * y^-1 * z ] T73.194 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, y^-1 * z * y * x^-1 * z^2 * y^-1, z * y * x * y^-1 * x * z * y^-1 * z ] T73.195 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z * y * x * y^-1 * x * z * y^-1 * z ] T73.196 : Triangle type {3,6,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z^2 ] T73.197 : Triangle type {3,6,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z^2 * y^-1 * x * z^3 ] T73.198 : Triangle type {3,6,26} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.199 : Triangle type {3,6,98} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-3 * x^-1 * z^4 ] T73.200 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-3 * y^2 * z^-3, z^-1 * x^-1 * z * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T73.201 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, y^8, (x * z^2 * y^-1 * z^-1)^2 ] T73.202 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-4 * x^-1 * z^3 * y^-1 ] T73.203 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1, z^-1 * y^3 * x^-1 * y^4 ] T73.204 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-2 * x * y^-1 * x * y^-1 * z^-2, y^8, z * y^3 * x^-1 * y^-1 * z^-1 * x ] T73.205 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y^8 ] T73.206 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T73.207 : Triangle type {3,8,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y^3 * x^-1 * y^4 ] T73.208 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-9, z^2 * y^-1 * z^2 * y^-2 * z * y^-2 ] T73.209 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x * z * y)^2, z^4 * y^-1 * x^-1 * z^4 ] T73.210 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * y^2 * x^-1 * z * y^2, x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z * y ] T73.211 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * z * y * z^-1 * y * z^-1 ] T73.212 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z ] T73.213 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * y^2 * x^-1 * z * y^2, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x ] T73.214 : Triangle type {3,9,9} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x * z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 ] T73.215 : Triangle type {3,10,30} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, y^10 ] T73.216 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^3 * x * z^2 * y ] T73.217 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (x * z * y)^2 ] T73.218 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z^3 * y^-2 * x * y^-1 * x * z * y^-1 * z * y^-1 ] T73.219 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * z^-1 * y^2 * z^-1 * x^-1 * y^4 * z^-1 ] T73.220 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, (z^-1 * y)^3, y^3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y ] T73.221 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, (y * z^-2 * y^3)^2 ] T73.222 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-2 * y)^2, y^6 * x * y^-1 * z^-1 * y^4 ] T73.223 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T73.224 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * y^4 * z^-3, y^2 * x^-1 * y * x^-1 * z * y * x * z^-1 ] T73.225 : Triangle type {3,12,12} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T73.226 : Triangle type {3,12,84} Group order 252 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * z^3, y^-1 * z * y^-1 * z^3 * y^-1 * x^-1 * z^2 * y^-1 * z^2 ] T73.227 : Triangle type {3,20,60} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * z^-1 * y^10 * z^-1 * y * z^-3 * y * z^-1 ] T73.228 : Triangle type {3,21,21} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^2 * z^-5 * y * z^-2 * y^2 * z^-2 * y^2 * z^-2 * y^2 * z^-1 ] T73.229 : Triangle type {3,26,78} Group order 234 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y * z^-2 * y * z^-1 * y * z^-1 * y^2 * z^-5 * y^2 ] T73.230 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-7 * y * z^-2 * y^2 * z^-1 * y^5 * z^-2 * y * z^-3 * y^2 ] T73.231 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-5 * x^-1 * y^-1 * z * y^-1 * z ] T73.232 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-6 * z^3 ] T73.233 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, z * y^-1 * z * y^-2 * x * y^-1 * z * y^-1 * z ] T73.234 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z * y^-4 * x * z^2 * y^-1 * z ] T73.235 : Triangle type {3,27,27} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, y^-5 * x^-1 * y^-1 * z * y^-1 * z ] T73.236 : Triangle type {3,30,30} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^4 * z^-4 ] T73.237 : Triangle type {3,33,77} Group order 231 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * z^3, y^2 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T73.238 : Triangle type {3,57,57} Group order 228 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y * z^-5 * y * z^-1 * y^2 * z^-2 * y * z^-1 * y^2 * z^-1 ] T73.239 : Triangle type {3,74,222} Group order 222 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-63 * z * y^-8 * z^2 ] T73.240 : Triangle type {3,75,75} Group order 225 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-64 * z * y^-8 * z^2 ] T73.241 : Triangle type {3,219,219} Group order 219 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-62 * z * y^-9 * z ] T73.242 : Triangle type {4,4,4} Group order 576 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (z^-1 * y)^3, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T73.243 : Triangle type {4,4,4} Group order 576 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-2 * z^-1 * x^-2 * z * y^-1 * z * x^-1 ] T73.244 : Triangle type {4,4,4} Group order 576 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, z^-1 * x^-1 * z * y * x^-1 * y^2 * x * z^-1 ] T73.245 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, (x * z^-1)^4, z^-1 * y * x^-1 * y * x^-1 * y^-1 * x * z * y ] T73.246 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z, y * z^-1 * x * y^-1 * x * y^-1 * z^2, (x^-1 * y^-1 * x * z)^3 ] T73.247 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (z^-1 * y)^3, (x * y^-1)^4, (y * x^-1 * z)^3 ] T73.248 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-2 ] T73.249 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y * x^-1 * z * y * z^-1 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z ] T73.250 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x^-1 * y * x * z * y^-1 * z * y^-1 * z^-2 ] T73.251 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, z * y^-1 * z * y^-1 * z * y^-2 * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T73.252 : Triangle type {4,4,4} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y * x^-1 * z * y * z^-1 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T73.253 : Triangle type {4,4,5} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y^-1 * z^-1)^2, z^-1 * x^-1 * y * x^-2 * z * x^-1 * z * y^-1, y * z^-1 * y * x^-2 * z * y^-1 * z * x^-1 ] T73.254 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^6, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1 ] T73.255 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^6, x^-1 * z^2 * x^-1 * y^-1 * x^2 * z^2 * x^-1 * z ] T73.256 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^6, (x * z^2 * y^-1)^2 ] T73.257 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * x * z^-1 * x^-1 * z * y * x ] T73.258 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, (x * y^-1)^6 ] T73.259 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, z^6, (x * y^-1)^6 ] T73.260 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T73.261 : Triangle type {4,4,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y * z^-1 * x^-2 * z^2 * x^-1, (x * z^2 * y)^2 ] T73.262 : Triangle type {4,4,10} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-3 * x^-1 * z * y^-1 * z^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z^-1 * y * x ] T73.263 : Triangle type {4,4,10} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x, z^10 ] T73.264 : Triangle type {4,4,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z^2, (x * z^-2 * y)^2 ] T73.265 : Triangle type {4,4,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x, x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * z * y * z^-3 ] T73.266 : Triangle type {4,4,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, y * z^-1 * x^-1 * y^-1 * x * z^-3 ] T73.267 : Triangle type {4,4,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-4 * x^-1 * z * y^-1 * z^-2 ] T73.268 : Triangle type {4,4,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4, y * x * z^-1 * y * x * z^-3 ] T73.269 : Triangle type {4,4,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * x * z^-8 * y ] T73.270 : Triangle type {4,4,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z * y * z^-1 * y * x^2 * z^4 ] T73.271 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^-6 * x^-1 * z^2 * y * x^-1 * z^3 * y * z^-1 * x * z^3 * y * z^-2 ] T73.272 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-6 * x^-1 * z^4 * y^-1 * x^-1 * y^-1 * z^-8 ] T73.273 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, y * z^-2 * x * z * y * x * z^5 ] T73.274 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * y * x^-1 * z^5 ] T73.275 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * y * x^-1 * z^5 ] T73.276 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-10 * x * z^8 * y * z^-1 ] T73.277 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^13 * y * x^-1 * y * x * y^-1 * x * y^-1 * z^-3 * x ] T73.278 : Triangle type {4,4,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^5 * y * z^-3 * x^-1 * z * y^-1 * z^-1 * x^-1 * z^8 ] T73.279 : Triangle type {4,4,38} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-24 * x * z^4 * y^-1 * z^-1 * x^-1 * z * y * z^-6 ] T73.280 : Triangle type {4,4,74} Group order 296 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-2 * y * z^-3 * x^2 * z * y * z^-4 ] T73.281 : Triangle type {4,4,74} Group order 296 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^58 * y^-1 * x^-1 * z^15 ] T73.282 : Triangle type {4,4,146} Group order 292 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-64 * x^-1 * y * z^-8 ] T73.283 : Triangle type {4,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, z^-1 * y * z^-1 * y * x^-1 * z * y^-1 * z * y^-1 ] T73.284 : Triangle type {4,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y^-1 * z * y^2 * x * y^-1 * z * y ] T73.285 : Triangle type {4,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^-3 * y * x * y^-1 * z^-1 * y ] T73.286 : Triangle type {4,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^-3 * y * x * z * y^2 ] T73.287 : Triangle type {4,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * z * y, y * x^-1 * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T73.288 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T73.289 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T73.290 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T73.291 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T73.292 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T73.293 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T73.294 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y^2 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T73.295 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3, z * y^-1 * z^-1 * x^-1 * z * x^-1 * z ] T73.296 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 ] T73.297 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T73.298 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x * z^3, z * y * z^-2 * y * x^-1 * y^-1 * z^-2 * x^-1 * z ] T73.299 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x^-1 * z^3, z * y * z^-2 * y * x^-1 * y^-1 * z^-2 * x * z ] T73.300 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z * y * x^-1 * z^2 * y^-1 * z^2 * y * z^-1 ] T73.301 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6 ] T73.302 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * x * z^-1 * x^-1 * z * x^-1 * z, z^4 * y^-1 * z^-2 * x^-1 * y^-1 * z^-1 * x * z^3 ] T73.303 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, z^-3 * x^-1 * z^2 * y^-1, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T73.304 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, y * z^-2 * x^-1 * z^3, x^-1 * y^-1 * z * y^2 * x * y^-1 * z * y^2 ] T73.305 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^-1 * y^-1 * z * y^2 * x * y^-2 * z^-1 * y ] T73.306 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-5 * x^-1 * y^-1 * x * z^4 ] T73.307 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, (x * z^-2)^2, y * z^-2 * x * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^3 ] T73.308 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^-3 * x^-1 * z^2 * y, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T73.309 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T73.310 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^5 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z^3 ] T73.311 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T73.312 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z * y^-1 * z^-1, (y * z^-1)^4 ] T73.313 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z^2 * y, (y * z^-1)^4 ] T73.314 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z * y^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * y * x * z^5 ] T73.315 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y^2)^2, z * y * x^-1 * y * x^-1 * y^-1 * x * z^2 ] T73.316 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-5 * x * y * z^-1 * x * z^4 ] T73.317 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, (x * z^-1 * y)^2, (x * z * y)^2, (x * y^-1)^4 ] T73.318 : Triangle type {4,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, y^6, (x * z^-1 * y)^2 ] T73.319 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^8, y * z^-1 * y^3 * z^-3 ] T73.320 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8, (y * z^-2 * y)^2 ] T73.321 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^8 ] T73.322 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, (x * z * x^-1 * y^-1)^2, z * y^2 * x^-2 * z^2 * y * x, y^2 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y ] T73.323 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y^-1 * x * y^-1 * z, (x^-1 * z * y)^2 ] T73.324 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y^-1 * z * y, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z, y^8 ] T73.325 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T73.326 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z * y^-1 * x * z * x^-1, (x^-1 * z * y)^2 ] T73.327 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y)^2, x * z^-1 * x^-2 * z^2 * y, z * x^-1 * y * x^-1 * y * x * y^-1, y^8 ] T73.328 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z * y^-1 * x * z * x^-1, (x * z * y)^2 ] T73.329 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^2 * z * y^-1, y^3 * x^-1 * z^3, y^8 ] T73.330 : Triangle type {4,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T73.331 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T73.332 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, x^-1 * z * y * z^-1 * y * x * y^-1 * z^-1 * y * z^-1 ] T73.333 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 * y ] T73.334 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * y^-1 * z * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * z^-1 * y ] T73.335 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T73.336 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, x^-1 * z * y * z^-1 * y * x * z * y^2 * z^-1 ] T73.337 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T73.338 : Triangle type {4,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y ] T73.339 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.340 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x ] T73.341 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * z * y, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T73.342 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * z * y, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T73.343 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x^-1 * y^-1 * z^-1, (y * z^-3)^2 ] T73.344 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-1 * y * z^-1 * y * x^-1 * z^2 * y * z^-1, y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^2 ] T73.345 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^2 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x^-1, y^-1 * z^-2 * x^-1 * y * x^-1 * z^4 ] T73.346 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^2, (x * z^-1 * y)^2, (y * z^-2)^2 ] T73.347 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, z^2 * y * x^-1 * y^-2 * z ] T73.348 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T73.349 : Triangle type {4,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, z * y^2 * x^-1 * z * y^-1 * z, z^2 * y * x^-1 * y^-2 * z ] T73.350 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.351 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-6 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z^-3 * x^-1 * y * z^-1 ] T73.352 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, y^-1 * z^-1 * x^-1 * z * y * x * z^4 ] T73.353 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^-2, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.354 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^7 * y^-1 * z^-4 * x^-1 * z^4 ] T73.355 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.356 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.357 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.358 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.359 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.360 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x * y^-1 * z^-8 ] T73.361 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.362 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-2 * x^-1 * z * y * x * z^2 * y^-1 * z^-1 ] T73.363 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.364 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, y^-1 * z^-1 * x^-1 * z * y * x * z^4 ] T73.365 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, (y * z^-1)^4, z^-1 * x^-1 * z^2 * y * x * z * y^-1 * z^-2 ] T73.366 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.367 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.368 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.369 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.370 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^2 * y * x * z^4 * y^-1 * z^-3 * x^-1 * z^5 ] T73.371 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T73.372 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T73.373 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^-2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T73.374 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T73.375 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T73.376 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T73.377 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^4 ] T73.378 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, y^2 * z^-1 * y^2 * z^-3 ] T73.379 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, y^2 * z^-1 * y^2 * z^-3 ] T73.380 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T73.381 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^8 ] T73.382 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * x^-2 * y^-1 * z * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T73.383 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T73.384 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1 ] T73.385 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x ] T73.386 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T73.387 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y, y^2 * x^-2 * y^-1 * z * x^-1 ] T73.388 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^8, z^-1 * y^3 * x^-1 * y^4, x^-1 * z^3 * y * x^-1 * z * y^-1 * z^-2 ] T73.389 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, (y * z^-2)^2, x^-1 * y * x^-2 * y^-2 * z, z^-2 * y * x^-1 * z * y^-2, z^-4 * x^-1 * z * y * z^-2 ] T73.390 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, z * y^2 * x^-1 * z * y^-1 * z, y^8, z^-1 * y^3 * x^-1 * y^4, z * y * z^-2 * x^-1 * z^4 ] T73.391 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, x^-1 * y * x^-2 * y^-2 * z, z * y^2 * x^-1 * z * y^-1 * z, z^-2 * y * x^-1 * z * y^2, z * y * z^-2 * x^-1 * z^4 ] T73.392 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, (y * z^-2)^2 ] T73.393 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T73.394 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T73.395 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, (y * z^-2)^2, y^4 * x^-1 * z * x^-1 * z ] T73.396 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^8, z * y^3 * x^-1 * y^-1 * z^2 * y^-1 ] T73.397 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y * x * y^-1 * x * z^2, y^8 ] T73.398 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1, y^8, y^2 * z^-1 * y^2 * z^-3 ] T73.399 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, z * y^2 * x^-1 * z * y^-1 * z, y^8, y^2 * z^-1 * y^2 * z^-3 ] T73.400 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, (x * z^-1)^4 ] T73.401 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T73.402 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^8, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T73.403 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^8, (x * z^-1)^4 ] T73.404 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-2 * x^-1 * z * y * x * z^3 * y ] T73.405 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^2 * y * x * z^5 * y * z^-2 * x^-1 * z^5 ] T73.406 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.407 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T73.408 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * y^-1 * z^-8 ] T73.409 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, (y * z^-1)^4, z^-1 * x^-1 * z^2 * y * x * z * y^-1 * z^-2 ] T73.410 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z * y * x^-1 * z * y * x * z^4 ] T73.411 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y * x * z^4 ] T73.412 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, y^8, z^-2 * y * z^-1 * y * z^-3 ] T73.413 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-2 * y * z^-1 * y * z^-3 ] T73.414 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^8 ] T73.415 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^2 * x^-2 * y^-1 * z * x^-1, y^8, y * z^-1 * y^2 * x^-1 * y * z^-2 * y ] T73.416 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T73.417 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z^4 * y^-1 * z^-5 * x^-1 * y * x^-1 * z^5 ] T73.418 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^2 * y * z^-1 * x^-1 * z^4 ] T73.419 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y^8, y^-1 * z^-2 * x^-1 * y^-1 * x * z^4 ] T73.420 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, (y * z^-1 * y^2)^2, z^-4 * x^-1 * y * z^-3 ] T73.421 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1)^4, y * z^-3 * x^-1 * z^4 ] T73.422 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1 * y^2)^2, z^-4 * x^-1 * y * z^-3 ] T73.423 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * z^-3 * x^-1 * z^4 ] T73.424 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4 ] T73.425 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4, (y * z^-3)^2, z^-4 * x^-1 * y * z^-3 ] T73.426 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4 ] T73.427 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-3)^2, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z, z^-4 * x^-1 * y * z^-3 ] T73.428 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * z * y * z^-7 ] T73.429 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, (y * z^-1)^4, z^-1 * x^-1 * z^2 * y * x * z^2 * y * z^-1 ] T73.430 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1)^4, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.431 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.432 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, (y * z^-1)^4, y * z^-3 * x^-1 * z^4 ] T73.433 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, (y * z^-1)^4, y * z^-3 * x^-1 * z^4 ] T73.434 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^8, (y * z^-1 * y^2)^2, y * z^-3 * x^-1 * z^4 ] T73.435 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, (y * z^-1 * y^2)^2, y * z^-3 * x^-1 * z^4 ] T73.436 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^8, (y * z^-1)^4, z^-1 * x^-1 * z^2 * y * x * z^2 * y * z^-1 ] T73.437 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1)^4, z * y * x^-1 * z * y * x * z^4 ] T73.438 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y, z^-4 * x^-1 * y * z^-3 ] T73.439 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, z^-4 * x^-1 * y * z^-3 ] T73.440 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-3)^2 ] T73.441 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2, (x * z * y)^2, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T73.442 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-3)^2 ] T73.443 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T73.444 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * y^-1 * x * z ] T73.445 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, (x * z^-1 * y)^2 ] T73.446 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^5 * y^-1 * z^-5 * x^-1 * y^-1 * z^-1 * x^-1 * z^3 ] T73.447 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T73.448 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T73.449 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.450 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T73.451 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^9 * y * x * z * y * z^-4 * x ] T73.452 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, y^-1 * z^-2 * x^-1 * y^-1 * x * z^4 ] T73.453 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-2 * z^2 * x^-1, y^8, y^-1 * z^-2 * x^-1 * y^-1 * x * z^4 ] T73.454 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^8, y^-1 * z^-1 * x^-1 * z * y * x * z^4 ] T73.455 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y^8, y^-1 * z^-1 * x^-1 * z * y * x * z^4 ] T73.456 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-4 * x^-1 * z^2 * y * z^-1 ] T73.457 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-2 * z^2 * x^-1, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T73.458 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4 ] T73.459 : Triangle type {4,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^8, y^-1 * z^-2 * x^-1 * y^-1 * x * z^4 ] T73.460 : Triangle type {4,10,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T73.461 : Triangle type {4,12,15} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1 * y)^2, (x^-1 * z * y)^2, x^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T73.462 : Triangle type {4,12,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, z * y * z^-1 * y^2 * z^-1 * x^-1 * z ] T73.463 : Triangle type {4,14,28} Group order 224 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z * y^-3 * x * y^-1 * z^2 ] T73.464 : Triangle type {4,14,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-2 * y^2 * z^-2 * y * z^-1 * y^2 * z^-1 ] T73.465 : Triangle type {4,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * y^-6 * z^2 * y^-3 * z * y^-1 * z^4 ] T73.466 : Triangle type {4,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^3 * y^-1 * z^2 * y^-4 * z * y^-2 * z^2 * y^-2 ] T73.467 : Triangle type {4,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, z^-2 * y * x^-1 * y^3 ] T73.468 : Triangle type {4,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (z^-1 * y)^3, x^-1 * y * x^-2 * y^-1 * z * y ] T73.469 : Triangle type {4,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (z^-1 * y)^3, y^3 * x^-1 * z^3 ] T73.470 : Triangle type {4,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T73.471 : Triangle type {4,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T73.472 : Triangle type {4,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1, z^-1 * y^4 * z^-3 ] T73.473 : Triangle type {4,26,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-5 * y^16 ] T73.474 : Triangle type {4,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^24 * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T73.475 : Triangle type {4,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^21 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y * z^-1 * y * z^-1 * y ] T73.476 : Triangle type {5,5,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * y^-2 * x^2 * y^-1 * z * x^-1, x^-1 * z * y^-1 * x^2 * z^2 * x^-1 ] T73.477 : Triangle type {5,5,5} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, (x * z^-2)^2 ] T73.478 : Triangle type {5,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, (z^-1 * y)^3, z * y * x^-2 * y^-1 * x * y^-1, x * z^-1 * x^-2 * z * y * z^-1 ] T73.479 : Triangle type {6,6,6} Group order 288 Chiral action Defining relators: [ x * y * z, x^6, y^6, (z^-1 * y)^3, z^6, z * y * x^-2 * y^2 * x, z^-2 * x^-2 * y * x * y^-1 ] T73.480 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^6, y * z^-1 * y * x^-1 * y * x * z ] T73.481 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^6, (x * z * y)^2 ] T73.482 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, y * x^-1 * y * x^-2 * z * y * x * y^-1 * z^-1 * y * x * z * y^-1 * z ] T73.483 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T73.484 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^6, (x * z * y)^2 ] T73.485 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T73.486 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6, z^-1 * y * x^-2 * y^-1 * x * y^-1, z^-1 * x^-1 * y * x^-1 * y^-2 * x ] T73.487 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3 ] T73.488 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T73.489 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, (z^-1 * y)^3, z^6, z^-2 * x^-2 * z * x^-1 * y, z^2 * y^2 * x * z^-1 * y * x ] T73.490 : Triangle type {6,6,6} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y^6, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T73.491 : Triangle type {6,6,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z^-1 * x^-1 * y * x^-1 * z * y^-1 * z^-1 ] T73.492 : Triangle type {6,8,24} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^-1 * z * y * x^-1 * y^-1 * z * y^-1 ] T73.493 : Triangle type {6,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * z^2, x^6, y^2 * x^2 * z^-1 * y ] T73.494 : Triangle type {6,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, x^-1 * z * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T73.495 : Triangle type {6,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, y^-2 * x^2 * y^-1 * z, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z^-2 ] T73.496 : Triangle type {6,8,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^2 * y * x^2 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T73.497 : Triangle type {6,9,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y^-1 * x^2 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T73.498 : Triangle type {6,9,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y ] T73.499 : Triangle type {6,9,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * z * y^2 * z^-2 ] T73.500 : Triangle type {6,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z^2 * y^-3 * z^4 ] T73.501 : Triangle type {6,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, y^-1 * z * y^-3 * x * y^-4 ] T73.502 : Triangle type {6,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T73.503 : Triangle type {6,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T73.504 : Triangle type {6,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^-3 * z^4 ] T73.505 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^6, z^-2 * x^2 * z^-2, (y * x^-1 * z)^3 ] T73.506 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (y * x^-1 * z)^3 ] T73.507 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, (y * x^-1 * z)^3 ] T73.508 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, (x * z * y^-1)^2, (x * z^-2)^2, y * x^-3 * z * x^-2 ] T73.509 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-2)^2, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * x^-3 * z * x^-2, y^3 * x^-1 * z^3 ] T73.510 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, (y^-2 * z * y^-3)^2 ] T73.511 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y * x^-3 * z * x^-2, y * x^-1 * y * x^-1 * y^-1 * x * z ] T73.512 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z * x^-2 ] T73.513 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, x^-1 * y * x^-1 * y * x^-1 * z * y * z^-2 ] T73.514 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^6, (y * x^-1 * z)^3 ] T73.515 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 * z^2 ] T73.516 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, z^-3 * x^-1 * z^2 * y^-1 ] T73.517 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^-1 * z^2 * y^-1 * z * y^-4 * z^3 ] T73.518 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^-2 * z^2 * y^-3 * z * y^-1 * z^3 ] T73.519 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^6, y^3 * x^-1 * y^-2 * z, y^-2 * z^3 * y^-4 * z * y^-2 ] T73.520 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * z^-1 * y^8 ] T73.521 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^-1 * z * y * x^-1 * y^-3 ] T73.522 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * x^-2 * z * y^-1 * x, z^-3 * x^-1 * z * y * z^-1, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T73.523 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^-3 * x^-1 * z * y * z^-1 ] T73.524 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, (y * x^-1 * z)^3 ] T73.525 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T73.526 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^6, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T73.527 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z * y^-1 * x^2 * z * y^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T73.528 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^-1 * x * y^-1 * x * z^2, y^3 * x^-1 * y^-2 * z ] T73.529 : Triangle type {6,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, x^-1 * z * x^-2 * z * y * z^-1, y^-1 * z * y * x^-1 * y^-3 ] T73.530 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T73.531 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T73.532 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y * z^-1 * y * z^-3 ] T73.533 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 * z^-3 * y * z^-1 * y * z^-2 ] T73.534 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^2 * z^-1 * y * x^-1 * y^4 ] T73.535 : Triangle type {6,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y * z^-1 * y * z^-3 ] T73.536 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T73.537 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T73.538 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x * y^-2 * x * z * y^-1, y^3 * x^-1 * z * y * z^-1 ] T73.539 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T73.540 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T73.541 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z ] T73.542 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T73.543 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T73.544 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T73.545 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * x^-1 * y^-4, z^-4 * x^-1 * z^2 * y * z^-1 ] T73.546 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2 ] T73.547 : Triangle type {6,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z * y^-2 ] T73.548 : Triangle type {6,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T73.549 : Triangle type {6,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T73.550 : Triangle type {6,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y^12 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^4 ] T73.551 : Triangle type {8,8,12} Group order 216 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * x^-1, y^2 * x^2 * z^-2 ] T73.552 : Triangle type {8,8,12} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z * y, y^-1 * z^-1 * x^2 * z * y^-1, (x * z^-1 * y)^2, x * y^-1 * x^3 * z^-2 * y ] T73.553 : Triangle type {8,8,12} Group order 216 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^2 * z^2, x^8, x^-1 * z * y^-1 * x^2 * z^-3 ] T73.554 : Triangle type {8,8,12} Group order 216 Chiral action Defining relators: [ x * y * z, z * y^-1 * x^2 * z^-1 * x^-1, (y^-1 * x)^3, y^3 * x * z^2, (x * z^-1 * y)^2 ] T73.555 : Triangle type {8,8,12} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-1 * y, (y^-1 * x)^3, (y * z^-1 * y)^2, x * z^-1 * x^-2 * y * x^-1 * y^-1 ] T73.556 : Triangle type {8,8,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, (y^-1 * x)^3, z * x^-3 * y^-3, x^-1 * z * y * x^-1 * z * x^-1 * z ] T73.557 : Triangle type {8,8,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (y^-1 * x)^3, z * x^-3 * y^-3, x^8 ] T73.558 : Triangle type {8,8,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * x^-3 * y^-3, x * z * x^-2 * y^-1 * x * y^-1 ] T73.559 : Triangle type {8,8,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, x * z * x^-2 * y^-1 * x * y^-1 ] T73.560 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * z^2 * y^-1, x^8 ] T73.561 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, (z^-1 * x)^3, z^-3 * x^-1 * z^2 * y^-1 ] T73.562 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * y * x * z * y^-1, x^8 ] T73.563 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x^-1 * y * x^-1 * z * y * z^-1, z^2 * y * x^-1 * z^2 * x^-1 ] T73.564 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y^-3, z * y^-1 * z * x^-1 * z * y^-2 ] T73.565 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T73.566 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T73.567 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3, x^8 ] T73.568 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-2 * z * x^-1 * z^3 * y^-1 ] T73.569 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-2 * z * y^-1 * z * y^-4 * z * y^-1 * z ] T73.570 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * y^-5 * z * y^-2 * z ] T73.571 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^2 * y^-1 * z^2 * y^-6 ] T73.572 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^8, y * x^-4 * z * x^-3 ] T73.573 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^8 ] T73.574 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, z^-4 * x^-1 * z^3 * y^-1 ] T73.575 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^8, z^-4 * x^-1 * z * y * z^-2 ] T73.576 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, y^-2 * z * x^-1 * z * y^-1 * z ] T73.577 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2 ] T73.578 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, x^8, y^-3 * x^2 * z * y^-1 * z ] T73.579 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, (y * z^-2)^2, x^8 ] T73.580 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-3 * x^2 * z * y^-1 * z ] T73.581 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y^-1 * z * x^-1 * y^-1 * x * z^3 ] T73.582 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, x^8 ] T73.583 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, y^-2 * x * y^-1 * x * z^2 * y^-1 ] T73.584 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-1 * x^-3 * z^2 * y ] T73.585 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * z^2 * y, z^-2 * x^-2 * z * y^-1 * x, z * y^-1 * z * x^-1 * y^-1 * z * y^-1 ] T73.586 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-2, z^-2 * x^-2 * z * y^-1 * x, x^8 ] T73.587 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^8 ] T73.588 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, z^-1 * x^-3 * z^2 * y ] T73.589 : Triangle type {8,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z * x^-2 * z * y * z^-1 ] T73.590 : Triangle type {8,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-9 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T73.591 : Triangle type {8,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^10 * z^-1 * y * z^-1 * y^7 * z^-2 ] T73.592 : Triangle type {8,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-9 * z^5 * y^-1 * z * y^-5 ] T73.593 : Triangle type {8,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T73.594 : Triangle type {9,9,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, (z^-1 * x)^3, z * y * x^-2 * z^3 ] T73.595 : Triangle type {9,9,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, z^2 * y * x * z^2, (z^-1 * x)^3 ] T73.596 : Triangle type {9,9,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, (z^-1 * x)^3, z^-2 * x^-2 * z * y * z^-1 ] T73.597 : Triangle type {10,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y * z^-1 * y * x^-1 * y^-1 * z * y, z^-1 * x^4 * z^-3 ] T73.598 : Triangle type {10,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, x^10 ] T73.599 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, y^2 * x^-1 * z^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T73.600 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y * z^-1 * x^-2 * y^-1 * z * x^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T73.601 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^-1 * y ] T73.602 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, y * x^-3 * z * x^-2, y^-1 * z * y * x^-1 * y^-3 ] T73.603 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T73.604 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-3 * y^-1 * x^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * x^4 * y^-2 * z^-1 ] T73.605 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2 ] T73.606 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y^-1 * x * z ] T73.607 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1 ] T73.608 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T73.609 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * y * x^-2 * y^-2 * z, y^-1 * x^4 * y^-3 ] T73.610 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z^-1, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * z^-2, y^-1 * x^4 * y^-3 ] T73.611 : Triangle type {12,12,12} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z * x^-2 * z * y^-1 * z^-1, y^-1 * x^4 * y^-3 ] T73.612 : Triangle type {12,12,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x * y^-1 * x * y^-1 * x * z * y^-1 * z^-1 ] T73.613 : Triangle type {12,12,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-1 * x * z * y^-1 * z^-1 * x * z^4 * y^-1 * z^-1 * x^-1 * z * y * z^-3 ] T73.614 : Triangle type {12,12,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^4 * y * x^-1 * z^4 ] T73.615 : Triangle type {12,15,20} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x * z^-1 * x * z^-3, x^-1 * y * x^-3 * y^4 ] T73.616 : Triangle type {12,24,56} Group order 168 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, z^-1 * x^-1 * y^-1 * x * y^-2, z^-4 * x^2 * z^-1 * x * z^-1 ] T73.617 : Triangle type {12,24,56} Group order 168 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * z * y * x^-1 * z^2, (z^-1 * y)^3 ] T73.618 : Triangle type {12,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^12 ] T73.619 : Triangle type {14,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1 ] T73.620 : Triangle type {14,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, y * x^-8 * y^2 * x^-4 ] T73.621 : Triangle type {14,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * y^3 * x^-1 * y^6 ] T73.622 : Triangle type {14,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * x^4 * z^-4 ] T73.623 : Triangle type {14,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3, y^-3 * x^2 * y^-3 ] T73.624 : Triangle type {15,15,15} Group order 180 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2, x^-6 * y^3 ] T73.625 : Triangle type {15,15,15} Group order 180 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x^2 * z * x^-1, (y^-1 * x)^3, z^-1 * y^2 * x * y^-2 ] T73.626 : Triangle type {16,40,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, z^-1 * y^5 * z^-1 * y * z^-2 ] T73.627 : Triangle type {16,40,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T73.628 : Triangle type {16,40,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^-3 * x^4 * y^-7 ] T73.629 : Triangle type {16,40,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^6 * z^-4 ] T73.630 : Triangle type {18,27,54} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-4 * y * x^-1 * z, z^2 * y^-3 * z^4 ] T73.631 : Triangle type {18,27,54} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * z * y, z^2 * y^-3 * x^-1 * y^-1 * z^3 ] T73.632 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^-2 * x^6 * y^-7 ] T73.633 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T73.634 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-1 * x^2 * y * z^-4 ] T73.635 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^5 * z^-1 * x * z^-1 * x ] T73.636 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z, x * y^-1 * x * y^-1 * x * y^-1 * x^3 * y^-1 * x * y^-3 * z * y^-1 ] T73.637 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1, y^-3 * x^2 * y^-3 ] T73.638 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^-5 * z * x^-7 * y * x^-5 ] T73.639 : Triangle type {18,27,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-4 * y^3, z^-2 * x^4 * z^-4 ] T73.640 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, x * z^-1 * x^2 * z^-3 * x * z^-1 * x^4 * z^-3 ] T73.641 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, z^-2 * x^3 * z^-2 * x ] T73.642 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x * z^-1 * x^2 * z^-3 * x * z^-1 * x^4 * z^-3 ] T73.643 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3, x * y^-1 * z^-1 * x^8 ] T73.644 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T73.645 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, x^-2 * y^3 * x^-1 * y^2 * x^-1 * y^3 ] T73.646 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x * z^-2 * x * z^-1 * x^5 * z^-1 * x ] T73.647 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^8 * z^-3 * x^4 * y^-3 * x^5 ] T73.648 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * z * y * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T73.649 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^6 * y^-1 * x^7 * z^-1 * x^6 ] T73.650 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x * y^-1 * z^-1 * x^8 ] T73.651 : Triangle type {20,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x * z^-1 * x * y^-2 * x^6 * z^-1 ] T73.652 : Triangle type {21,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x^-1 * y^-1 * x^2 * z^-1 * y, y * x^-1 * y^4 * x^-2 * y^4 ] T73.653 : Triangle type {21,21,21} Group order 168 Chiral action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * y^-1 * z, z^-1 * x * y^-1 * x * z^-1 * x, (x * z * y)^2 ] T73.654 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y * z^-1 * y * z^-5 * y^6 ] T73.655 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^7 * y^-4 * z * y^-2 ] T73.656 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-6 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T73.657 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^-4 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T73.658 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-22 ] T73.659 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^-6 * x * y^-6 * x * y^-2 ] T73.660 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-5 * x^5 * y^-6 * x * y^-3 ] T73.661 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^-5 * x * y^-2 * z^3 * y^-4 ] T73.662 : Triangle type {22,77,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T73.663 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-11 * z^2 * y^-7 ] T73.664 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^21 * x^-1 * y * x^-1 * y^2 ] T73.665 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T73.666 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^7 * z^-4 * x^9 ] T73.667 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * x, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T73.668 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-9 * z^2 * y^-5 ] T73.669 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^7, x^4 * z^-4 * x^6 ] T73.670 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^-2 * y^6 * x^-4 * y^2 ] T73.671 : Triangle type {38,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-23 * y * x^-8 * z * x^-6 ] T73.672 : Triangle type {39,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-1 * z^19 * y^-2 * x * y^-3 * x * y^-3 ] T73.673 : Triangle type {39,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z * y^-2 * x * y^-1 * z, x^5 * y^-1 * x * z^-2 ] T73.674 : Triangle type {39,39,39} Group order 156 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, x^-4 * z * x^-1 * z, y * x^-1 * y * x^-1 * y^3 ] T73.675 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^19 * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^2 ] T73.676 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y ] T73.677 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-2, x^-2 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 ] T73.678 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T73.679 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T73.680 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z * x^-6 * y * x^-7 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T73.681 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T73.682 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, y^-4 * x^4 * y^-6 * x * y^-1 * x * y^-1 ] T73.683 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^13 * z^-2 * y^6 * z^-2 * y^4 ] T73.684 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-1 * y * z^-9 * x * z^-4 * x^2 * z^-4 * y * z^-1 ] T73.685 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-30 * y * x^-1 * y * x^-1 * y * x^-16 ] T73.686 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-3 * x^7, z^-1 * y * z^-1 * y * z^-4 * y^3 * z^-4 ] T73.687 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-6, z^-1 * y * z^-1 * y * z^-4 * y^3 * z^-4 ] T73.688 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^-2 * x^4 * y^-7 ] T73.689 : Triangle type {50,75,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-1, z^-1 * y * z^-1 * y * z^-4 * y^3 * z^-4 ] T73.690 : Triangle type {51,51,51} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^16 * x^-3 * y^8 ] T73.691 : Triangle type {51,51,51} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^6 * z^-3 * y^2 * x^-6 * y^4 ] T73.692 : Triangle type {51,51,51} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, x * y^-1 * x^6 * y^-5 * x^2 ] T73.693 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^7 * z^-2 * y^3 * x^-3 * y^6 ] T73.694 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^40 * x^-2 * y^8 ] T73.695 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^5 * z^-4 * x^4 * y^-2 * x^2 ] T73.696 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^8 * y^-6 * x^3 ] T73.697 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-8 * y * z^-4 * y^2 * x^2 * z^-4 * y * z^-1 * y ] T73.698 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^2 ] T73.699 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-23 * x * y^2 * z^-5 ] T73.700 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-5 * y * z^-4 * y^5 * z^-1 * y * z^-1 ] T73.701 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^4 * z^-2 * x^3 * y^-6 * x^3 ] T73.702 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^6 * x^-4 * y^2 ] T73.703 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T73.704 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * x, y * z^-1 * y * z^-4 * y^3 * z^-4 ] T73.705 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^5 * z^-3 * y^2 * x^-2 * y^4 ] T73.706 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^7, x^4 * z^-4 * x^4 * y^-2 * x ] T73.707 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^4 * y^-4 * x, z^-7 * y^3 * z^-4 ] T73.708 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^5 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T73.709 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^3 * z^-1 * y^4 * x^-4 * y^2 ] T73.710 : Triangle type {74,148,148} Group order 148 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^3 * y^-1 * x^12 * y^-1 * x^58, y * z^-1 ] T73.711 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x^2 * z^-1 * x * z^-4 * x^4 * z^-2 ] T73.712 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x^-2 * y^-1, y^-60 * x * y^-13, x * z^-1 ] T73.713 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^2 * z^-1 * x * z^-4 * x^4 * z^-2 ] T73.714 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * x^-5 * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2 ] T73.715 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-5 * x^2 * z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-7 ] T73.716 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * y^-7 * z^4 * y^-1 * z^5 ] T73.717 : Triangle type {147,147,147} Group order 147 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * x^2 * z^-4, y^3 * z^-2 * y^8 ] Genus 74 T74.1 : Triangle type {2,4,150} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-30 * x * y * z^-119 ] T74.2 : Triangle type {2,4,296} Group order 592 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y^-1 * z^-112 ] T74.3 : Triangle type {2,6,6} Group order 876 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, z * y^-1 * z * y * x * y^-1 * z * y^-1 * z * y * x * z * y^-3 * z * y^-2 * z * y^-2 * z * y^-1 * z * y * x * y^-1 ] T74.4 : Triangle type {2,6,76} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-42 * x * z^12 * y * x * z * y^-1 * z^-19 ] T74.5 : Triangle type {2,6,222} Group order 444 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-38 * x * z * y * x * z^18 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T74.6 : Triangle type {2,8,8} Group order 584 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y * x * z * y^3 * z^-1 * y * x * z ] T74.7 : Triangle type {2,8,27} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-7 * x * z^2 * y^-1 * z^-7 * x * z * y^-1 * z^-6 * x * y^-1 * z^-1 ] T74.8 : Triangle type {2,8,100} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-26 * x * z^5 * y * x * y^-1 * z^-17 ] T74.9 : Triangle type {2,10,185} Group order 370 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-6 * x * z^22 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-3 ] T74.10 : Triangle type {2,16,44} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-5 * z^-1 * x * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1, z^3 * y * x * z * y * x * z * y * z^-6 * x * y^-1 * z^-3 * x * z^4 ] T74.11 : Triangle type {2,21,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^3 * y^-1 * z^-4, y * z^-1 * x * z * y^2 * z^-2 * y * z^-1 ] T74.12 : Triangle type {2,24,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^9 * z^-1 * y * z^-1, z^-1 * x * z^2 * y * z^-4 * y * z^2 * y^-1 * z^-4 ] T74.13 : Triangle type {2,52,78} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-2, y^-12 * z^4 * y^-6 * z^2 * y^-2 ] T74.14 : Triangle type {2,76,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-1 * y * z^-2 * y * z^-2 * y^7 * z^-4 * y^18 ] T74.15 : Triangle type {2,149,298} Group order 298 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^107 * y^-40 * z ] T74.16 : Triangle type {2,150,150} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^42 * z^-108 ] T74.17 : Triangle type {2,296,296} Group order 296 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^41 * z^-107 ] T74.18 : Triangle type {3,3,76} Group order 456 Chiral action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z * y^-1 * z^-4 * x^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T74.19 : Triangle type {3,6,6} Group order 438 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * z^-1 * x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y * x * z ] T74.20 : Triangle type {3,6,6} Group order 438 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-1 * z^2 * y^-1 * z * y^-2 ] T74.21 : Triangle type {3,76,76} Group order 228 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^63 * y^-10 * z * y^-1 ] T74.22 : Triangle type {3,222,222} Group order 222 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-63 * z * y^-10 ] T74.23 : Triangle type {4,4,75} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, (x * z^2 * y^-1)^2, z^-1 * y * z^-1 * x^-2 * z^2 * y * z^-1 ] T74.24 : Triangle type {4,4,75} Group order 300 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^59 * y^-1 * x^-1 * z^15 ] T74.25 : Triangle type {4,4,148} Group order 296 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^58 * y^-1 * x * z^15 ] T74.26 : Triangle type {4,8,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^8 * y * x * z^6 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-8 * x^-1 ] T74.27 : Triangle type {4,10,24} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, x^-1 * z^6 * y * x^-1 * y^-1 * x * z * y * z^-2 ] T74.28 : Triangle type {4,16,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^3 * y * x * z * y * x^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z ] T74.29 : Triangle type {4,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-2 * y * z^-5 * y * z^-2 * y^3 * z^-1 * y * z^-1 * y^8 * z^-1 ] T74.30 : Triangle type {4,27,27} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^12 * y^-6 * z^2 * y^-3 * z * y^-2 ] T74.31 : Triangle type {4,51,68} Group order 204 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-1 * z^2 * y^-4 * z * y^-2 * z^2 * y^-1 * z ] T74.32 : Triangle type {4,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-18 * z^3 * y^-1 * z * y^-10 * z * y^-1 * z * y^-5 * z * y^-7 ] T74.33 : Triangle type {5,38,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-8 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T74.34 : Triangle type {5,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-9 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T74.35 : Triangle type {5,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-7 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T74.36 : Triangle type {6,6,38} Group order 228 Chiral action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, z^-2 * y * x^2 * z^2 * y ] T74.37 : Triangle type {6,6,38} Group order 228 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-1 * y^2 * x^2 * z^-3, y^2 * z^-1 * x^2 * z^3 ] T74.38 : Triangle type {6,6,38} Group order 228 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-23 * x^-1 * y * x * z^5 * y^-1 * z^-8 ] T74.39 : Triangle type {6,6,111} Group order 222 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-19 * x * z * y^-1 * z^-1 * x * z^5 * y * z^-1 * x^-1 * z^7 * y ] T74.40 : Triangle type {6,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z^10 ] T74.41 : Triangle type {6,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-2)^2, x * z * y * x^-1 * y^-1 * z^-2, x * z^-1 * x^3 * z * y^2 ] T74.42 : Triangle type {6,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (y^-1 * x)^3, z^-2 * x^-2 * y^-1 * z^-1 * y ] T74.43 : Triangle type {6,14,15} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, z * y * x^2 * z * y^-1, x * z^-1 * x^-2 * y^3, z^2 * y * x^-1 * y * z^-1 * x^-1 ] T74.44 : Triangle type {6,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T74.45 : Triangle type {8,8,50} Group order 200 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^-2 * y * x^-2 * z^2 * y * z^-1 ] T74.46 : Triangle type {8,8,50} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^10 * y * x^-1 * y * x^-1 * z^13 ] T74.47 : Triangle type {8,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z^-1 * y * z^-1 * y^6 * z^-1 * y * z^-1 * y^2 * x * z^-1 * y * z^-1 * y * z^-3 * y ] T74.48 : Triangle type {10,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^5 * z^-5 * y^7 ] T74.49 : Triangle type {12,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 * z^2 * y^-2 ] T74.50 : Triangle type {12,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-1 * z * y^-2 * x * y^-4 * z^2 * y^-1 ] T74.51 : Triangle type {14,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * z^-1 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T74.52 : Triangle type {14,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z * y^-1 * x * y^-1 * x * z^3 ] T74.53 : Triangle type {14,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-3 * x^2 * z^-3, z^-2 * x * y^-1 * x * z^2 * y^-1 ] T74.54 : Triangle type {14,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * y * z^-2 ] T74.55 : Triangle type {14,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x^3 * y^-1 * z^-3 ] T74.56 : Triangle type {15,33,55} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T74.57 : Triangle type {16,16,22} Group order 176 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * z * y * z^-1 * x^-1 * z^4 * y * x^-1 * y * x^-1 * y * z^-1 ] T74.58 : Triangle type {20,32,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^14 * z^-2 * x * y^-1 * x * y^-1 * x^2 ] T74.59 : Triangle type {20,32,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T74.60 : Triangle type {21,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z * x^-1, z^-1 * x^-3 * y^-1 * x^2, y * x^-1 * y * x^-1 * y^2 * z^-1 ] T74.61 : Triangle type {21,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z, x * z^-1 * x * z^-1 * x * z^-3 ] T74.62 : Triangle type {21,21,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, z * y * x^-2 * z * x^-1 * y^-1 ] T74.63 : Triangle type {21,24,24} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, x^5 * z * x^-1 * y, z^-1 * y^4 * z^-3 ] T74.64 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, (y^-5 * x * y^-1)^2 ] T74.65 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T74.66 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T74.67 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^2 * z^-1 * x * z^-4 * x^5 * z^-1 ] T74.68 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-4 * z^3 * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T74.69 : Triangle type {26,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T74.70 : Triangle type {32,32,40} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * y^-1 * z^-1, z^-1 * x * y^-1 * x * z^-1 * x, y^-2 * x * y^-1 * x * y^-3 ] T74.71 : Triangle type {32,32,40} Group order 160 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^2, x^-1 * z * y^-1 * x * z^-1 * y, z * x^-4 * z^4 ] T74.72 : Triangle type {32,32,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z * x^-4 * z^4 ] T74.73 : Triangle type {32,32,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T74.74 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^5 * z^-1 * y, x^3 * z^-1 * x^4 * y^-5 * x^3 ] T74.75 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y * x^-1 * y^11 ] T74.76 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^6 * x^-1 * z^9 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T74.77 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-2 * z^18 * x^-3 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T74.78 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-4 * y^7 ] T74.79 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^2 * z^-1 * x^4 * y^-5 * x^2 ] T74.80 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-11 * x^2 * z^-5 ] T74.81 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^7 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T74.82 : Triangle type {38,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^7 * z^-3 * x^6 * z^-1 * x^4 ] T74.83 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x^2 * z^-3, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T74.84 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2, y^-4 * x^2 * y^-2 * z * y^-1 ] T74.85 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^-3 * z * x^-2 * z * x^-5 * z^2 ] T74.86 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, x^-1 * y^6 * x^-2 * y^2 ] T74.87 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, y^-1 * z * y^-1 * z * x^-1 * z^4 ] T74.88 : Triangle type {39,52,52} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x * z^-1 * x * z^-1 * x * y^-2 * x^8 ] T74.89 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^75, y * z^-1 ] T74.90 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T74.91 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^5 * z^-3 * x^2 * y^-5 * x^4 ] T74.92 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^25 * x^-3 * z^11 ] T74.93 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^5 * z^-3 * y^2 * x^-2 * y^4 ] T74.94 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^4 * z^-4 * x^4 * y^-2 * x ] T74.95 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T74.96 : Triangle type {75,150,150} Group order 150 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T74.97 : Triangle type {76,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z * y^-7 * z * y^-1 * x * y^-1 * x ] T74.98 : Triangle type {76,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-4 * x * y^-4 * z * y^-1 * x^4 ] T74.99 : Triangle type {76,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3, y^-3 * x * y^-1 * x * y^-4 ] T74.100 : Triangle type {76,76,76} Group order 152 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^5 * z^-1 * x * z^-2, y^-1 * x * y^-1 * x^3 * y^-4 ] T74.101 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x^-2 * y^-1, y^-60 * x * y^-14, x * z^-1 ] T74.102 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^39 * x^-4 * y^8 ] T74.103 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^14 * x^-1 * y^4 * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^2 ] T74.104 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-1 * y^5 * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^2 ] T74.105 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y^4 * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y * x^-1 ] T74.106 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T74.107 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T74.108 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-5 * x^2 * y^-6 * x * y^-1 * x * y^-1 ] T74.109 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-3 * y^6 * x^-4 * z * x^-3 ] T74.110 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y * x^-1 * y^6 * x^-4 * y^2 ] T74.111 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^-1 * y^6 * x^-6 ] T74.112 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5 * x, z^-3 * x * z^-4 * x * y * z^-4 ] T74.113 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-4 * y, z^-4 * x * z^-4 * x * y * z^-4 ] T74.114 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-4 ] T74.115 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^5 * z^-1 * y, x^3 * z^-4 * x^6 ] T74.116 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T74.117 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y * z^-1 * y * z^-1 * y * z^-4 * y^4 * z^-3 ] T74.118 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^6 * z^-4 * x^4 * y^-2 * x^3 ] T74.119 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^2 * x^2 * z^-6 ] T74.120 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^9 * z^-2 * y^8 * z^-1 * y * z^-1 * y ] T74.121 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^3 * z^-3, y^-3 * x^4 * y^-8 ] T74.122 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^2 * z^-1 * y * z^-1 * y * z^-4 * y^5 * z^-1 * y ] T74.123 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, z^-7 * y^3 * z^-4 ] T74.124 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-14 * y * x^-8 * y * x^-7 ] T74.125 : Triangle type {149,149,149} Group order 149 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^4 * y^-4 * x, y^2 * z^-1 * y * z^-4 * y^5 * z^-2 ] Genus 75 T75.1 : Triangle type {2,3,12} Group order 1776 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x * z^2 * y * z^-1 * y * z^-1 * x * z^2 * y * x * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T75.2 : Triangle type {2,4,8} Group order 1184 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * x * y^-1 * z^-2 * y * z^-1 * y ] T75.3 : Triangle type {2,4,8} Group order 1184 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * x * y^-1 * z^-2 * y * z^-1 * x ] T75.4 : Triangle type {2,4,12} Group order 888 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, x * z * y^-1 * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 ] T75.5 : Triangle type {2,4,78} Group order 624 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-61 * x * z^8 * y * x * z * y^-1 * z^-6 ] T75.6 : Triangle type {2,4,152} Group order 608 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y * z^-120 ] T75.7 : Triangle type {2,4,152} Group order 608 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-68 * x * z * y^-1 * z^-6 ] T75.8 : Triangle type {2,4,300} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-30 * x * y^-1 * z^-119 ] T75.9 : Triangle type {2,6,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-5 ] T75.10 : Triangle type {2,6,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, x * z * y * x * z * y * x * y^-1 * z^-5 ] T75.11 : Triangle type {2,8,8} Group order 592 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T75.12 : Triangle type {2,8,8} Group order 592 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y^-1 * z * y * x * z * y * z^-1 * y^2 * z^-1 * y * z^-1 * x * z * y * x ] T75.13 : Triangle type {2,8,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y * x * z^6 * y * z^-1 * x * z^6 ] T75.14 : Triangle type {2,8,52} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^37 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^6 ] T75.15 : Triangle type {2,8,52} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^18 * y * x * z^19 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-3 * x * z ] T75.16 : Triangle type {2,8,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-14 * x * z^20 * y * z^-2 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T75.17 : Triangle type {2,8,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-18 * x * z^18 * y * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T75.18 : Triangle type {2,12,12} Group order 444 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, x * y^-1 * z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T75.19 : Triangle type {2,12,12} Group order 444 Chiral action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * z * y^3 * x * y^-2 * z ] T75.20 : Triangle type {2,12,32} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-1 * x * z^16 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-5 ] T75.21 : Triangle type {2,12,32} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, z^-7 * x * z * y^-1 * z^-7 ] T75.22 : Triangle type {2,14,175} Group order 350 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^7 * z^-3, z^14 * y * z^-2 * x * y * z^-5 * x * z^2 ] T75.23 : Triangle type {2,21,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, z^2 * y^-1 * z^5 * y^-10 * z^3 ] T75.24 : Triangle type {2,22,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * z^-1 * x * z^5 ] T75.25 : Triangle type {2,24,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-10 * z^-1 * y * x, x * z^2 * y^-2 * z^3 * y * x * z * y * z^-6 ] T75.26 : Triangle type {2,24,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-10 * z^-1 * y * x, x * z^2 * y^-2 * z^3 * y * x * z^2 * y^-1 * z^-5 ] T75.27 : Triangle type {2,28,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^9 * z^-2 * y * z^-2 ] T75.28 : Triangle type {2,32,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-2 * z^4 * y^-4 * z^4 ] T75.29 : Triangle type {2,32,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-18 * z^4 * y^-5 * z^4 * y^-1 ] T75.30 : Triangle type {2,40,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, z * y^-3 * z * y^-12 * z * y^-1 * z ] T75.31 : Triangle type {2,40,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-7 * z^4 * y^-4 * z^4 * y^-1 ] T75.32 : Triangle type {2,52,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-19 * y * z^-2 * y^9 * z^-2 * y^17 * z^-1 ] T75.33 : Triangle type {2,62,155} Group order 310 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-4 * x * z, y^-17 * z^4 * y^-6 * z^2 * y^-1 * z ] T75.34 : Triangle type {2,78,78} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-74 * z * y^-1 ] T75.35 : Triangle type {2,151,302} Group order 302 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^108 * y^-42 ] T75.36 : Triangle type {2,152,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-42 * y^2 * z^-1 * y^29 * z^-1 ] T75.37 : Triangle type {2,152,152} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^43 * z^-108 * y ] T75.38 : Triangle type {2,300,300} Group order 300 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^42 * z^-107 * y ] T75.39 : Triangle type {3,3,6} Group order 888 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z * y * x * z * y * z^-1 * y * x * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * z * y^-1 * z^-1 * x * z^-1 * x^-1 * y * x * z * y * x^-1 * y * x ] T75.40 : Triangle type {3,3,151} Group order 453 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z^4 * y^-1 * x^-1 * z^3 * y^-1 * z^-2 ] T75.41 : Triangle type {3,4,12} Group order 444 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, y^-2 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T75.42 : Triangle type {3,4,12} Group order 444 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (y * x^-1 * z)^3, x * z * y * z^-1 * y * x^-1 * z * y^2 * z^-1 ] T75.43 : Triangle type {3,4,12} Group order 444 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z^2 * y * z^-1 ] T75.44 : Triangle type {3,9,9} Group order 333 Chiral action Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x^-1 * y^-1 * x * z, y^-1 * z * x^-1 * y^-1 * x * y^-2 * z ] T75.45 : Triangle type {3,9,9} Group order 333 Chiral action Defining relators: [ x^3, x * y * z, y^2 * z^-1 * x^-1 * y * z^-2, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 ] T75.46 : Triangle type {3,9,9} Group order 333 Chiral action Defining relators: [ x^3, x * y * z, z * y^3 * z^-1 * x, z^-1 * y * z^-1 * y * x * z^2 * y ] T75.47 : Triangle type {3,40,40} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, y^6 * z^-1 * y^2 * z^-1 ] T75.48 : Triangle type {3,40,40} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T75.49 : Triangle type {3,76,228} Group order 228 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-65 * z * y^-8 * z^2 ] T75.50 : Triangle type {3,225,225} Group order 225 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-64 * z * y^-10 ] T75.51 : Triangle type {4,4,4} Group order 592 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T75.52 : Triangle type {4,4,4} Group order 592 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z ] T75.53 : Triangle type {4,4,6} Group order 444 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * z^-1 ] T75.54 : Triangle type {4,4,39} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-30 * x * y^-1 * x^-1 * y^-1 * z^-7 ] T75.55 : Triangle type {4,4,76} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-30 * x^-1 * z * y * z^-6 ] T75.56 : Triangle type {4,4,76} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-30 * x^-1 * y^-1 * z^-7 ] T75.57 : Triangle type {4,4,76} Group order 304 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^60 * y^-1 * x^-1 * z^15 ] T75.58 : Triangle type {4,4,150} Group order 300 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^59 * y^-1 * x * z^15 ] T75.59 : Triangle type {4,6,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, z^3 * y^-1 * x^-1 * z^3 ] T75.60 : Triangle type {4,6,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x * y^-1 * z^-1, (x * z^-2)^2 ] T75.61 : Triangle type {4,6,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^3 * y^-1 * x^-1 * z^3, y * x * z * y * x^-1 * z * y * z^-2 * y^-1 * z^-2 * x^-1 * z ] T75.62 : Triangle type {4,6,44} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-3 * x^-1 * z^7 * y^-1 * z^-1 * x^-1 * z^2 * y * z^-7 ] T75.63 : Triangle type {4,8,8} Group order 296 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y^-1 * z * y^-2 * x * y^-2 * z^-1 * y * z^-1 * y ] T75.64 : Triangle type {4,8,8} Group order 296 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y ] T75.65 : Triangle type {4,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * y * x^2 * z * y * x, z^2 * y * z^-2 * x * z^4 ] T75.66 : Triangle type {4,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, y * x^-1 * y * x^2 * z^2 * x^-1, z^4 * y^-1 * x^-1 * z^4 ] T75.67 : Triangle type {4,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, z^9 ] T75.68 : Triangle type {4,8,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-16 * x * y^-1 * x * y^-1 * z^-4 * x * z^2 * y^-1 * z^-5 ] T75.69 : Triangle type {4,8,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-16 * x * y^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-7 ] T75.70 : Triangle type {4,10,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^10 ] T75.71 : Triangle type {4,12,20} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, z^-2 * y * x^2 * z * y * z^-1, z * y^3 * x^-1 * y^-1 * z * x^-1 ] T75.72 : Triangle type {4,12,20} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, z^-2 * y * x^2 * z * y * z^-1, z * y^3 * x^-1 * z * y * x ] T75.73 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^-1 * y * x^-1 * z^3 ] T75.74 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, z * y^2 * x^-1 * z^3 ] T75.75 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y * x^-1 * y^-1 * x * z * y * z^-2, y * x^-1 * y^-2 * z^-1 * y^2 * x^-1 * y^-4 * z^-1 * y ] T75.76 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z^3 * y * x^-1 * y^-1 * z^-1 * x^-1 * z^3 ] T75.77 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z^3 * y * x^-1 * y^-1 * z^-1 * x * z^3 ] T75.78 : Triangle type {4,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^9 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-6 * x^-1 * z ] T75.79 : Triangle type {4,12,57} Group order 228 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-1 * x^-1 * z^6 * y * z^-4 * x * z * y^-1 * z^-5 ] T75.80 : Triangle type {4,14,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1, z^2 * y^-2 * z^3 * y^-4 * z^3 ] T75.81 : Triangle type {4,14,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^3 * x^-1 * y^-1 * z^4 * y^-1 * x * y^-4 * z ] T75.82 : Triangle type {4,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-3 * y * z^-2 * y^2 * z^-2 * y^2 * z^-2 * y ] T75.83 : Triangle type {4,51,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^25 * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T75.84 : Triangle type {4,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-35 * z * y^-1 * z * y^-5 * z * y^-7 ] T75.85 : Triangle type {4,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-20 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T75.86 : Triangle type {4,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-5 * y^4 * z^-1 * y * z^-1 * y^9 ] T75.87 : Triangle type {4,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-6 * z^2 * y^-6 * z * y^-2 ] T75.88 : Triangle type {4,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^23 * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T75.89 : Triangle type {4,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^26 * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T75.90 : Triangle type {6,6,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z * y * x^-2 * y^-1 * x * y^-1, z * x^-1 * y * x^-1 * y^-2 * x, z * y^-1 * z^-1 * x^-1 * z * y * x ] T75.91 : Triangle type {6,6,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z * y * x^-2 * y^-1 * x * y^-1, z * x^-1 * y * x^-1 * y^-2 * x, x * z * y * x^-1 * y^-1 * z^-2 ] T75.92 : Triangle type {6,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * x^-1 * y^-4, z * y * x^-1 * z * y * x^-1 * z^4 ] T75.93 : Triangle type {6,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^2 * y * z^-1 ] T75.94 : Triangle type {6,31,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-2 * z^6 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T75.95 : Triangle type {6,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^2 * z^-1 * y * z^-1 * y^2 * x^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T75.96 : Triangle type {6,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^9 * z^-1 * y ] T75.97 : Triangle type {6,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T75.98 : Triangle type {7,26,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T75.99 : Triangle type {7,27,27} Group order 189 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-3 * z * y^-3 * z * y^-1 * z ] T75.100 : Triangle type {7,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-6 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T75.101 : Triangle type {7,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T75.102 : Triangle type {7,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^5 * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T75.103 : Triangle type {8,8,26} Group order 208 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3, x^8 ] T75.104 : Triangle type {8,8,26} Group order 208 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^2 * y^-1 * x^2 * y^-1 * z^2 ] T75.105 : Triangle type {8,8,26} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-7 * x * z^5 * y * x * z * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z * y * z^-4 ] T75.106 : Triangle type {8,8,26} Group order 208 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x^-1 * y * x * z^5 * y^-1 * z^-1 * x * z^6 ] T75.107 : Triangle type {8,8,100} Group order 200 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^11 * y * x^-1 * z^4 * y * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T75.108 : Triangle type {8,8,100} Group order 200 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^5 * y^-1 * z^-1 * x^-1 * z^4 * y^-1 * z^-7 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T75.109 : Triangle type {8,12,48} Group order 192 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y^2 * x^-1 * y * z^-2 ] T75.110 : Triangle type {8,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^8, z^3 * y * x^-1 * z^4 ] T75.111 : Triangle type {8,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, z^3 * y * x^-1 * z^4 ] T75.112 : Triangle type {8,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, x^8, x^-1 * z * y^4 * x^-1 * y^-2 * z ] T75.113 : Triangle type {8,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, x^-1 * z * y^4 * x^-1 * y^-2 * z ] T75.114 : Triangle type {8,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^10 * z^-1 * y * z^-1 * y^6 * z^-1 * y * z^-1 ] T75.115 : Triangle type {8,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^3 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T75.116 : Triangle type {9,57,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-8 * z^5 * y^-1 * z * y^-4 ] T75.117 : Triangle type {9,57,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-5 * y * z^-5 * y^6 * z^-2 ] T75.118 : Triangle type {11,16,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T75.119 : Triangle type {11,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T75.120 : Triangle type {11,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^2 * z^-1 * y * z^-5 * y^6 ] T75.121 : Triangle type {11,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^4 * z^-5 * y^6 ] T75.122 : Triangle type {11,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-3 * y * z^-5 * y^2 * z^-4 ] T75.123 : Triangle type {11,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-9 * y^2 * z^-4 ] T75.124 : Triangle type {12,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T75.125 : Triangle type {12,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x * z^2 * y^-1 * x * y^-1 * x * z * y^-1 * z^-2 ] T75.126 : Triangle type {12,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z^3 * y * x^-1 * y * x^-1 * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * z^3 ] T75.127 : Triangle type {12,12,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4, x * y^-2 * x * y^-1 * x^4 * y^-1 * x^2 ] T75.128 : Triangle type {12,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^4 * z^-4 * y^6 ] T75.129 : Triangle type {12,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y * z^-3 * y^3 * z^-1 * y * z^-2 * y^2 * z^-1 ] T75.130 : Triangle type {12,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y * z^-1 * y^5 * z^-1 * y * z^-2 * y^2 * z^-1 ] T75.131 : Triangle type {14,24,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T75.132 : Triangle type {14,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x, y^5 * z^-1 * y * z^-1 ] T75.133 : Triangle type {14,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-4 * x^2 * y^-4 ] T75.134 : Triangle type {14,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, z^-3 * y^2 * z^-3 ] T75.135 : Triangle type {14,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x * z^-1 * x^2 * y * z^-4 ] T75.136 : Triangle type {14,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^-2 * z * x^-3 * y * x^-8 ] T75.137 : Triangle type {14,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y * z^-2, z^-3 * x^2 * z^-3 ] T75.138 : Triangle type {14,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3, x^-5 * z^2 * y^2 ] T75.139 : Triangle type {14,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, x^-5 * z^2 * y^2 ] T75.140 : Triangle type {15,33,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, y^8 * x^-5 * y^3 ] T75.141 : Triangle type {16,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T75.142 : Triangle type {16,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T75.143 : Triangle type {16,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T75.144 : Triangle type {16,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T75.145 : Triangle type {16,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T75.146 : Triangle type {20,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, x * y^-1 * z^-1 * x^8 ] T75.147 : Triangle type {20,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^4 * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T75.148 : Triangle type {20,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^3 * z^-3, x^-1 * y^6 * x^-5 * y^2 ] T75.149 : Triangle type {20,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x * y^-1 * z^-1 * x^8 ] T75.150 : Triangle type {21,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, z^2 * y^-2 * x * y^-7 ] T75.151 : Triangle type {21,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-2 * x^2 * y^-1 * x, x * y^-2 * x * z * y^-1 ] T75.152 : Triangle type {21,21,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, z^-4 * y * x * z^-1 * y * z^-4 ] T75.153 : Triangle type {21,28,28} Group order 168 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z * y^-1 * x^2 * z^2, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T75.154 : Triangle type {21,28,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-2 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-2, x * y^-2 * x * z * y^-1, (y * z^-1 * y)^2 ] T75.155 : Triangle type {21,28,28} Group order 168 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3, y * x^-4 * z * y * x^-1 * z ] T75.156 : Triangle type {24,24,28} Group order 168 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y * x^-1 ] T75.157 : Triangle type {24,24,28} Group order 168 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, y^-1 * x^3 * y^-2 ] T75.158 : Triangle type {24,24,28} Group order 168 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^-2, x^-1 * z * y^-1 * x * z^-1 * y, y * x^-3 * y * x^-1 * z ] T75.159 : Triangle type {24,24,28} Group order 168 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^-2, (y^-1 * x)^3, x^-1 * z * y^-1 * x * z^-1 * y ] T75.160 : Triangle type {24,24,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x * z * y^-1 * x * y^-1 * x * y^-1 * z^-3 ] T75.161 : Triangle type {24,24,28} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x * z * y^-1 * x * y^-1 * x * z * y^-1 * z^-2 ] T75.162 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T75.163 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-4 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T75.164 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T75.165 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^2 * x^-11 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T75.166 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T75.167 : Triangle type {26,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-5 * y^2 * x^-5 * y^2 * x^-6 * y^2 * x^-7 ] T75.168 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-3 * y^5 * x^-1 * y^12 * x^-1 * y * x^-1 * y * x^-1 * y ] T75.169 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^6 * x^-4 * z * x^-3 ] T75.170 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-3 ] T75.171 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T75.172 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T75.173 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-6 * x^3 * y^-6 * x * y^-3 ] T75.174 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^4 * z^-5 * y^6 ] T75.175 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-15 * z^2 * x^-6 * y^2 * x^-8 ] T75.176 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-2 * y * x^-1 * z^4 * x^-4 * z^2 * x^-5 ] T75.177 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-2 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T75.178 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z^-9 * y^2 * z^-4 ] T75.179 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^5 * x^-1 * y^9 * z^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y ] T75.180 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-1 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T75.181 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^6 * z^-1 * y^7 * z^-2 * y * x^-1 * y * x^-1 * y^2 ] T75.182 : Triangle type {31,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-1 * z^11 * x^-1 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T75.183 : Triangle type {32,32,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y^-1 * x * z^2, y^-1 * x^4 * y^-3 ] T75.184 : Triangle type {32,32,80} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z * x^-1 * z^2 ] T75.185 : Triangle type {32,32,80} Group order 160 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z * x^-1 * z^2 * y^-1 * z * x^-3 * z^3 * y^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T75.186 : Triangle type {32,32,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x * z^-2 * x * z^-1 * x^6 * z^-1 ] T75.187 : Triangle type {32,32,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * x^-2 * z^3 ] T75.188 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^8 * z^-4 * x^9 ] T75.189 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^21 * x^-1 * y * x^-1 * y * x^-1 * y ] T75.190 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T75.191 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-4 * x * z^-4 * x^2 * z^-4 ] T75.192 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z * x^-1 * z^7 * y^-2 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T75.193 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-2 * z * y^-6 * z^5 * y^-6 ] T75.194 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T75.195 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-4 * x^5 * y^-6 * x * y^-2 ] T75.196 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-19 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T75.197 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^5 * z^-2 ] T75.198 : Triangle type {39,52,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^5 * z^-4 * x^6 ] T75.199 : Triangle type {40,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-1 * x^4 * z^-3 ] T75.200 : Triangle type {40,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2, x^6 * y^-2 ] T75.201 : Triangle type {40,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, x^-1 * y^-4 * z^-1 * y^3, y^-1 * z * y^-3 * x * y^-5 ] T75.202 : Triangle type {40,40,40} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * y^-1 * z^-1, (y^-1 * x * y^-3 * x)^2 ] T75.203 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^-2 * y^6 * x^-2 * z^3 * x^-4 ] T75.204 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-9 * y^2 * z^-4 ] T75.205 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^2 * z^-1 * y^9 ] T75.206 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-15 * x^2 * z^-6 ] T75.207 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-19 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T75.208 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T75.209 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T75.210 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^7 * z^-5 * y^9 ] T75.211 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-34 * z * x^-8 * z^2 * x^-7 ] T75.212 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T75.213 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T75.214 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-11 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T75.215 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T75.216 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^9 * x^-1 * y^11 * x^-1 * y^3 * z^-1 * y^6 ] T75.217 : Triangle type {51,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T75.218 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x, y^-4 * x * z^2 * y^-1 ] T75.219 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * y * x^-1 * z, y^-1 * z^2 * y^-2 * x^-1 * z^4 ] T75.220 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^6 * y^-2, y^-1 * z * y^-2 * x^-1 * z^3 ] T75.221 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x * z^-1 * x * z^-1 * x^4 * y^-1 * z^-1 * x * y^-1 * x ] T75.222 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, y * x^-11 * y * x^-1 * z * x^-4 ] T75.223 : Triangle type {52,52,78} Group order 156 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^15 * x^-1 * y^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T75.224 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-7 * z^4 * x^-1 * z^4 ] T75.225 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^3 * z^-4, x^-1 * y^6 * x^-6 ] T75.226 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * x^-1 * y^4 * x^-1 * y * x^-1 * y^11 * x^-1 * y * x^-1 * y^2 ] T75.227 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^40 * x^-4 * y^8 ] T75.228 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^4 * z^-1 * y * z^-4 * y^8 ] T75.229 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^8 * y^-6 * x^3 ] T75.230 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^2 * x^-1 * y^6 * x^-6 * y^2 ] T75.231 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^4 * y^-4 * x, z^-9 * y * z^-4 ] T75.232 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T75.233 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T75.234 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^8 * z^-1 * y^9 * z^-1 * y^9 * z^-1 * y * z^-1 * y ] T75.235 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-8 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z ] T75.236 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y^3 * z^-4, y^3 * z^-1 * y^4 * x^-4 * y^2 ] T75.237 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^5 * z^-1 * y * z^-1 * y * z^-4 * y^7 * z^-1 * y * z^-1 * y ] T75.238 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^4 * z^-4 * x * y^-6 * x^2 ] T75.239 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-12 * y * x^-1 * y * x^-1 * y^2 ] T75.240 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^4 * y^-1 * x^12 * y^-1 * x^59, y * z^-1 ] T75.241 : Triangle type {76,152,152} Group order 152 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-23 * y * x^-8 * y * x^-6 ] T75.242 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x^-2 * y^-1, y^-61 * x * y^-14, x * z^-1 ] T75.243 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^41 * x^-2 * y^8 ] T75.244 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^15 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^2 ] T75.245 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^13 * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^2 ] T75.246 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y^5 * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y^2 ] T75.247 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T75.248 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T75.249 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y^6 * x^-8 ] T75.250 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x * y^-1 * x^6 * y^-6 * x^2 ] T75.251 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^2 ] T75.252 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^7 * x^-5 * y ] T75.253 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-2, z^-3 * x * z^-4 * x * y * z^-4 ] T75.254 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-2 * y^3, z^-4 * x * z^-4 * x * y * z^-4 ] T75.255 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T75.256 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^2 * z^-1 * y * z^-4 * y^5 * z^-2 ] T75.257 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^5 * z^-1 * y, x^5 * z^-4 * x * y * z^-4 * x^3 ] T75.258 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^7 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^4 ] T75.259 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^5 * z^-4 * y^2 * x^-1 * y^5 ] T75.260 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^4 * z^-3, x^-2 * y^6 * x^-2 * z^3 * x^-3 ] T75.261 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^3 * z^-1 * y * z^-4 * y^7 ] T75.262 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^3 * z^-1 * y * z^-1 * y * z^-4 * y^2 * x^-1 * y^6 ] T75.263 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-4 * y^7, x^2 * z^-1 * x * z^-4 * x^2 * z^-4 ] T75.264 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, x^-2 * y^11 ] T75.265 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^16 * z^-1 * y^5 * x^-1 * y^5 * z^-1 * y * z^-1 * y ] T75.266 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-1 * x * y^-1 * x * y^-1 * z^2 * y^-9 * x * y^-1 * x * y^-1 * x * y^-1 ] T75.267 : Triangle type {151,151,151} Group order 151 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] Genus 76 T76.1 : Triangle type {2,3,12} Group order 1800 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z * y * z^-2 * x * z * y * z^-1 * x * y * x * y^-1 * z^-3 * x, z^-1 * x * z^2 * y * z^-1 * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T76.2 : Triangle type {2,3,15} Group order 1500 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1, z^-4 * x * z^3 * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 ] T76.3 : Triangle type {2,3,16} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^6 * y * x * z * y^2 * x * z^3 * y^-1 * z^-1, y * z^-1 * x * z^3 * y * x * z^2 * y * x * z * y * z^-2 * x * z^3 ] T76.4 : Triangle type {2,4,10} Group order 1000 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^10 ] T76.5 : Triangle type {2,4,10} Group order 1000 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^10, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T76.6 : Triangle type {2,4,154} Group order 616 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-32 * x * y * z^-121 ] T76.7 : Triangle type {2,4,304} Group order 608 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y^-1 * z^-120 ] T76.8 : Triangle type {2,5,20} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T76.9 : Triangle type {2,6,6} Group order 900 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T76.10 : Triangle type {2,6,6} Group order 900 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x * z * y^-1 * z^-2 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z * y^-1 * z^-3 * y * z^-2 * y * z^-1 * y * z^-1 ] T76.11 : Triangle type {2,6,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, x * z * y * x * z * y^2 * x * y^3 * z^-1 * y * x * z * y ] T76.12 : Triangle type {2,6,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T76.13 : Triangle type {2,6,28} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-11 * x * z^9 * y * x * y^-1 * z^-6 ] T76.14 : Triangle type {2,6,78} Group order 468 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-11 * x * z^4 * y * z^-2 * x * z^5 * y^-1 * z^-2 ] T76.15 : Triangle type {2,6,78} Group order 468 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-41 * x * z * y * x * z^21 * y^-1 * x * y^-1 * z^-12 ] T76.16 : Triangle type {2,6,78} Group order 468 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-44 * x * z^12 * y * x * z * y^-1 * z^-19 ] T76.17 : Triangle type {2,6,228} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^62 * y * z^-1 * x * z^7 * y^-1 * z^-3 * x * z ] T76.18 : Triangle type {2,9,18} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T76.19 : Triangle type {2,9,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z^3 * y^2 * z^-4 ] T76.20 : Triangle type {2,9,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z^3 * y^-1 * z^-4 ] T76.21 : Triangle type {2,10,10} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^10, z^10 ] T76.22 : Triangle type {2,10,10} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y^10, (y * z^-1 * y^3)^2, z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T76.23 : Triangle type {2,10,10} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^10, z^10 ] T76.24 : Triangle type {2,10,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-3 * x * z^22 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T76.25 : Triangle type {2,10,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-16 * x * z^3 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-7 ] T76.26 : Triangle type {2,10,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^10 ] T76.27 : Triangle type {2,10,190} Group order 380 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^26 * y^-1 * z^-9 * x * z^2 ] T76.28 : Triangle type {2,15,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, z^2 * y^-1 * z^3 * y^-5 * z^3 * y^-1 ] T76.29 : Triangle type {2,18,171} Group order 342 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-5 * z^4)^2, z^8 * y * z^-4 * x * z^6 ] T76.30 : Triangle type {2,20,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, z^-2 * y^4 * z^-4 ] T76.31 : Triangle type {2,24,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^9 * z^-1 * y * z^-1, x * z^3 * y * z^-4 * y * z * y^-1 * z^-5 ] T76.32 : Triangle type {2,54,54} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-21 * y * z^-2 * y^9 * z^-2 * y^15 * z^-3 ] T76.33 : Triangle type {2,78,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-44 * y^2 * z^-1 * y^29 * z^-1 ] T76.34 : Triangle type {2,153,306} Group order 306 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^109 * y^-42 * z ] T76.35 : Triangle type {2,154,154} Group order 308 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^44 * z^-110 ] T76.36 : Triangle type {2,304,304} Group order 304 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^43 * z^-109 ] T76.37 : Triangle type {3,3,6} Group order 900 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z * y * x * z * y * z^-1 * x^-1 * z * y * x^-1 * y * x * z * y * x * z^-1 * x ] T76.38 : Triangle type {3,3,8} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, z^3 * y * x^-1 * z^2 * y^-1 * x, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x, y * x^-1 * y * x * y^-1 * z^-1 * x * z * y * z^-1 * x^-1 * z ] T76.39 : Triangle type {3,3,78} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^4 * y^-1 * z^-4 * x^-1 * z^5 ] T76.40 : Triangle type {3,4,6} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, y^-1 * z^-1 * x^-1 * z * y^2 * z^-1 * x * z * y^-1 ] T76.41 : Triangle type {3,4,6} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-2 * y * z^-1 * y * x^-1 * z * y^-1 * z * y^-1 ] T76.42 : Triangle type {3,4,6} Group order 600 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-1 * x * z^2 * y^2 * z^-2 * y * z^-1 ] T76.43 : Triangle type {3,5,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 ] T76.44 : Triangle type {3,5,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z * y^-1 * z^-1 * x * z * y^-1 ] T76.45 : Triangle type {3,5,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-5 ] T76.46 : Triangle type {3,5,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^-5, z^-3 * x^-1 * z^2 * y^-1 ] T76.47 : Triangle type {3,5,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1 ] T76.48 : Triangle type {3,6,6} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, x * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y ] T76.49 : Triangle type {3,6,6} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * z * y^-1 * z^2 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T76.50 : Triangle type {3,6,6} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * y)^3, y * x * z * y * x^-1 * y^2 * x^-1 * y * x^-1 * y^-2 * x * y^-1 * z ] T76.51 : Triangle type {3,6,6} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^-1 * z^2 * y^2 * x^-1 * z * y^-1 * z * y^-1 * z ] T76.52 : Triangle type {3,6,6} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y^2 * z^-1 * y * z^-2 * y * z^-1 * y^2 * x^-1 * y^-2 * z^-2 * y^2 * z^-1 ] T76.53 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (y * z^-1 * y)^2, (x * z * y)^2 ] T76.54 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, y * z^-1 * y * x^-1 * z^2 * y ] T76.55 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z * x^-1 * y^-2 * x * z * y^-1 * z, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T76.56 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, y^6, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T76.57 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, z^-2 * x^-1 * y * x^-1 * y * z^-1 * x * y^-1 ] T76.58 : Triangle type {3,6,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T76.59 : Triangle type {3,6,52} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^-4 * x^-1 * z * y^-1 * z^-2 ] T76.60 : Triangle type {3,12,12} Group order 300 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^2 * y^2 * x^-1 * y^-1 * z^-1 * x^-1 ] T76.61 : Triangle type {3,12,12} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y ] T76.62 : Triangle type {3,12,12} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z * y^-1 * z^2 * y * x * y^-1 * z * y^-1 * z * y^-1 ] T76.63 : Triangle type {3,21,42} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, z^-3 * y^2 * z^-1 * y * z^-1 * y^2 * z^-1 * y^3 * z^-6 * y ] T76.64 : Triangle type {3,28,28} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-9 * y^12 * z^-1 * y * z^-1 * y^2 * z^-1 ] T76.65 : Triangle type {3,77,231} Group order 231 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-66 * z * y^-8 * z^2 ] T76.66 : Triangle type {3,78,78} Group order 234 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-67 * z * y^-8 * z^2 ] T76.67 : Triangle type {3,78,78} Group order 234 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^65 * y^-10 * z * y^-1 ] T76.68 : Triangle type {3,78,78} Group order 234 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-11 * y * z^-1 * y * z^-1 * y^2 * z^-5 * y^2 ] T76.69 : Triangle type {3,228,228} Group order 228 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-65 * z * y^-9 * z ] T76.70 : Triangle type {4,4,5} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * z^-1 * y * x * z^-1 * x * z^-1 ] T76.71 : Triangle type {4,4,5} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T76.72 : Triangle type {4,4,5} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z * y * z^-1 * x^-1 * y^-1 * x * z, z * y^-1 * x * y^-1 * x * y^-1 * z^-1 * x^-1 ] T76.73 : Triangle type {4,4,5} Group order 500 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T76.74 : Triangle type {4,4,5} Group order 500 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1 ] T76.75 : Triangle type {4,4,77} Group order 308 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-68 * x^-1 * y^-1 * z^-8 ] T76.76 : Triangle type {4,4,152} Group order 304 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^60 * y^-1 * x * z^15 ] T76.77 : Triangle type {4,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, (z^-1 * x)^3, z^6 ] T76.78 : Triangle type {4,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, (z^-1 * x)^3, z^6 ] T76.79 : Triangle type {4,6,12} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (z^-1 * x)^3, x * z^-1 * y * x^-1 * y^-1 * z^-1 * y ] T76.80 : Triangle type {4,6,12} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 ] T76.81 : Triangle type {4,6,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z * y * x * z * y * x^-1 * z * y * z^-1 * x^-1 * z^2 * y^-1 * z^-2 ] T76.82 : Triangle type {4,6,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 * z ] T76.83 : Triangle type {4,6,16} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^2, y * z^-3 * x^-1 * z^4 ] T76.84 : Triangle type {4,6,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, x^-1 * z^8 * y * x * z^4 * y^-1 * z^-3 * x^-1 * y^-1 * z^-4 ] T76.85 : Triangle type {4,12,114} Group order 228 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-1 * x^-1 * z^6 * y * z^-4 * x * z^2 * y * z^-4 ] T76.86 : Triangle type {4,14,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z * y^-1 * z^-2, z^2 * y^-1 * z^4 * y^-1 * x * y^-3 * z^3 ] T76.87 : Triangle type {4,20,55} Group order 220 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * y^7 * z^-1, z^-1 * x^-1 * z^3 * y * z^-1 * x^-1 * y * z^-4 ] T76.88 : Triangle type {4,22,44} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z, z * y^-1 * z^2 * y^-3 * z^3 * y^-1 ] T76.89 : Triangle type {4,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-2 * z * y^-1 * z * y^-7 ] T76.90 : Triangle type {4,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, z * y^-6 * z^3 * y^-1 * z * y^-3 * z^3 ] T76.91 : Triangle type {4,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-2 * y * z^-5 * y * z^-2 * y^14 * z^-1 ] T76.92 : Triangle type {4,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^23 * z^-3 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T76.93 : Triangle type {5,5,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, y^-5, y * x^-1 * y * x^-1 * y^2 * z^-1 ] T76.94 : Triangle type {5,5,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, y^-5, x^-2 * y^-1 * x^2 * z * x^-1 * y, (x * y^-1 * z^-1 * y)^2 ] T76.95 : Triangle type {5,5,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, (y^-1 * x)^3, y^-5, x^-1 * y^-2 * x^2 * y^-1 * z * x^-1 ] T76.96 : Triangle type {5,10,10} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z * y^-1)^5 ] T76.97 : Triangle type {5,10,10} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * y * z^-2 * y^2 * z^-1 * y ] T76.98 : Triangle type {5,10,10} Group order 250 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (y * z^-1 * y)^2, z * y^2 * x^-1 * z * y^-1 * z ] T76.99 : Triangle type {5,10,10} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, (y * z^-1 * y * z^-2)^2 ] T76.100 : Triangle type {5,10,10} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z ] T76.101 : Triangle type {5,39,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^10 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T76.102 : Triangle type {5,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^2 * z^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T76.103 : Triangle type {5,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^2 * z^2, x^-1 * z * y * x * y^-1 * z^-1, y^5 * z^-1 * y * z^-1 ] T76.104 : Triangle type {5,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-13 * z * y^-1 ] T76.105 : Triangle type {5,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3 ] T76.106 : Triangle type {5,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z * y^-1 * z * y^-1 * z^6 * y^-3 * z * y^-10 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-7 ] T76.107 : Triangle type {5,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T76.108 : Triangle type {5,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^24 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T76.109 : Triangle type {5,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-8 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T76.110 : Triangle type {5,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-10 * z^3 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T76.111 : Triangle type {6,6,6} Group order 300 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^6, y^-1 * z * x^-1 * y * x^-2 * y^-2 * x * y^-1 * x ] T76.112 : Triangle type {6,6,6} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, x * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y ] T76.113 : Triangle type {6,6,14} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z^-1 * y, y^6, x^-1 * y * x^-2 * y * z^-1 * y ] T76.114 : Triangle type {6,6,14} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, y^6, x * z^-1 * y * x^-1 * y^-1 * z^-1 ] T76.115 : Triangle type {6,6,14} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x^-1 * y * x * z^5 ] T76.116 : Triangle type {6,6,14} Group order 252 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^-1 * x * z^4 * y * x * z^2 * y * z^-5 ] T76.117 : Triangle type {6,6,39} Group order 234 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * z^-1 * x * z^3 ] T76.118 : Triangle type {6,6,39} Group order 234 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2, x * z^-1 * y * x^-1 * z * y^-1 * z^-1 ] T76.119 : Triangle type {6,6,39} Group order 234 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y * x * z^2, y^-1 * z^-1 * x^-2 * z * y^-1 * z ] T76.120 : Triangle type {6,6,39} Group order 234 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^-2 * y * z^-1 * x * z^-3 ] T76.121 : Triangle type {6,6,39} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-2 * x * y^-1 * z^-4 * x * z * y * x^-1 * z^3 * y ] T76.122 : Triangle type {6,6,39} Group order 234 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^19 * y^-1 * z^-6 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T76.123 : Triangle type {6,6,39} Group order 234 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^39 ] T76.124 : Triangle type {6,6,114} Group order 228 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-23 * x^-1 * y^-1 * x * y^-1 * z^-4 * x * z * y * z^-7 ] T76.125 : Triangle type {6,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z * y * x^-2 * z * y * x, z * y^2 * x^-1 * z * y^-1 * z ] T76.126 : Triangle type {6,8,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, y^-2 * x^2 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T76.127 : Triangle type {6,9,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y ] T76.128 : Triangle type {6,9,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, (y * x^-1 * z)^3, z^-4 * x^-1 * z^3 * y^-1 ] T76.129 : Triangle type {6,9,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, (y * x^-1 * z)^3, z^-4 * x^-1 * z^3 * y^-1 ] T76.130 : Triangle type {6,9,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-3 * x * z * y^-1 * z * y^-1 ] T76.131 : Triangle type {6,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^-2 * x * y^-1 * x * z * y * z^-1 ] T76.132 : Triangle type {6,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-2 * x^-1 * z^3 ] T76.133 : Triangle type {6,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-6 * x * y^-1 * z^-1 * x * z^5 * y^-1 * z^-1 * x^-1 ] T76.134 : Triangle type {6,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^-2 * x * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-3 * x * z^2 * y^-1 * z^-1 ] T76.135 : Triangle type {6,22,33} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^3 * y^-7 ] T76.136 : Triangle type {6,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-4 * z^6 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T76.137 : Triangle type {8,10,40} Group order 200 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x * z^-1 * y^2 * z^-2, x^8 ] T76.138 : Triangle type {8,10,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * x^-1 * z * x^-1 * y^-3, x^8 ] T76.139 : Triangle type {9,9,9} Group order 225 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y ] T76.140 : Triangle type {9,9,12} Group order 216 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x * z * y^-1 * x * z^-2 ] T76.141 : Triangle type {9,9,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^-9 ] T76.142 : Triangle type {9,20,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y ] T76.143 : Triangle type {9,30,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2, x^-9 ] T76.144 : Triangle type {9,30,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y^-1 * x^2, y^-1 * z * x^-2 * z^3, x * y^-1 * x * y^-1 * x * y^-3 ] T76.145 : Triangle type {9,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^2 * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T76.146 : Triangle type {9,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^6 * z^-5 * y^8 ] T76.147 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^10 ] T76.148 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, (x * z^-1 * x^2)^2, x^10 ] T76.149 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, z^-1 * y^4 * z^-3, x^10 ] T76.150 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^10, x^10 ] T76.151 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-4 * x * z * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-5 ] T76.152 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-2 * x * z^6 * y * x * z^2 * y^-1 * z^-8 ] T76.153 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^5 * y * z^-1 * x * z^2 * y * z^-1 * x^-1 * y * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T76.154 : Triangle type {10,10,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^10, x^10 ] T76.155 : Triangle type {10,10,95} Group order 190 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-6 * x * z * y^-1 * x * z^2 * y^-1 * z^-8 ] T76.156 : Triangle type {10,10,95} Group order 190 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-1 * x * z * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T76.157 : Triangle type {10,18,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T76.158 : Triangle type {10,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, z * y * z^-1 * x^-1 * z^3, y^-2 * z * x^-1 * y^-3 ] T76.159 : Triangle type {10,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-3 * x^2 * y^-3, z^-3 * x^2 * z^-3 ] T76.160 : Triangle type {10,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * x^2 * y^-3, z^-3 * x^2 * z^-3 ] T76.161 : Triangle type {10,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, x^10 ] T76.162 : Triangle type {10,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^10 ] T76.163 : Triangle type {10,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-7 * z^5 * y^-1 * z * y^-3 ] T76.164 : Triangle type {10,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-7 * z^5 * y^-1 * z * y^-1 * z^2 ] T76.165 : Triangle type {10,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-6 * x * y^-1 * z^5 * y^-5 ] T76.166 : Triangle type {12,15,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-2, x^-1 * y * x^-7 * y^4 ] T76.167 : Triangle type {12,15,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1, z^-1 * x * z^-2 * x^4 * z^-1 * x * z^-1 * x ] T76.168 : Triangle type {12,15,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, z^-3 * y * z^-5 * y^2 * z^-4 ] T76.169 : Triangle type {12,18,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * y^-1 * x, (x * z^-3)^2 ] T76.170 : Triangle type {12,18,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * x, x^-12 ] T76.171 : Triangle type {12,20,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^12 ] T76.172 : Triangle type {12,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^12 ] T76.173 : Triangle type {12,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^4 * z^-3 * y^7 ] T76.174 : Triangle type {12,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^-1 * z^2 * y^-1 * z * y^-2 * x * y^-4 * z * y^-1 * z ] T76.175 : Triangle type {14,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, x * y^-1 * x^4 * y^-1 * x * y^-4 ] T76.176 : Triangle type {14,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x * z^-2 * x^2 * z^-2 * x * z^-1 * x^5 * z^-1 * x ] T76.177 : Triangle type {14,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^4 * y^-4, z^-1 * x * z^-1 * x^3 * z^-4 ] T76.178 : Triangle type {14,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, x * z^-2 * x * z^-1 * x^3 * z^-1 * x * z^-2 ] T76.179 : Triangle type {14,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x * y^-2 * x^3 * z^-1 * x^6 * z^-2 * x * y^-1 ] T76.180 : Triangle type {15,15,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * y)^3, x^-6 * y^3 ] T76.181 : Triangle type {15,15,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, (y^-1 * x)^3, z^2 * x^-3 * z^4 ] T76.182 : Triangle type {15,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^-1 * y, (x * y^-2)^2, x^-1 * z * y^-1 * x * z^2 ] T76.183 : Triangle type {15,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^3 ] T76.184 : Triangle type {15,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T76.185 : Triangle type {15,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^2 * z^-4, y^-3 * x^6 * y^-8 ] T76.186 : Triangle type {15,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^7, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T76.187 : Triangle type {16,16,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z^4 * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T76.188 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T76.189 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T76.190 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T76.191 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T76.192 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^-2 * x^5 * y^-4 * z * y^-2 ] T76.193 : Triangle type {18,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x ] T76.194 : Triangle type {20,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T76.195 : Triangle type {20,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 ] T76.196 : Triangle type {20,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T76.197 : Triangle type {21,24,56} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^3 * z^-3, x * y^-1 * x^6 * y^-7 ] T76.198 : Triangle type {21,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, (y^-1 * x)^3 ] T76.199 : Triangle type {21,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z * y^-1, y^-1 * z * x^-2 * z^3 ] T76.200 : Triangle type {21,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, (z^-1 * x)^3 ] T76.201 : Triangle type {21,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y * x * z^2, x^-1 * y * x^-4 * y * x^-1 * y ] T76.202 : Triangle type {21,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-3 * y^-1 * x^2, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T76.203 : Triangle type {24,24,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, y * z^-1 * x^-1 * y * x^-1 * z^4 ] T76.204 : Triangle type {27,54,54} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y * z^-1 * y^2 * z^-2, x^7 * y^-1 * x * z^-1 ] T76.205 : Triangle type {27,54,54} Group order 162 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^7 * y^-1 * x * z^-1 ] T76.206 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^15 * y^-3 * x^4 * y^-3 * x^5 ] T76.207 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-4 * x * z^-4 * x^2 * z^-4 ] T76.208 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-14 * y^2 * x^-8 * z * y * x^-3 ] T76.209 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^7 * z^-1 * x * z^-1 ] T76.210 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-4 * z * x^-1 * z, y^4 * x^-1 * y * z^-1 * y * z^-1 ] T76.211 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, y^6 * x^-2 * y * z^-1 * y^2 ] T76.212 : Triangle type {27,54,54} Group order 162 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, x^-4 * y * x * z^-1, z * x^-1 * z^6 * y^-1 * z * y^-1 * z^4 ] T76.213 : Triangle type {32,40,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^14 * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T76.214 : Triangle type {32,40,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^-3 * y^6 * x^-4 * z * x^-4 ] T76.215 : Triangle type {32,40,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^3 * x^-5 * z^12 ] T76.216 : Triangle type {32,40,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^-5 * x * y^-1 * z^5 * y^-4 ] T76.217 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * x^-7 * y^7 ] T76.218 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T76.219 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^4 * z^-4 * x^6 ] T76.220 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^8 * x^-3 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y ] T76.221 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T76.222 : Triangle type {39,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-24 * y^2 * x^-6 * y^2 * x^-7 ] T76.223 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-5 * z * y^-8 * x^5 * y^-10 ] T76.224 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^13 * x^-1 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T76.225 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-6 * x^4 * y^-6 * x * y^-1 * x * y^-2 ] T76.226 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T76.227 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^4 * z^-3 * x^7 ] T76.228 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T76.229 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^2 * z^-1 * y * z^-5 * y^6 ] T76.230 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-3 * z^4 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T76.231 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-4 * x^4 * y^-8 ] T76.232 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-33 * y * x^-1 * y * x^-9 * y * x^-7 ] T76.233 : Triangle type {52,78,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T76.234 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^4 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T76.235 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^6 * z^-4 * x^7 ] T76.236 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^10 * x^-6 * y * x^-1 * y^3 ] T76.237 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-4 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T76.238 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^25 * x^-2 * y^-1 * z^12 ] T76.239 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T76.240 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-14 * y^2 * x^-3 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T76.241 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^18 * z^-2 * y^8 * z^-1 * y^3 ] T76.242 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^8, y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T76.243 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^8 * y^-6 * x^2 ] T76.244 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-4 * y * z^-5 * y^2 * z^-4 ] T76.245 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-46 * x^2 * z^-4 ] T76.246 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^11 * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y ] T76.247 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^8 * z^-4 * x^4 * y^-2 * x^4 ] T76.248 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^3 * z^-1 * y^13 * x^-1 * y^5 * z^-1 * y^3 ] T76.249 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T76.250 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-20 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T76.251 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^8 * y^-4 * x ] T76.252 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-3 * x^3 * y^-4 * z * y^-2 ] T76.253 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 * y * z^-1 ] T76.254 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T76.255 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T76.256 : Triangle type {77,154,154} Group order 154 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^77, y * z^-1 ] T76.257 : Triangle type {78,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-18 * z * y^-9 * x^3 * y^-10 ] T76.258 : Triangle type {78,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^6 * z^-4 * x^4 * y^-2 * x^2 ] T76.259 : Triangle type {78,78,78} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^4 * z^-4 * x^6 ] T76.260 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x^-2 * y^-1, y^-61 * x * y^-15, x * z^-1 ] T76.261 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^16 * x^-5 * y^7 ] T76.262 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, z^-11 * y^6 * z^-1 * y * z^-1 ] T76.263 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T76.264 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y^2 * z^-4, y^-1 * x^6 * y^-4 * z * y^-2 ] T76.265 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-3 * z^8 * x^-1 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T76.266 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10 * y^-1, z^-9 * y * z^-4 ] T76.267 : Triangle type {153,153,153} Group order 153 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^5 * z^-4 * y * x^-1 * y^5 ] Genus 77 T77.1 : Triangle type {2,4,42} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-23 * x * z^5 * y * z^-5 * x * y^-1 * z^-7 ] T77.2 : Triangle type {2,4,80} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-64 * x * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T77.3 : Triangle type {2,4,80} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-21 * x * z^10 * y * x * z * y^-1 * z^-6 ] T77.4 : Triangle type {2,4,156} Group order 624 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y * z^-122 ] T77.5 : Triangle type {2,4,308} Group order 616 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-32 * x * y^-1 * z^-121 ] T77.6 : Triangle type {2,6,6} Group order 912 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x * z * y^-1 * z^-2 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z * y^-1 * z^-3 * y * z^-1 * y * z^-2 * y * z^-1 ] T77.7 : Triangle type {2,6,15} Group order 570 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^2 * x * y^-2 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T77.8 : Triangle type {2,6,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^2 * y * x * z^6 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T77.9 : Triangle type {2,6,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-2 * x * z * y * x * y^-1 * z^-5 ] T77.10 : Triangle type {2,6,231} Group order 462 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-42 * x * z^21 * y^-1 * z^-7 * x * z^2 * y^-1 * z^-3 ] T77.11 : Triangle type {2,8,9} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, z^-4 * x * y * z^-4, y * x * y^-1 * z * y^3 * x * y^-2 * z^-1 * y ] T77.12 : Triangle type {2,8,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^5 * y * z^-9 * x * y^-1 * z^-10 * x * z^2 ] T77.13 : Triangle type {2,8,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-4 * x * z * y * x * z^5 * y * z^-2 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-6 ] T77.14 : Triangle type {2,8,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^37 * y * x * z * y * x * y^-1 * z^-8 * x * z^3 ] T77.15 : Triangle type {2,8,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^41 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-3 * x * z ] T77.16 : Triangle type {2,10,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^10, (y * z^-1 * y^3)^2, z^-1 * y * z^-2 * y^3 * z^-2 * y * z^-1 * y ] T77.17 : Triangle type {2,10,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^10, y * x * z * y^3 * x * y^-1 * z^-1 * y ] T77.18 : Triangle type {2,10,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z^3 * y^-2 * z^-1 * x * y^-1 * z, y^10, x * z * y^-4 * z^-1 * y^3 * z^-1 ] T77.19 : Triangle type {2,10,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, y^10, (y * z^-2 * y^2)^2 ] T77.20 : Triangle type {2,12,12} Group order 456 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y^12, x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T77.21 : Triangle type {2,12,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T77.22 : Triangle type {2,12,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * z^2 * y^-2 * z^-3 * y, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * z^-1 * x * z * y^-2 * z^5 ] T77.23 : Triangle type {2,12,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^12, x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-6 ] T77.24 : Triangle type {2,12,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, y^12 ] T77.25 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y * x * y^-1 * z * y * x * y^-10 * z^-1 * y, z^-4 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-4 ] T77.26 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z * y * z^-1 * x * z^2 * y * z^-1 * x * z^3 * y * z^-1 * x * z * y^-1 * z^-5 * x * z^3 * y^-1 * z^-1 * x ] T77.27 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, x * z^2 * y * z^-3 * x * z^5 * y * z^-1 * x * y^-1 * z^-10 ] T77.28 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^11 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T77.29 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^2 * y * z^-2 * x * z * y^-1 * z^-5 * x ] T77.30 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^3 * y * z^-2 * x * z * y^3 * x * y^-1 * z^-3 * x ] T77.31 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^3 * y * z^-2 * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T77.32 : Triangle type {2,16,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^6 * y * z^-5 * x, y^2 * x * z * y * x * y^-6 * z^-1 * x * y^-1 * z^-1 * y^3 ] T77.33 : Triangle type {2,16,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^9 * y * z^-4 * x * z * y^-1 * z^-5 ] T77.34 : Triangle type {2,16,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, x * z^10 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T77.35 : Triangle type {2,18,45} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, y^-2 * z * y^-2 * z^4 ] T77.36 : Triangle type {2,20,36} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-3 * z * y * x * z * y * x * y^-4 * z^-1 * x * y^-1 * z^-1 * x * y^-6, z * y * x * z^3 * y * x * z^6 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T77.37 : Triangle type {2,24,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-10 * z^4 * y^-5 * z^4 * y^-1 ] T77.38 : Triangle type {2,24,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y * x * z^5 ] T77.39 : Triangle type {2,28,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-14 * z^4 * y^-5 * z^4 * y^-1 ] T77.40 : Triangle type {2,30,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^7 * y^-4 * z^4 ] T77.41 : Triangle type {2,42,42} Group order 336 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-2 * y, y^-3 * z^22 * y^-1 * z * y^-1 * z^2 * y^-10 * z^2 ] T77.42 : Triangle type {2,42,42} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-42 ] T77.43 : Triangle type {2,46,161} Group order 322 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^3 * y^-1 * z^-2 * x, y^-10 * z^4 * y^-6 * z^3 ] T77.44 : Triangle type {2,80,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-47 * y^30 * z^-1 * y ] T77.45 : Triangle type {2,80,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-6 * y * z^-1 * y^10 * z^-4 * y^15 * z^-3 ] T77.46 : Triangle type {2,80,80} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-23 * z^3 * y^-9 * z^2 * y^-1 ] T77.47 : Triangle type {2,155,310} Group order 310 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^110 * y^-44 ] T77.48 : Triangle type {2,156,156} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^45 * z^-110 * y ] T77.49 : Triangle type {2,308,308} Group order 308 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^44 * z^-109 * y ] T77.50 : Triangle type {3,6,6} Group order 456 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z^-1 * x^-1 * y^-1 * z^2 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * y ] T77.51 : Triangle type {3,6,6} Group order 456 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^2 * z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * x^-1 * y^-2 * z^-2 * y^2 * z^-2 ] T77.52 : Triangle type {3,7,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-7, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y ] T77.53 : Triangle type {3,15,15} Group order 285 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * y * x^-1 * y * x * z * y ] T77.54 : Triangle type {3,60,60} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^7 * z^-1 * y * z^-1 ] T77.55 : Triangle type {3,60,60} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^2 * z^-4 * y^5 * x * z^-1 * y * z^-2 * y^2 * z^-2 * y ] T77.56 : Triangle type {3,231,231} Group order 231 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-66 * z * y^-10 ] T77.57 : Triangle type {4,4,21} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^21 ] T77.58 : Triangle type {4,4,21} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^5 * y * z^-1 * x * z^2 * y * z^-2 * x * z * y * x * z^7 ] T77.59 : Triangle type {4,4,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^-3, z^-4 * x^-1 * z * y^-1 * z^-2 ] T77.60 : Triangle type {4,4,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, x * z * y^-2 * x * z^-3 ] T77.61 : Triangle type {4,4,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x^2 * z * y * z^-1 ] T77.62 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-28 * x * z^3 * y * z^-1 * x * z * y * z^-5 ] T77.63 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^9 * y * z^-1 * x * z^9 ] T77.64 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-10 * x * y^-1 * x * y^-1 * z^-8 ] T77.65 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^9 * y * z^-2 * x^-1 * z^8 ] T77.66 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^28 * y * z^-6 * x^-1 * z^5 ] T77.67 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-7 * x^-1 * z * y * z^-1 * x * z^8 * y * z^-1 ] T77.68 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^6 * y^-1 * x * z^6 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-3 * x ] T77.69 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^5 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 * x^-1 * z^8 ] T77.70 : Triangle type {4,4,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^5 * y * z^-3 * x^-1 * z * y^-1 * x * z^9 ] T77.71 : Triangle type {4,4,78} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^3, y * x^-1 * z * y^-1 * x * z^-3 ] T77.72 : Triangle type {4,4,78} Group order 312 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-61 * x * y^-1 * x * y^-1 * z^-15 ] T77.73 : Triangle type {4,4,154} Group order 308 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-68 * x^-1 * y * z^-8 ] T77.74 : Triangle type {4,6,132} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, x^-1 * z^8 * y * x * z^4 * y^-1 * z^-3 * x^-1 * z * y * z^-3 ] T77.75 : Triangle type {4,8,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x^-1 * z * y * x * z^3 * y ] T77.76 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^4 * y^-1 * z^-4 * x^-1 * y^-1 * z^-2 * x^-1 * z^4 ] T77.77 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-5 * x^-1 * y^-1 * z^-1 * x * z * y * z^-7 ] T77.78 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-4 * x * z^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z^4 * y * z^-1 ] T77.79 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * z * y * x * z^4 * y^-1 * z^-3 * x^-1 * z^3 * y^-1 * z^-1 ] T77.80 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-14 * x * y^-1 * z^-7 * x^-1 * y^-1 * z^-9 ] T77.81 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-5 * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-8 ] T77.82 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-1 * x^-1 * z * y * x^-1 * z^5 * y * z^-2 * x^-1 * y * z^-4 ] T77.83 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^6 * y^-1 * z^-1 * x * y^-1 * z^-7 * x^-1 ] T77.84 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * y^-1 * z^-8 ] T77.85 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * z * y * z^-7 ] T77.86 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * z^-4 * x * y^-1 * x * z^5 * y * x * z^7 ] T77.87 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-1 * x^-1 * z * y * x * z^4 * y^-1 * z^-3 * x^-1 * y * z^-4 ] T77.88 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z^-1 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^4 * y * x^-1 * y * x^-1 * z^4 * y^-1 ] T77.89 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^6 * y^-1 * z^-1 * x * y^-1 * z^-7 * x ] T77.90 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x * z * y * z^-7 ] T77.91 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z^9 * y * x^-1 * y * x^-1 * z^5 ] T77.92 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^2 * y * x^-1 * z^4 * y^-1 * z^-3 * x^-1 * z^5 ] T77.93 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^2 * y * x^-1 * z^5 * y * z^-2 * x^-1 * z^5 ] T77.94 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^4 * y * x^-1 * y * x^-1 * z^5 ] T77.95 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-1 * x^-1 * z * y * x^-1 * z^5 * y * z^-2 * x^-1 * z^3 * y^-1 * z^-1 ] T77.96 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^9 * y * z^-1 * x^-1 * z^5 ] T77.97 : Triangle type {4,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^10 * y * x * y^-1 * z^-1 * x^-1 * z^3 ] T77.98 : Triangle type {4,9,9} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * z^-1 * x^-1 * y^-1 * x * z, y^-9 ] T77.99 : Triangle type {4,10,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x * z, y^10 ] T77.100 : Triangle type {4,12,30} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z^3 * x^-1 * z * y^-1 * z ] T77.101 : Triangle type {4,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, z * y * z^-1 * y^2 * z^-1 * x * z ] T77.102 : Triangle type {4,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x * z^2 * y * z^-7 ] T77.103 : Triangle type {4,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * y, z^3 * y * x * z^2 * y^-1 ] T77.104 : Triangle type {4,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z, y^-2 * x * y^-1 * x * y^-1 * z * x^-1 ] T77.105 : Triangle type {4,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * y * x * z^-1 * y, y * z^-1 * x^-2 * z^2 * x^-1 ] T77.106 : Triangle type {4,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, y * x^-1 * z * y * z^-1 * x * z^4 * y^-1 * z^-4 * x * z ] T77.107 : Triangle type {4,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, y * x^-1 * z * y * z^-1 * x * z^4 * y^-1 * z^-4 * x^-1 * z ] T77.108 : Triangle type {4,20,110} Group order 220 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * y^7 * z^-1, z^-1 * x^-1 * z^3 * y * z^-6 ] T77.109 : Triangle type {4,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-4 * y^2 * z^-5 * y^6 * z^-1 * y^7 * z^-2 ] T77.110 : Triangle type {4,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^3 * z^-2 * y * z^-1 * y^5 * z^-1 * y^3 * z^-1 * y^10 * z^-1 ] T77.111 : Triangle type {4,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^2 * z^-1 * y^6 * z^-5 ] T77.112 : Triangle type {4,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-34 * z * y^-1 * z * y^-5 * z * y^-7 ] T77.113 : Triangle type {4,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-23 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T77.114 : Triangle type {5,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, z^-1 * y^3 * z^-2, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T77.115 : Triangle type {5,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, (x * z * y^-1)^2 ] T77.116 : Triangle type {5,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-2 * y^-1 * x * z^-1, x * z^-1 * x^-2 * z * y^-2, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T77.117 : Triangle type {5,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, (x^-1 * z * y)^2, y^2 * x^-2 * z^2 * x^-1 ] T77.118 : Triangle type {6,6,30} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, x * z^4 * y * x^-1 * y * x * y^-1 * z^-3 ] T77.119 : Triangle type {6,6,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, y * x^-1 * y * x^-1 * z^3 ] T77.120 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x^-1 * z * y)^2, y * x^-3 * z * x^-2, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T77.121 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * x^-1, z * y * z^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^-3 ] T77.122 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T77.123 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, (y * z^-1 * y^2)^2 ] T77.124 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^4 * x^-1 * z^4 ] T77.125 : Triangle type {6,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y^3 * x * y^-1 * z^-1 ] T77.126 : Triangle type {6,10,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-1 * x * z^3 ] T77.127 : Triangle type {6,12,12} Group order 228 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, z * y * z^-1 * y * x * z * y * x ] T77.128 : Triangle type {6,12,12} Group order 228 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, y * z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T77.129 : Triangle type {6,18,99} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^-1 * x * z^2 * y^-1 * z^-2 * x^-1 * z^3 * y^-1 * z^-1 ] T77.130 : Triangle type {6,18,99} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^-1 * x * z^2 * y^-1 * z^-2 * x^-1 * y^-1 * z^-4 ] T77.131 : Triangle type {6,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^7 * z^-3 * y * z^-1 * y * z^-1 * y ] T77.132 : Triangle type {6,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-4 * z * y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T77.133 : Triangle type {6,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, (y * z^-2 * y)^2 ] T77.134 : Triangle type {6,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z^2 * y^-1 * z * x^-1 * y^-1 * z^3 ] T77.135 : Triangle type {6,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y ] T77.136 : Triangle type {6,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-2 * y * z^-1 * y^3 * z^-3 * y * z^-1 * y * z^-1 * y ] T77.137 : Triangle type {6,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^4 * z^-3 ] T77.138 : Triangle type {6,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-5 * z^5 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T77.139 : Triangle type {8,8,14} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^-3 * x * z^6 * y * z^-4 ] T77.140 : Triangle type {8,8,14} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^-1 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-5 ] T77.141 : Triangle type {8,8,52} Group order 208 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * y^-1 * z^-2 ] T77.142 : Triangle type {8,8,52} Group order 208 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z * x^-1 * z^3 ] T77.143 : Triangle type {8,8,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x^-1 * y * x^-1 * z^13 ] T77.144 : Triangle type {8,8,52} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-7 * x * z^5 * y * x * z * y * z^-3 * x * z * y * z^-6 ] T77.145 : Triangle type {8,16,48} Group order 192 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T77.146 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, z^-2 * y^3 * z^-2 * y ] T77.147 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, z^-2 * y^3 * z^-2 * y ] T77.148 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, x^8 ] T77.149 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^8 ] T77.150 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, x^8, (y * z^-1)^4 ] T77.151 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-3 * y^2 * z^-3 ] T77.152 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x^-1 * z^9 * y^-1 ] T77.153 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^5 * y^-1 * z^-2 * x^-1 * z^4 ] T77.154 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, y^-1 * z^-1 * x^-1 * y^-1 * z^-3 * x * z^6 ] T77.155 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^5 * y^-1 * z^-2 * x^-1 * z^4 ] T77.156 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-1 * x^-1 * z^3 * y * x * z * y * z^-5 ] T77.157 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^3 * y^-1 * z^-1 * x^-1 * z^2 * y * z^-4 * x ] T77.158 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-6 * x^-1 * z^5 * y^-1 ] T77.159 : Triangle type {8,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^-3 * x^-1 * y * x^-1 * z^2 * y * z^-5 ] T77.160 : Triangle type {8,23,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-3 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-4 ] T77.161 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^8, z^-1 * y^3 * x^-1 * y^-4 ] T77.162 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x^8, y^4 * x^-1 * y^-1 * z^-1 * y^2 ] T77.163 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, (y^-1 * z * y^-1 * z^3)^2 ] T77.164 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, (y^-2 * z * y^-1 * z * y^-1)^2 ] T77.165 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^3 * y^-2 * z * y^-6 ] T77.166 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^8 ] T77.167 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-2 * z * x^-1 * y^-1 * z^2, x^8 ] T77.168 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-6 ] T77.169 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^11 * y^-1 * z^2 * y^-5 * z * y^-1 * z^2 ] T77.170 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^14 * y^-1 * z * y^-4 * z * y^-2 ] T77.171 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^4 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^9 * z^-1 ] T77.172 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-2 * x^-1 * y^-1 * z^4 ] T77.173 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z * y^-1 * z * y^-2 * z * y^-1 * z^3 ] T77.174 : Triangle type {8,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z * y^-1 * z * y^-2 * x^-1 * y^-1 * z^3 * y^-1 ] T77.175 : Triangle type {8,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T77.176 : Triangle type {8,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^4 * z^-1 * y * z^-1 * y * z^-5 * y^9 ] T77.177 : Triangle type {8,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-3 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-3 ] T77.178 : Triangle type {9,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z * y^-2 * x * y^-1 * z, x^-9 ] T77.179 : Triangle type {9,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y * x^-1 * y * x^-1 * y^3, z * x^-1 * z * x^-1 * z^3 ] T77.180 : Triangle type {10,36,36} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z^-1 * y^7 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T77.181 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, x * z * x^-2 * z^2 * y ] T77.182 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * z * y)^2 ] T77.183 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^4 * y^-3, x^2 * z^-1 * x^2 * z^-3 ] T77.184 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x ] T77.185 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z^-4 * x^-1 * z^3 * y^-1 ] T77.186 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * z^2 * y^-1, z^-2 * x^-2 * z * y^-1 * x, y^-1 * x^4 * y^-3 ] T77.187 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * z * y)^2, x^-1 * y * x^-2 * y^-2 * z, z * y^2 * x^-1 * z * y^-1 * z, y^-1 * x^4 * y^-3 ] T77.188 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z^-1, y * x * y^-1 * x * z^-2, (x * z * y)^2, y^-1 * x^4 * y^-3 ] T77.189 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z * y * z^-2 * x^-1 * z^4 ] T77.190 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-2 * x^-2 * z * y^-1 * x, y^-1 * x^4 * y^-3 ] T77.191 : Triangle type {12,12,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * x^4 * y^-3 ] T77.192 : Triangle type {12,16,16} Group order 192 Chiral action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^-1 * y^-1 * x^3 * z * y^-1 * z ] T77.193 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^-1 * y, x * y^-2 * x * z * y^-1, z * x^-3 * z^3 ] T77.194 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^-1 * y, y * z^-1 * x^2 * y^-1 * z ] T77.195 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z * y^-1 * x^2 * z^2 ] T77.196 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * x^-3 * y^3, z * x^-3 * z^3, z^-2 * x^-2 * z * x^-1 * y^-1 ] T77.197 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z^2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z ] T77.198 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^-1 * y * z^-1 * x^-2 * z * y * z^-2 ] T77.199 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^3 * z * x^-1 * y^-1, z^-1 * y^4 * z^-3 ] T77.200 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-1 * z * y^-1 * x^2 * z * y^-1 * z * y^-1 ] T77.201 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, x^-1 * y^-1 * x^3 * z * y * z^-1, z^-2 * y^3 * z^-2 * y ] T77.202 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^2 * z^-1 * y * z^-1 * y^2 * x^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T77.203 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^-1 * z * y^-1 * x * z * x^-1 * y^-1 * z ] T77.204 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-12, y^-6 * z * y^-1 * z * y^-4 * z * y^-1 * z ] T77.205 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^-12 ] T77.206 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2, x * z^-1 * x^-2 * y * z^-1 * x^-7 * y ] T77.207 : Triangle type {12,16,16} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-4 * z * x^-3, x^-12 ] T77.208 : Triangle type {12,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, z^-9 * y * z^-4 ] T77.209 : Triangle type {12,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^12 ] T77.210 : Triangle type {14,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T77.211 : Triangle type {14,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T77.212 : Triangle type {14,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T77.213 : Triangle type {15,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-3, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T77.214 : Triangle type {15,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * x^2 * z^-4, y^-4 * x^2 * y^-7 ] T77.215 : Triangle type {16,16,88} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, y * z^-1 * x * z * y^-1 * z^-3 * x * z^4 ] T77.216 : Triangle type {16,16,88} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^2 * y^-1 * z^-3 * x * y^-1 * x^-1 * z^4 ] T77.217 : Triangle type {16,16,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * x * z * y * z^-3 * x * z^4 ] T77.218 : Triangle type {18,20,20} Group order 180 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-1 * y * x * z^-1 * y * z^-1 * y * z^-1 * x^-2 * y * z^-1 * y * z^-1 ] T77.219 : Triangle type {21,24,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^4 * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T77.220 : Triangle type {21,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z^-3 * x * z^-2 * x * z^-1 * y * z^-3 ] T77.221 : Triangle type {21,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y * z^-1 * x^2 * z^-2, x * y^-3 * x^-1 * y^3, y^2 * x^-3 * y^4 ] T77.222 : Triangle type {21,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-8 * y^2 * x^-10 * z^2 * x^-1 ] T77.223 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^3 * z^-5 * y^6 ] T77.224 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-9 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T77.225 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^7 * y^-4 * z * y^-2 ] T77.226 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-7 * y * x^-8 * z * x^-7 ] T77.227 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^5 * z^-4 * y * x^-3 * y^4 ] T77.228 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T77.229 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^6 * z^-4 * y * x^-6 * y * x^-1 * y^2 ] T77.230 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-3 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T77.231 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, z^-5 * x * z^-4 * x * y * z^-4 ] T77.232 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T77.233 : Triangle type {23,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T77.234 : Triangle type {24,24,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x^-1 * z^3 * y * z^-3, y * z^-1 * y * z^-5 * y * x * z^-4 ] T77.235 : Triangle type {24,24,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * y^-1 * x * z^3 ] T77.236 : Triangle type {28,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x, y^-3 * x^2 * y^-3 ] T77.237 : Triangle type {28,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^7 * z^-1 * x * z^-1 ] T77.238 : Triangle type {28,28,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * z^-3 * x * z^-1 * x * z^-2 * x^3 * z^-4 ] T77.239 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-16 * z^2 * x^-6 * y^2 * x^-8 ] T77.240 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T77.241 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-8 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T77.242 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z^-10 * y * z^-4 ] T77.243 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T77.244 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^-2 * y^6 * x^-4 * z * x^-3 ] T77.245 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-1 * z * x^-1 * z^5 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z^6 ] T77.246 : Triangle type {32,80,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^2 * z^-4 ] T77.247 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-6, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T77.248 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x * z^-1 * x^2 * z^-3 * x * z^-1 * x^3 * z^-1 * x * z^-2 ] T77.249 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, x * z^-1 * x^2 * z^-3 * x * z^-1 * x^3 * z^-1 * x * z^-2 ] T77.250 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^3 * x^-2 * z * x^-2 * z * x^-1 * z^5 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T77.251 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^27 * y^-1 * x^8 * z^-1 * x^4 ] T77.252 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^2 * z^-1 * x^3 * y^-2 * x^7 * z^-1 * x^6 ] T77.253 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^8 * z^-3 * x^6 * z^-1 * x^4 ] T77.254 : Triangle type {40,80,80} Group order 160 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-4 * y * x^-1 * y * x^-5 * z * x^-2 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T77.255 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * x^-4 * y^3 * z^-1 * y^5 ] T77.256 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^5 * z^-1 * y^4 * x^-6 * y^4 ] T77.257 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^6 * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^8 ] T77.258 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T77.259 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T77.260 : Triangle type {78,156,156} Group order 156 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^5 * y^-1 * x^12 * y^-1 * x^60, y * z^-1 ] T77.261 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-47 * x * z^-4 ] T77.262 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x^-2 * y^-1, y^-62 * x * y^-15, x * z^-1 ] T77.263 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-15 * y * x^-3 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T77.264 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-14 * y^2 * x^-7 ] T77.265 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-2 * y * x^-1 * z^4 * x^-2 * z^4 * x^-6 ] T77.266 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T77.267 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T77.268 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T77.269 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T77.270 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-3 * y^6 * x^-6 * y * x^-2 ] T77.271 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^9, z^-9 * y * z^-4 ] T77.272 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T77.273 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-3, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 ] T77.274 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-1 ] T77.275 : Triangle type {155,155,155} Group order 155 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^2 * z^-4 ] Genus 78 T78.1 : Triangle type {2,3,28} Group order 1176 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^15 * y * z^-1 * x * z^5 * y * z^-1 * x * z^6 ] T78.2 : Triangle type {2,4,81} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-64 * x * z^8 * y * x * z * y^-1 * z^-6 ] T78.3 : Triangle type {2,4,158} Group order 632 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-34 * x * y * z^-123 ] T78.4 : Triangle type {2,4,312} Group order 624 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y^-1 * z^-122 ] T78.5 : Triangle type {2,6,14} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^14 ] T78.6 : Triangle type {2,6,14} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^14 ] T78.7 : Triangle type {2,6,80} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-66 * x * y^-1 * x * y^-1 * z^-12 ] T78.8 : Triangle type {2,8,54} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^34 * y * z^-9 * x * z^10 ] T78.9 : Triangle type {2,8,54} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-8 * x * z * y^-1 * z^-7 * x * z * y^-1 * z^-8 ] T78.10 : Triangle type {2,10,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, y^10, y * z^-2 * y^3 * z^-1 * y^2 * z^-1 ] T78.11 : Triangle type {2,10,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, y^2 * x * y^-2 * z * y^-1 * z^-2, y^10, z^-3 * y^3 * z^-1 * y * z^-2 ] T78.12 : Triangle type {2,10,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^10, y * z^-1 * y^4 * z^-3 * y ] T78.13 : Triangle type {2,10,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, x * z^2 * y^-2 * z^-1 * y * z^-2, y^10, (y * z^-2 * y^2)^2 ] T78.14 : Triangle type {2,10,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^24 * y * z^-2 * x * y^-1 * z^-9 * x * z^2 ] T78.15 : Triangle type {2,12,64} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-1 * x * z^16 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T78.16 : Triangle type {2,14,28} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^-6 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-6 ] T78.17 : Triangle type {2,14,28} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-8 * z * x * y^-5 ] T78.18 : Triangle type {2,14,28} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-2 * z^4 * y^-1)^2, z^9 * y * x * z^4 * y^-1 * z^-13 * x ] T78.19 : Triangle type {2,14,182} Group order 364 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-2 * z^4 * y^-1)^2, x * z^7 * y^-1 * x * z^4 * y^-1 * z^-13 ] T78.20 : Triangle type {2,20,45} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-1 * y^5 * z^-2 * y * z^-1, x * z * y * z^-1 * x * y^-1 * z^-5 ] T78.21 : Triangle type {2,28,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y^-2 * z^4 ] T78.22 : Triangle type {2,42,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y^-3 * z^3 ] T78.23 : Triangle type {2,42,56} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, x * y^-6 * z^-1 * y^5, y^9 * z^-1 * y^3 * z^-1 ] T78.24 : Triangle type {2,81,81} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-77 * z * y^-1 ] T78.25 : Triangle type {2,106,159} Group order 318 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-20 * y * z^-2 * y^9 * z^-2 * y^16 * z^-1 * y ] T78.26 : Triangle type {2,157,314} Group order 314 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^111 * y^-44 * z ] T78.27 : Triangle type {2,158,158} Group order 316 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^46 * z^-112 ] T78.28 : Triangle type {2,312,312} Group order 312 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^45 * z^-111 ] T78.29 : Triangle type {3,3,14} Group order 588 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-14 ] T78.30 : Triangle type {3,3,157} Group order 471 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^6 * y^-1 * z^-1 * x^2 * z^5 ] T78.31 : Triangle type {3,14,14} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z * y * z^-1 * x^-1 * y^-3, z^-2 * x * y^-1 * x * y^-1 * z^-2 ] T78.32 : Triangle type {3,14,14} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, x^-1 * z * x^-1 * z * y^3 * x^2 * y^-1 * z^-2 * x * z * y ] T78.33 : Triangle type {3,14,14} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3, y^-1 * z * y * z^-1 * x^-1 * y^-4 ] T78.34 : Triangle type {3,14,14} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z * y^-1 * z^-1 * y^3 * x * z^8 ] T78.35 : Triangle type {3,79,237} Group order 237 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-68 * z * y^-8 * z^2 ] T78.36 : Triangle type {3,80,80} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^67 * y^-10 * z * y^-1 ] T78.37 : Triangle type {3,234,234} Group order 234 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-67 * z * y^-10 ] T78.38 : Triangle type {4,4,79} Group order 316 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-62 * x * y^-1 * x * y^-1 * z^-15 ] T78.39 : Triangle type {4,4,156} Group order 312 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-61 * x * y^-1 * z^-16 ] T78.40 : Triangle type {4,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, (z^-1 * y)^3 ] T78.41 : Triangle type {4,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y^6, z^2 * y * x * z^-1 * x^-1 ] T78.42 : Triangle type {4,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-2)^2, y * x^-1 * y * x^2 * y^-1 * z * x^-1, x^-1 * z * y^2 * x^-1 * z * y * z^-1 ] T78.43 : Triangle type {4,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, (y * z^-1 * y)^2, z^8, z^2 * y * x * y^-1 * x * z^2 * y^-1 * z ] T78.44 : Triangle type {4,9,36} Group order 252 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, x^-1 * z^2 * y * x * y^-1 * z^-2, y^-9 ] T78.45 : Triangle type {4,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x^-1 * z, y^10 ] T78.46 : Triangle type {4,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^9 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-6 * x * z ] T78.47 : Triangle type {4,53,212} Group order 212 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-21 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T78.48 : Triangle type {4,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^33 * z^-1 * y^5 * z^-1 * y * z^-1 * y^11 * z^-1 ] T78.49 : Triangle type {4,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^12 * y^-6 * z^2 * y^-4 * z^2 ] T78.50 : Triangle type {4,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-22 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T78.51 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z^2 * x^-1 * y^-2, z * y * x^-2 * y * x^-1 * z ] T78.52 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z^2 * y^-1 * x * z * x^-1, y^2 * x^-2 * y * z^-1 * x^-1 ] T78.53 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z * x^-1 * y^-1 * x * y^-1 * z, y^2 * x^-2 * y * x^-1 * y ] T78.54 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z * y^-1 * x * z * x^-1, y^2 * x^-2 * z^2 * x^-1 ] T78.55 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^-2 * z * x^-1 * z, z^-2 * x^-2 * y^2 * x ] T78.56 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^2 * z^2, x * z^-1 * x^-2 * y^2 * z^-1 ] T78.57 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z * y^-2 * x * z * x^-1, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T78.58 : Triangle type {5,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z * x^-1 * y^-1 * x * z * y^-1, y^2 * x^-2 * z * x^-1 * z ] T78.59 : Triangle type {5,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^14 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T78.60 : Triangle type {5,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^12 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T78.61 : Triangle type {6,6,7} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z * y, (y^-1 * x)^3 ] T78.62 : Triangle type {6,6,7} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z * x^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1 ] T78.63 : Triangle type {6,6,7} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * z * y^2, z^3 * y^-1 * x^-1 * z^3 ] T78.64 : Triangle type {6,6,7} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-1 * y * z^-1 * x^2 * z^-1 * y * z^-1, z^3 * y^-1 * x^-1 * z^3 ] T78.65 : Triangle type {6,6,7} Group order 294 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^3 * y^-1 * x^-1 * z^3 ] T78.66 : Triangle type {6,6,7} Group order 294 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^3 * y^-1 * x^-1 * z^3 ] T78.67 : Triangle type {6,6,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^40 ] T78.68 : Triangle type {6,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x * z^-1 * y * z^-1 * y ] T78.69 : Triangle type {6,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, z^-2 * y * x * z^-1 * y, x * z^-1 * x^-2 * z * y^-1 * z^-1 ] T78.70 : Triangle type {6,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^9 * z^-1 * y ] T78.71 : Triangle type {7,27,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T78.72 : Triangle type {7,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T78.73 : Triangle type {7,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7, x^2 * z^-1 * x^2 * z^-3 ] T78.74 : Triangle type {7,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x^-7 ] T78.75 : Triangle type {7,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-7 ] T78.76 : Triangle type {7,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, z^-2 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^9 * z^-1 * y ] T78.77 : Triangle type {7,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-5 ] T78.78 : Triangle type {7,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^5 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T78.79 : Triangle type {7,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T78.80 : Triangle type {8,8,27} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^13 * y * x * z^13 ] T78.81 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z^-1, y * z^-1 * x^-2 * y^2 * x^-1, x * z * x^-2 * y^-1 * z^-2, y^-1 * z * x^-2 * y * x^-1 * y^-1 ] T78.82 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * x * y^-1 * z^-1, y * x^-3 * y * z^-1 * y, z^-1 * x^-3 * z^2 * y^-1 ] T78.83 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-2)^2, z^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y ] T78.84 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, (y * z^-2)^2 ] T78.85 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, (x * y^-1 * x)^2, (x * z^-1 * x)^2, z * y^-2 * x * z * x^-1 ] T78.86 : Triangle type {10,10,10} Group order 220 Chiral action Defining relators: [ x * y * z, (x * y^-1 * x)^2, (x * z^-1 * x)^2, z * x^-1 * y^-1 * x * z * y^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T78.87 : Triangle type {10,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y, y^-1 * z * y^-4 * z * y^-1 * z ] T78.88 : Triangle type {10,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y, y^-1 * z * y^-5 * z * y^-1 ] T78.89 : Triangle type {12,12,32} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x, z^3 * y * x^-1 * y * x^-1 * y * z^-5 * x^-1 * z^5 ] T78.90 : Triangle type {13,14,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-9 * y * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.91 : Triangle type {13,15,15} Group order 195 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x, y^2 * x^-1 * z^2, y^-1 * z * y^-1 * z^2 * y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-2 ] T78.92 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x * y * z^-4, y^4 * z^-3 * y^2 * x^-2 * y^4 ] T78.93 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-2, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.94 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^2 * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.95 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-5 * y^2 * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.96 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.97 : Triangle type {13,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y^2 * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T78.98 : Triangle type {14,14,14} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, (x * y^-3)^2, y^-2 * z * y * x^-1 * y^-1 * z^-1 * y^5 * x * y^-3 ] T78.99 : Triangle type {14,14,14} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^4 * z^-2, (x * y^-2)^2, y * x * y^-1 * z * y^3 * x^-1 * y^-4 * z * y * x * z^-1 * y ] T78.100 : Triangle type {14,14,14} Group order 196 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6 * z^-2, y^3 * x * y^-5 * z^-1 * y^5 ] T78.101 : Triangle type {14,14,14} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y, (x^-4 * z * x^-1 * z)^2, y^-5 * z * x^-1 * z * y^2 * x * y^-2 * z^-1 * x * y^-2 ] T78.102 : Triangle type {14,14,14} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-9 * x * y * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T78.103 : Triangle type {14,14,91} Group order 182 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^-7 * x * z * y^-1 * z^-4 ] T78.104 : Triangle type {14,14,91} Group order 182 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, y^-1 * x * y^-1 * x * y^-1 * z^-4 * x * z * y^-1 * x * z^4 ] T78.105 : Triangle type {14,14,91} Group order 182 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, z^-2 * x * z^5 * y * x^-1 * z * y * z^-3 ] T78.106 : Triangle type {14,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T78.107 : Triangle type {14,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T78.108 : Triangle type {14,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T78.109 : Triangle type {18,18,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T78.110 : Triangle type {21,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, y^6 * z^-2 ] T78.111 : Triangle type {21,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, y * z^-1 * y * z^-1 * y * z^-3 ] T78.112 : Triangle type {21,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, z^-1 * y^4 * z^-3 ] T78.113 : Triangle type {24,28,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T78.114 : Triangle type {24,28,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * z * y^-2, z^-8 * y^2 * z^-4 ] T78.115 : Triangle type {24,42,56} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-2 * y * x^-2 * y * x^-1 * y * x^-8 * z^3 * x^-8 ] T78.116 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T78.117 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x * y^-3 * x * y^-3 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x ] T78.118 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T78.119 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T78.120 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T78.121 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T78.122 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^-1 * y^6 * x^-7 ] T78.123 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-3 * z^3 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T78.124 : Triangle type {27,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^9 * x^-6 * y * x^-1 * y^2 ] T78.125 : Triangle type {28,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * z^-1 * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T78.126 : Triangle type {28,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^3 ] T78.127 : Triangle type {28,28,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^2 * z^-3 ] T78.128 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y^-1 * x)^3, z^2 * y * x^-1 * z * y^-1 ] T78.129 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, y^-1 * x^5 * y^-1 * x * y^-4 ] T78.130 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y^2 * x^-1 * y^-3, x^-6 * y^3 ] T78.131 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, x * z^-2 * x^2 * z^-2 * x * z^-1 * x^5 * z^-1 * x ] T78.132 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z * x^-2 * z^2 ] T78.133 : Triangle type {28,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^4 * y^-4, z^-2 * x^4 * z^-4 ] T78.134 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-24 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T78.135 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T78.136 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T78.137 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T78.138 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^3 * z^-3, y^2 * z^-1 * y^9 ] T78.139 : Triangle type {40,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-10 * x^5 * y^-10 ] T78.140 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-5 * z^2 * y^-8 * x^3 * y^-3 * z^2 * y^-7 ] T78.141 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-6 * x^3 * y^-6 * x * y^-3 ] T78.142 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-18 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T78.143 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-4 * x * z^-4 * x^2 * z^-4 ] T78.144 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T78.145 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^4 ] T78.146 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-9 * z^2 * y^-4 ] T78.147 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T78.148 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^17 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T78.149 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-3 * y * x^-1 * z^3 * x^-3 * z^4 * x^-7 ] T78.150 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-2 * y^5 * x^-3 * z^2 * x^-3 ] T78.151 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T78.152 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-4 * z * y^-1 * z * y^-9 * z * y^-7 ] T78.153 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^2 * z^-1 * y * z^-5 * y^6 ] T78.154 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^5 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T78.155 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^-3 * y^5 * x^-3 * z^2 * x^-4 ] T78.156 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T78.157 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^2 * z^-1 * y^9 ] T78.158 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-36 * z * x^-8 * z^2 * x^-7 ] T78.159 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T78.160 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^-2 * z^4 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T78.161 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^5 * z^-3 * y^2 * x^-2 * y^5 ] T78.162 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^4 * z^-3 * x^7 ] T78.163 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T78.164 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y ] T78.165 : Triangle type {53,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-12 * y^3 * x^-13 ] T78.166 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-25 * z * y^-14 ] T78.167 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-40 * x^4 * y^-10 ] T78.168 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T78.169 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^11 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-3 ] T78.170 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T78.171 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-4 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T78.172 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T78.173 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T78.174 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x * y^-1 * x^6 * y^-7 ] T78.175 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-1 * z^3 * y^-1 * z^4 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T78.176 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T78.177 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^3 * z^-2 * x^4 * y^-4 * x ] T78.178 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-5 * x * z^-4 * x * y * z^-4 ] T78.179 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^5 * z^-3 * y^8 ] T78.180 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y * z^-1 * y * z^-5 * y^6 ] T78.181 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T78.182 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T78.183 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^5 * z^-2 * x^3 * y^-6 * x^3 ] T78.184 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^24 * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T78.185 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^8 * y^-1 * z^4 * x^-1 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T78.186 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-10 * z * y^-2 * z * y^-1 * z * y^-5 * x^2 * y^-11 ] T78.187 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T78.188 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^5 * z^-1 * x * z^-1 * x * z^-4 * x^9 ] T78.189 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T78.190 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T78.191 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^7 * y^-6 ] T78.192 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^3 ] T78.193 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^2 * x^-1 * z^3 * x^-1 * z * x^-9 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T78.194 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^2 * z^-1 * y^9 ] T78.195 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T78.196 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^5 * z^-4 * x * y^-6 * x^2 ] T78.197 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, y^-1 * x^6 * y^-4 * z * y^-2 ] T78.198 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T78.199 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, x^-1 * y^6 * x^-7 ] T78.200 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T78.201 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^4 ] T78.202 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^2 * x^-11 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T78.203 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T78.204 : Triangle type {79,158,158} Group order 158 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^79, y * z^-1 ] T78.205 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x^-2 * y^-1, y^-62 * x * y^-16, x * z^-1 ] T78.206 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^41 * x^-2 * y^10 ] T78.207 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-19 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T78.208 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^6 * x^-1 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y ] T78.209 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^6 * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y * x^-1 * y ] T78.210 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T78.211 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T78.212 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^5 * z^-2 * y^3 * x^-6 * y * x^-1 * y^2 ] T78.213 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^5 * z^-3 * y^2 * x^-6 * y^3 ] T78.214 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x * y^-1 * x^6 * y^-6 * x ] T78.215 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^-2 * y^6 * x^-2 * z^3 * x^-4 ] T78.216 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x * y^-1 * x^11 ] T78.217 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, y^-7 * z^5 * y^-1 * z * y^-1 * z * y^-1 ] T78.218 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T78.219 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-4 * y^6, x^3 * z^-3 * x^7 ] T78.220 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * x^-4 * y^-1 * z^5 * y^-1 * z * y^-1 * z^4 ] T78.221 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x^2 * z^-1 * x * z^-4 * x^6 ] T78.222 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T78.223 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^9 * x^-2 * y^-1 * z^12 ] T78.224 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^-9 * z^2 * y^-4 ] T78.225 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-2, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T78.226 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^-7 * z^5 * y^-1 * z * y^-3 ] T78.227 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^-2 * y^6 * x^-6 * y * x^-1 ] T78.228 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-1 * z^2 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-5 ] T78.229 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^18 * x^-1 * z^13 ] T78.230 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T78.231 : Triangle type {157,157,157} Group order 157 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 ] Genus 79 T79.1 : Triangle type {2,3,12} Group order 1872 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, y * z^-1 * x * z * y * x * z * y * x * z * y^-1 * z^2 * y * x * z^2 * y * z^-1 * x * z^2 * y * z^-2 * x * z * y^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x * z^2 ] T79.2 : Triangle type {2,4,16} Group order 832 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 * y, x * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T79.3 : Triangle type {2,4,16} Group order 832 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T79.4 : Triangle type {2,4,28} Group order 728 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 * y, z * y * x * z^5 * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x ] T79.5 : Triangle type {2,4,30} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-4)^2 ] T79.6 : Triangle type {2,4,160} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y * z^-124 ] T79.7 : Triangle type {2,4,160} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-72 * x * z * y^-1 * z^-6 ] T79.8 : Triangle type {2,4,316} Group order 632 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-34 * x * y^-1 * z^-123 ] T79.9 : Triangle type {2,6,9} Group order 702 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y^-2 * z * y^-1 * z * y * x * z * y^2 * x * y^-2 * z * y^-2 * z^-1 * y * x ] T79.10 : Triangle type {2,6,9} Group order 702 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y^-1 * z * y * x * z * y * x * z * y^-2 * z * y^2 * z^-1 * y * x * y^-1 * z^-1 * y * x ] T79.11 : Triangle type {2,6,9} Group order 702 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * y^-1 * z^-1 * x * y^-2 * z^-1 * x * z * y * z^-1 * y^2 * x * y^-1 * z^-1 * y * x * y^-2 * z^-1 * y ] T79.12 : Triangle type {2,6,12} Group order 624 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, z^2 * y^-1 * z^2 * y^-1 * z^2 * y^-1 * z^2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x ] T79.13 : Triangle type {2,6,21} Group order 546 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * x * z * y^3 * z^-1 * x * y^-1 * z^-1 * x ] T79.14 : Triangle type {2,6,81} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^8 * y * z^-2 * x * z * y * z^-1 * x * z^3 * y^-1 * z^-6 * x * y^-1 * z^-1 * x * z ] T79.15 : Triangle type {2,6,81} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^44 * y * x * z^22 * y^-1 * x * y^-1 * z^-8 * x * z^4 ] T79.16 : Triangle type {2,6,237} Group order 474 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-44 * x * z^21 * y^-1 * x * y^-1 * z^-12 ] T79.17 : Triangle type {2,7,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, (y * z^-3)^2, x * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^-1 ] T79.18 : Triangle type {2,8,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T79.19 : Triangle type {2,8,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T79.20 : Triangle type {2,9,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T79.21 : Triangle type {2,12,18} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y * x * z * y^-3 * z^-1 * y * x * y^-1 * z, y^12, (y * z^-1 * y^4)^2 ] T79.22 : Triangle type {2,12,18} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y^12, z * y * z^-1 * y^4 * x * y^-1 * z^-2 * x ] T79.23 : Triangle type {2,12,18} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y, z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x ] T79.24 : Triangle type {2,12,18} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-4 * z^-1 * y^3, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y * x * z^6 * y * z^-1 * x * z * y^-1 * z^-6 * x * z ] T79.25 : Triangle type {2,12,18} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-1 * x * z * y * z^-1 * x * z * y * z^-4 * x * y^-1 * x * z^4 * y^-1 * z^-2 ] T79.26 : Triangle type {2,12,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^12, z^-3 * x * z^4 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 ] T79.27 : Triangle type {2,12,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-1 * x * z^14 * y * z^-4 * x * z^4 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 ] T79.28 : Triangle type {2,15,30} Group order 390 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * z * y * x * y^-1 * z^-2 * x * z^2, y * z^-2 * y * z^-1 * y^5 * z^-2 * y * z^-1 * y ] T79.29 : Triangle type {2,16,16} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1, (y^-2 * z * y^-1 * z * y^-1 * z * y^-1)^2 ] T79.30 : Triangle type {2,16,16} Group order 416 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-1 * z ] T79.31 : Triangle type {2,28,28} Group order 364 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1, y * z^-1 * y * z^-1 * y^5 * z^-2 * y * z^-1 * y ] T79.32 : Triangle type {2,30,30} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-4 * z^-4 ] T79.33 : Triangle type {2,42,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-2 * z^3 * y^-13 * z^3 ] T79.34 : Triangle type {2,159,318} Group order 318 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^112 * y^-46 ] T79.35 : Triangle type {2,160,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-47 * y^31 * z^-1 ] T79.36 : Triangle type {2,160,160} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^47 * z^-112 * y ] T79.37 : Triangle type {2,316,316} Group order 316 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^46 * z^-111 * y ] T79.38 : Triangle type {3,3,6} Group order 936 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z * y * x^-1 * y * x * z * y * x * z * y * x * z * y ] T79.39 : Triangle type {3,3,42} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x ] T79.40 : Triangle type {3,4,6} Group order 624 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, x^-1 * y^-1 * z^-1 * x * z^2 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x * z^2 * y^-1 * x * z * y^-1 * z^-2 ] T79.41 : Triangle type {3,4,12} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-2 ] T79.42 : Triangle type {3,4,12} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-3 * x^-1 * y^-1 * z^-1 * y ] T79.43 : Triangle type {3,4,12} Group order 468 Chiral action Defining relators: [ x^3, x * y * z, y^4, z * y^-1 * z^-1 * x^-1 * z^2 * y^-1, z * y * x^-1 * y * x^-1 * y * x * z * y^-1 ] T79.44 : Triangle type {3,5,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y^-2 * x * y^-1 * z^2 ] T79.45 : Triangle type {3,6,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^2 * y * x^-1 * z * y^-1 ] T79.46 : Triangle type {3,6,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * z * y^-1 * z^-1, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y^-1 * z^-1 ] T79.47 : Triangle type {3,6,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z ] T79.48 : Triangle type {3,6,28} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * x * y^-1 * x * z * y^-1 * z^-1, y * x * z * y * x * z^3 ] T79.49 : Triangle type {3,8,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-3 * y^2 * z^-3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T79.50 : Triangle type {3,8,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y^2 * z^-1 * x^-1 * z^3, y^2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, y^8 ] T79.51 : Triangle type {3,8,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, z^-2 * y * x^-1 * y^-1 * z * y^-1, y^2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, y^8 ] T79.52 : Triangle type {3,9,9} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x * z * y * x * z * y * x^-1 * y * x * z * y^-1 * z^-1 ] T79.53 : Triangle type {3,9,9} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x * z * y * x * z * y * x^-1 * y * x * z^-1 * x * z^-1 ] T79.54 : Triangle type {3,9,9} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, x * z * y * x * z * y * x^-1 * y^-1 * z * y^-1 * z * y ] T79.55 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^2 * x * z * y * x^-1, (y^-2 * z * y^-1)^3 ] T79.56 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3, z^-1 * y^3 * x^-1 * y^-4 ] T79.57 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y, y^-3 * x * z * y^-1 * z * y^-3 * z^2 * y^-1 ] T79.58 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y^-1 * z * y, x^-1 * y * x^-1 * y * x^-1 * z * y^3 ] T79.59 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T79.60 : Triangle type {3,12,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T79.61 : Triangle type {3,21,21} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-1 * z * y^-1 * x * y^-1 * z * y^-1 ] T79.62 : Triangle type {3,28,84} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-11 * y * z^-2 * y^6 * z^-4 * y^3 * z^-1 ] T79.63 : Triangle type {3,80,240} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-69 * z * y^-8 * z^2 ] T79.64 : Triangle type {3,81,81} Group order 243 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-7 * y * z^-2 * y^2 * z^-1 * y^5 * z^-2 * y * z^-1 * y * z^-2 * y ] T79.65 : Triangle type {3,81,81} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-70 * z * y^-8 * z^2 ] T79.66 : Triangle type {3,237,237} Group order 237 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-68 * z * y^-9 * z ] T79.67 : Triangle type {4,4,8} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * y^-1 * z^-2 * y * z^-1 * y * x * y^-1 * z^-1 * x * z * y * x * z * y ] T79.68 : Triangle type {4,4,8} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * y^-1 * z^-2 * y * z^-1 * y * x * y^-1 * z^-1 * x * z * y * x^-1 * z * y ] T79.69 : Triangle type {4,4,8} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * x^-1 ] T79.70 : Triangle type {4,4,8} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, z * x^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 * x ] T79.71 : Triangle type {4,4,14} Group order 364 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T79.72 : Triangle type {4,4,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z^-2)^2, (y * z^-2)^2 ] T79.73 : Triangle type {4,4,80} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-9 * x^-1 * z * y * x * z * y^-1 * z^-3 ] T79.74 : Triangle type {4,4,80} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^2 * z^2 * y^-1, z^-4 * x^-1 * y^-1 * z^-3 ] T79.75 : Triangle type {4,4,80} Group order 320 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-63 * x * y^-1 * x * y^-1 * z^-15 ] T79.76 : Triangle type {4,4,80} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-27 * x^-1 * z^4 * y * z^-1 * x * y^-1 * z^-6 ] T79.77 : Triangle type {4,4,80} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-27 * x^-1 * z^4 * y * z^-1 * x * z * y * z^-5 ] T79.78 : Triangle type {4,4,80} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^28 * y^-1 * z^-6 * x^-1 * z^5 ] T79.79 : Triangle type {4,4,158} Group order 316 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-62 * x * y^-1 * z^-16 ] T79.80 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * z * x^-1 * y * x * z^-1 * x^-2 * y * x * z^2 ] T79.81 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z^2 ] T79.82 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, y^-1 * z^-1 * x^-1 * z * y * x^-1 * y^-2 * z^-1 * y * x ] T79.83 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T79.84 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3, x * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z^-1 ] T79.85 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y^-1 * z * y ] T79.86 : Triangle type {4,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^6 ] T79.87 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * y * x^-1 * z * y^-1 * z^2, z^-4 * x^-1 * z^3 * y^-1 ] T79.88 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T79.89 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T79.90 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T79.91 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T79.92 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-1 * x^-1 * y * x^-2 * y^-1 * z^-1 * y * x ] T79.93 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^2 * x^-2 * y^-1 * z * x^-1 ] T79.94 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^-2, z^-4 * x^-1 * z^3 * y^-1 ] T79.95 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-5 * x * z^2 * y^-1 * z^-16 ] T79.96 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^5 * y * z^-1 * x^-1 * y * z^-3 * x^-1 * z ] T79.97 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T79.98 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z^2 * y, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T79.99 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-6 * x * z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-11 ] T79.100 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-6 * x * y * z^-2 * x * z^2 * y ] T79.101 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z^-3 * x^-1 * y^-1 * x * z * y * z^-2 ] T79.102 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z^-1 * y)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T79.103 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z * y^2 * x^-1 * z * y^-1 * z, y * x * z^2 * y^-1 * x * z^4 ] T79.104 : Triangle type {4,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1, y^6 ] T79.105 : Triangle type {4,7,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-7, z^3 * y^-1 * x^-1 * z^3, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T79.106 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T79.107 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z * y^2 * x^-1 * z^2 * y^-1 ] T79.108 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1 ] T79.109 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z^-1 * x ] T79.110 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2 ] T79.111 : Triangle type {4,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x * z^-1 * x^-1 ] T79.112 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z * y^-1 * x * y^-1 * x * z^3 ] T79.113 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y * x^-1 * z * y^-2, y^8, z * y^3 * x^-1 * z^4 ] T79.114 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y, y^-1 * z^6 * x * z^5 ] T79.115 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y, y^-1 * z^5 * y^-1 * x^2 * z^5 ] T79.116 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y * z^-2, y^8 ] T79.117 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y * x^-1 * z * y^-2, y^8, y^-1 * z^-1 * y^2 * x^-1 * z^4 ] T79.118 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z * x^-1 * y * x^-2 * z^4 ] T79.119 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, z * y^3 * x^-1 * z^4 ] T79.120 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T79.121 : Triangle type {4,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (x * z * y^-1)^2, z^-2 * x * y^-1 * x * y^-1 * z^-2 ] T79.122 : Triangle type {4,8,64} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^8 * y^-1 * z^-3 * x^-1 * z^4 ] T79.123 : Triangle type {4,8,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-14 * x * y^-1 * z^-7 * x * y^-1 * z^-9 ] T79.124 : Triangle type {4,8,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * z^-4 * x * y^-1 * z^-1 * x^-1 * z^12 ] T79.125 : Triangle type {4,10,20} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^2 * x^-1 * y^-1 * x * z * y^-1 * x ] T79.126 : Triangle type {4,12,21} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^-1 * z^7 * y * x * z^10 * y^-1 * z^-2 ] T79.127 : Triangle type {4,12,60} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-5 * y^2 * z^-1 * y * z^-2 ] T79.128 : Triangle type {4,12,60} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y * z^-2 ] T79.129 : Triangle type {4,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^-1 * z^2 * y * z^-7 ] T79.130 : Triangle type {4,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x * z, z^7 * x^-1 * y^-1 * z^4 ] T79.131 : Triangle type {4,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z, y^-1 * z^10 * y^-1 ] T79.132 : Triangle type {4,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, y * x^-1 * z^9 * y * x^-1 * z^2 * y^-1 * z^-5 * x^-1 * z ] T79.133 : Triangle type {4,15,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * y^-1 * z^2 * y^-2 * z^2 * y^-2 * z^3 ] T79.134 : Triangle type {4,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (z^-1 * y)^3, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T79.135 : Triangle type {4,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T79.136 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, y * z^-3 * y^2 * z^-2 * y * z^-3 * y^4 * z^-1 * y^10 * z^-1 ] T79.137 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y * z^-1 * y * z^-1 * y^3 * z^-3 * y * z^-2 * y^2 * z^-1 * y * z^-2 * y^7 * z^-2 ] T79.138 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1, z^2 * y^-2 * z^3 * y^-1 * z * y^-1 * z^4 ] T79.139 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1, y^-3 * z^5 * y^-3 * z * y^-2 ] T79.140 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^2 * y^-1 * z^4 * y^-1 * x * y^-5 * x ] T79.141 : Triangle type {4,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1, y^-3 * z^5 * y^-1 * z^2 * y^-1 * z * y^-1 ] T79.142 : Triangle type {4,44,55} Group order 220 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, y^2 * z^-1 * y^4 * z^-1 * y * z^-1 * y ] T79.143 : Triangle type {4,44,55} Group order 220 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x * z, y * z^-3 * y * z^-1 * y * z^-3 * y ] T79.144 : Triangle type {4,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^22 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T79.145 : Triangle type {4,106,212} Group order 212 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-24 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T79.146 : Triangle type {6,6,6} Group order 312 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z^-1 * y * x^-1 * y * x^-1 * y^-1 * z * x^-1 * y^-1 * z^-1 * x * z^-1 * x^-1 * z * y * x * z * y ] T79.147 : Triangle type {6,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-1 * x * z^-1 * x^-1 * z * y * x ] T79.148 : Triangle type {6,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T79.149 : Triangle type {6,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T79.150 : Triangle type {6,6,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, y^6, z^-2 * x^-2 * z * x^-1 * y ] T79.151 : Triangle type {6,9,18} Group order 234 Chiral action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, x^-1 * z^2 * y * z^-2 * y * z^-1 * x^-1 * z * y ] T79.152 : Triangle type {6,9,18} Group order 234 Chiral action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, y * z^-1 * x * z * y * z^-1 * y * z^-1 * x * z^2 ] T79.153 : Triangle type {6,12,36} Group order 216 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, z * y * x * y^-1 * x * z^3 ] T79.154 : Triangle type {6,12,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, z * y^-1 * z^-1 * x^-1 * z^3 ] T79.155 : Triangle type {6,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-8 * x * y^-1 * z^-1 * x * z^5 * y^-1 * z^-2 ] T79.156 : Triangle type {6,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^-2 * x * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x * y * z^-1 * x^-1 * z^4 * y * z^-2 ] T79.157 : Triangle type {6,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * x^2 * y^-1 * z * y^-1 ] T79.158 : Triangle type {6,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y ] T79.159 : Triangle type {6,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y * z^-1 * x^-2 * y^-1 * z^-1 * y ] T79.160 : Triangle type {6,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^-1 * z^2 * y^-2 * x^-1 * z * y^-1 * z^2 ] T79.161 : Triangle type {6,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y * x^-2 * y^-2 * x, z * y * x^-2 * y * x * z ] T79.162 : Triangle type {6,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y^8 * z^-1 ] T79.163 : Triangle type {6,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y * z^-7 * y^4 * z^-1 * y * z^-4 ] T79.164 : Triangle type {6,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T79.165 : Triangle type {6,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T79.166 : Triangle type {6,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T79.167 : Triangle type {6,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z^2 * y^-1 * z * y^-2 * z * y^-2 ] T79.168 : Triangle type {6,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T79.169 : Triangle type {6,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-10 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T79.170 : Triangle type {6,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-2 * y * z^-1 * y^3 * z^-3 * y * z^-1 * y^2 * z^-1 ] T79.171 : Triangle type {8,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (y^-1 * x)^3, y^-1 * z^-2 * x * z^2, z * x^-3 * y^-3, z^-2 * x^-2 * y * z^-1 * x ] T79.172 : Triangle type {8,8,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-2)^2, (y * z^-2)^2, z * x^-3 * y^-3, x * z * x^-2 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-1 * x ] T79.173 : Triangle type {8,9,24} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y^2 * z^-2, x^8 ] T79.174 : Triangle type {8,9,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x^8, y^-9 ] T79.175 : Triangle type {8,16,16} Group order 208 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y * x^-1 * z * y * x * z * y^-1 * z ] T79.176 : Triangle type {8,16,16} Group order 208 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, y * x^-1 * z * y * x^-1 * z * y^-1 * z ] T79.177 : Triangle type {8,16,16} Group order 208 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, z^-1 * x^-1 * z * y * x * y^-1 * z^-1 * y ] T79.178 : Triangle type {8,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T79.179 : Triangle type {8,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x^8, z * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T79.180 : Triangle type {8,46,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T79.181 : Triangle type {9,9,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, x^-1 * z * x^-2 * y^-1 * z * x^-1, z^-1 * x^-1 * y * x^-1 * z * x^-1 * y^-1 ] T79.182 : Triangle type {9,9,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, x^-1 * z * x^-2 * y^-1 * z * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T79.183 : Triangle type {9,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, z * y^2 * x^-1 * z * y^-1 * z, x^-9, y^3 * z^-1 * x^-1 * y^-3 * z^-1 ] T79.184 : Triangle type {9,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (y * z^-2)^2, x^-1 * z * y * x^-1 * y * x * z ] T79.185 : Triangle type {9,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, z * y^2 * x^-1 * z * y^-1 * z, z^-1 * y^4 * z^-3, x^-9 ] T79.186 : Triangle type {9,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (x^-1 * z * y)^2, x^-9 ] T79.187 : Triangle type {9,21,63} Group order 189 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-3 * z^3 * y^-2 * z * y^-6 * z * y^-2 * z * y^-2 ] T79.188 : Triangle type {9,21,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T79.189 : Triangle type {9,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^2 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T79.190 : Triangle type {9,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-6 * z^5 * y^-6 ] T79.191 : Triangle type {10,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^4 * z^-1 * y * z^-5 * y * x^-1 * y^6 ] T79.192 : Triangle type {12,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z * y * z^-2 * x^-1 * z^4 ] T79.193 : Triangle type {12,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-3 * x^-1 * y^-1 * x * z * y^-1 * z^-2 ] T79.194 : Triangle type {12,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-2 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-3 * x * z * y^-1 * x * y^-1 * z^-3 ] T79.195 : Triangle type {12,12,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T79.196 : Triangle type {12,16,24} Group order 192 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, x^-2 * z * x^-1 * z * x^-6 * y^-1 * z ] T79.197 : Triangle type {12,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^2 * z^-2, x^-1 * z * y^3 * x * y^-3 * z^-1 ] T79.198 : Triangle type {12,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^4 * x^-1 * y^-2 * z^-1 * y ] T79.199 : Triangle type {12,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^3, z^-1 * x * z^-1 * x^3 * z^-1 * x * z^-2 ] T79.200 : Triangle type {12,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^2 * z^-1 * y * z^-5 * y^6 ] T79.201 : Triangle type {12,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, z * x^-1 * z * x^-1 * y^-1 * z^2, x^-1 * y^3 * x^-1 * y * x^-3 * y * x^-1 ] T79.202 : Triangle type {12,36,45} Group order 180 Chiral action Defining relators: [ x * y * z, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z * x^-3 * z * x^-1 * z ] T79.203 : Triangle type {12,36,45} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x * z^-2 * x^3 * z^-3 ] T79.204 : Triangle type {12,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-2 * x^3 * y^-1 * z^-2 ] T79.205 : Triangle type {12,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z^-3 * x^3 * z^-3 * x ] T79.206 : Triangle type {15,15,15} Group order 195 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y^-1, y^2 * x^-3 * y^4 ] T79.207 : Triangle type {15,20,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x * y^-2 * x^8 * y^-6 ] T79.208 : Triangle type {15,20,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-2 * y * z^-1 * y^2 * x^-1 * y * x^-1 * y^3 ] T79.209 : Triangle type {15,20,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, z^-3 * y * x^2 * z^-4 ] T79.210 : Triangle type {16,22,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^2 * z^-4, y^-2 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T79.211 : Triangle type {21,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^11 * y^-6 * x * y^-1 * x * y^-1 * x^2 ] T79.212 : Triangle type {21,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T79.213 : Triangle type {21,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^3 * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T79.214 : Triangle type {21,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 ] T79.215 : Triangle type {21,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^4 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T79.216 : Triangle type {24,42,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, z^-4 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T79.217 : Triangle type {24,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, y^-5 * x^5 * y^-6 * x * y^-3 ] T79.218 : Triangle type {24,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 ] T79.219 : Triangle type {28,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T79.220 : Triangle type {28,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T79.221 : Triangle type {28,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-3 ] T79.222 : Triangle type {28,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^-4 * x^4 * y^-8 ] T79.223 : Triangle type {28,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-7 * y * x^-1 * y * x^-1 * y * x^-11 * y * x^-1 * y * x^-1 * y * x^-2 ] T79.224 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-3 * y^6 * x^-4 * z * x^-4 ] T79.225 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^2 * z^-1 * y * z^-5 * y^6 ] T79.226 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^19 * y^-1 * x^8 * y^-2 * x * y^-1 * x * y^-1 * x ] T79.227 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-6 * x^4 * y^-6 * x^2 * y^-3 ] T79.228 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T79.229 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, x^3 * z^-1 * x * z^-4 * x^6 ] T79.230 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^5 * z^-4 * y * x^-1 * y^5 ] T79.231 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T79.232 : Triangle type {33,55,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T79.233 : Triangle type {42,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, z^-1 * x^3 * z^-2, y^-3 * x^2 * y^-3 * x * y^-3 ] T79.234 : Triangle type {42,42,42} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, z^-2 * x^2 * y^-1 * x, z^-1 * x^-3 * y * z^-1 * y ] T79.235 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T79.236 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^19 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T79.237 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, y^-2 * x^6 * y^-7 ] T79.238 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T79.239 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^8 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * y^-2 * x^9 * z^-1 * x^2 ] T79.240 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-10 * y * z^-4 ] T79.241 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-17 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T79.242 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, x^8 * y^-6 * x^2 ] T79.243 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, (y^-5 * x * y^-1)^2 ] T79.244 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^49 * y^-1 * x * y^-1 * x * y^-1 * x ] T79.245 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^10 * y^-6 * x^4 ] T79.246 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T79.247 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T79.248 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^-2 * y^5 * x^-3 * z^2 * x^-3 ] T79.249 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T79.250 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^4 * z^-3 * x^7 ] T79.251 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^10 * x^-1 * y^-1 * z^5 * y^-1 * z * y^-1 * z^5 ] T79.252 : Triangle type {54,81,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-13 * x * y^-1 * x * y^-1 ] T79.253 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^4 ] T79.254 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T79.255 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^5 * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T79.256 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T79.257 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z * x^-5 * z * x^-2 * z * x^-1 * z^5 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T79.258 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-48 * x^2 * z^-4 ] T79.259 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-6, z^-9 * y * z^-4 ] T79.260 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-6, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T79.261 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^6 * y^-1 * x^12 * y^-1 * x^61, y * z^-1 ] T79.262 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^27 * y^-1 * x^8 * y^-1 * x^4 ] T79.263 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^8 * z^-3 * x^6 * y^-1 * x^4 ] T79.264 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T79.265 : Triangle type {80,160,160} Group order 160 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T79.266 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x^-2 * y^-1, y^-63 * x * y^-16, x * z^-1 ] T79.267 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^3 * x^-1 * y^6 * x^-6 * y^4 ] T79.268 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^5 * z^-4 * y * x^-3 * y^4 ] T79.269 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^8 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T79.270 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x^3 * z^-2 * x^8 ] T79.271 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T79.272 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T79.273 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-2 * x^6 * y^-7 ] T79.274 : Triangle type {159,159,159} Group order 159 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-6 ] Genus 80 T80.1 : Triangle type {2,4,162} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-36 * x * y * z^-125 ] T80.2 : Triangle type {2,4,320} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y^-1 * z^-124 ] T80.3 : Triangle type {2,6,6} Group order 948 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x * z * y^-1 * z * y^-1 * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-2 * y * z^-1 * y * z^-2 * y ] T80.4 : Triangle type {2,6,82} Group order 492 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-82 ] T80.5 : Triangle type {2,6,240} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-44 * x * z^22 * y^-1 * x * z^7 * y^-1 * z^-5 ] T80.6 : Triangle type {2,8,108} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^34 * y * x * y^-1 * z^-7 * x * z^11 ] T80.7 : Triangle type {2,10,42} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^27 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z^6 ] T80.8 : Triangle type {2,12,34} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^19 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z^6 ] T80.9 : Triangle type {2,12,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-2 * x * z^9 * y * x * z^3 * y^-1 * z^-16 ] T80.10 : Triangle type {2,18,22} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^3 * x * y^-1 * z * y * x * y^-10 * z^-1 * y, z^-3 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-3 ] T80.11 : Triangle type {2,18,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^7 * y * z^-4 * x * z^2 * y^-1 * z^-4 ] T80.12 : Triangle type {2,20,90} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^9 * y * z^-2 * x * z^4 * y^-1 * z^-1 * x ] T80.13 : Triangle type {2,22,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-9 * z^4 * y^-5 * z^4 ] T80.14 : Triangle type {2,34,170} Group order 340 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y^-20 * z^4 * y^-5 * z^4 * y^-1 ] T80.15 : Triangle type {2,42,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-6 * y * z^-1 * y^10 * z^-4 * y^18 * z^-1 ] T80.16 : Triangle type {2,56,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y * z^-1 * y^6 * z^-5 * y ] T80.17 : Triangle type {2,66,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, z^3 * y^-16 * z^4 * y^-5 * z^3 * y^-1 * z ] T80.18 : Triangle type {2,82,164} Group order 328 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-48 * y^33 ] T80.19 : Triangle type {2,161,322} Group order 322 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^113 * y^-46 * z ] T80.20 : Triangle type {2,162,162} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^48 * z^-114 ] T80.21 : Triangle type {2,320,320} Group order 320 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^47 * z^-113 ] T80.22 : Triangle type {3,6,6} Group order 474 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z^2 * y^-2 * z^2 * y^-1 * z * y^-1 * z ] T80.23 : Triangle type {3,6,6} Group order 474 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * z * y^-1 * z * y * x * z * y * x^-1 * y * x * z * y * x * z * y * x^-1 ] T80.24 : Triangle type {3,8,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y^8, z^2 * y * z^-1 * x^-1 * z^3 ] T80.25 : Triangle type {3,8,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z * y^2 * x^-1 * z * y^-1 * z, y^8, y * z^-1 * y^2 * x * y^-1 * z^-1 * y ] T80.26 : Triangle type {3,22,44} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-1 ] T80.27 : Triangle type {3,82,82} Group order 246 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^13 * z^-68 * y ] T80.28 : Triangle type {3,240,240} Group order 240 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-69 * z * y^-10 ] T80.29 : Triangle type {4,4,81} Group order 324 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-64 * x * y^-1 * x * y^-1 * z^-15 ] T80.30 : Triangle type {4,4,160} Group order 320 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-63 * x * y^-1 * z^-16 ] T80.31 : Triangle type {4,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, y * x^-1 * z^9 * y * x^-1 * z^2 * y^-1 * z^-5 * x * z ] T80.32 : Triangle type {4,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y * z^-1 * y * x * z * y^2, z^3 * y * x * z^2 * y^-1 ] T80.33 : Triangle type {4,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^5 * x^-1 * y^-3 * z * y, x^-1 * z^6 * y * x^-1 * y^-1 * x * z * y * z^-2 ] T80.34 : Triangle type {4,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1 * x * z * y^-1 * z^-2, z^2 * y^-1 * z^4 * y^-1 * x * z * y^-1 * z^4 ] T80.35 : Triangle type {4,44,110} Group order 220 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x * z, z^-4 * y * z^-2 * y * z^-3 ] T80.36 : Triangle type {4,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^32 * z^-1 * y^5 * z^-1 * y * z^-1 * y^12 ] T80.37 : Triangle type {5,41,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^25 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T80.38 : Triangle type {5,42,42} Group order 210 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-1 * z^7 * y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-8 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-7 ] T80.39 : Triangle type {5,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^14 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T80.40 : Triangle type {5,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^16 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T80.41 : Triangle type {6,6,41} Group order 246 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-32 * x * y^-1 * x^-1 * y * z^-7 ] T80.42 : Triangle type {6,6,120} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-26 * x^-1 * z^6 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T80.43 : Triangle type {6,8,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z^-1 * x * z^3 * y * z^-2 * x^-1 * y^-1 * z^-2 ] T80.44 : Triangle type {6,14,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-3 * x * z^3 ] T80.45 : Triangle type {6,15,70} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, z^2 * y^-1 * x * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1 ] T80.46 : Triangle type {6,34,34} Group order 204 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z * y^-1 * z * y^-4 * z * y^-10 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-6 ] T80.47 : Triangle type {6,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T80.48 : Triangle type {8,8,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^13 * y * x^-1 * z^4 * y * z^-1 * x^-1 * z^7 ] T80.49 : Triangle type {8,92,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-5 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T80.50 : Triangle type {8,92,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T80.51 : Triangle type {9,22,22} Group order 198 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^-9 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-2 * z ] T80.52 : Triangle type {9,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-11 * y^6 * z^-1 * y * z^-1 ] T80.53 : Triangle type {9,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T80.54 : Triangle type {10,10,21} Group order 210 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^5 * y^-1 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^4 ] T80.55 : Triangle type {10,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^2 * y^-6 * z^10 ] T80.56 : Triangle type {10,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-8 * z^4 * y^-6 ] T80.57 : Triangle type {11,17,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T80.58 : Triangle type {11,18,18} Group order 198 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-11, y^-7 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^2 ] T80.59 : Triangle type {11,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-1 * y * z^-5 * y^3 * z^-3 ] T80.60 : Triangle type {11,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-4 * y * z^-5 * y^2 * z^-4 ] T80.61 : Triangle type {11,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T80.62 : Triangle type {11,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^-7 * z^4 * y^-5 ] T80.63 : Triangle type {11,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T80.64 : Triangle type {12,12,17} Group order 204 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^2 * y * x * z^2, (x^-4 * y^2)^2 ] T80.65 : Triangle type {12,12,17} Group order 204 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^3 * y^-1 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^2 ] T80.66 : Triangle type {12,12,96} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-1 * x^-1 * z * y * z^-4 * x^-1 * z * y^-1 * x * z^4 ] T80.67 : Triangle type {12,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x * z^-2 * x^2 * z^-2 * x^5 * y^-1 * x ] T80.68 : Triangle type {12,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^2, y^-3 * x^2 * y^-3 ] T80.69 : Triangle type {15,36,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * z * x^-2 * y * z^-1 * x^-1, y^2 * z^-4 * y^6 ] T80.70 : Triangle type {15,36,36} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, z^-3 * y^8 * z^-1 ] T80.71 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T80.72 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T80.73 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T80.74 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^7 * z^-4 * x^2 * y^-4 * x^4 ] T80.75 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-1 * y * x^-1 * y^6 * x^-6 * y^3 ] T80.76 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, y^-3 * x^4 * y^-7 ] T80.77 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-3 * x^5 * y^-6 * x * y^-1 ] T80.78 : Triangle type {17,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^7 * z^-4 * x^2 * y^-4 * x^4 ] T80.79 : Triangle type {18,18,90} Group order 180 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8 * y^-2, z * y * z^-4 * x * z^4 ] T80.80 : Triangle type {18,18,90} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x * z^-2 * x^2 * z^-2 * y * z^-1, z^-5 * x^-1 * y * z^-4 ] T80.81 : Triangle type {20,20,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, y^-3 * x^2 * y^-3, z^3 * y * z^-1 * x * z^4 ] T80.82 : Triangle type {20,20,45} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * x * z^-3 * y * z^-1 * x * z^-2 * y * z^-1, x^-1 * y * z^-3 * x^-1 * z * y * z^-3 ] T80.83 : Triangle type {21,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T80.84 : Triangle type {21,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T80.85 : Triangle type {21,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-5 * y * x^-8 * z * x^-7 ] T80.86 : Triangle type {22,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-2 * x^-1 * z^4, y^6 * x^-2 * y^4 ] T80.87 : Triangle type {22,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-3 * x^2 * y^-3, z^2 * y * z^-1 * x^-1 * z^4 ] T80.88 : Triangle type {22,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-3)^2, z^3 * y * x^-1 * z^4 ] T80.89 : Triangle type {22,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T80.90 : Triangle type {22,22,88} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, x * z^-1 * x^2 * z^-3 * x^3 * z^-4 ] T80.91 : Triangle type {24,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x * z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T80.92 : Triangle type {24,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-4 * y^6 ] T80.93 : Triangle type {28,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3, x * y^-1 * x^4 * y^-1 * x * y^-4 ] T80.94 : Triangle type {28,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x * z^-2 * x^2 * z^-2 * x * z^-1 * x^6 * z^-1 ] T80.95 : Triangle type {28,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x^3 * y^-4, z^-1 * x * z^-1 * x^3 * z^-4 ] T80.96 : Triangle type {33,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^6 * z^-3 * y^3 * z^-4 * y^4 ] T80.97 : Triangle type {33,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^6 ] T80.98 : Triangle type {33,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-7 ] T80.99 : Triangle type {33,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^15 * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T80.100 : Triangle type {33,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-4 * z^4 * x^-5 * z * x^-5 ] T80.101 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x * z^3 * y^-1 * x * y^-5 ] T80.102 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, x * y^-1 * x * y^-1 * x * z^2 * y^-1 ] T80.103 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * y * z^-2, (x * z^-3)^2 ] T80.104 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z^2 * y, z^3 * y^-2 * x^-1 * y^-1 * z^3 ] T80.105 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x^3 * y^-1 * z^-2 ] T80.106 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y^-1 * x * z^2, x^5 * z^-1 * x * z^-1 ] T80.107 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^2 * z^-1 * x^7 * z^-1 * x ] T80.108 : Triangle type {34,34,85} Group order 170 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * x^-1 * z^3 * x^-4 * z^6 * y^-1 * z^3 ] T80.109 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T80.110 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x * y^-1 * x^6 * y^-7 ] T80.111 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-4 * y * z^-5 * y^2 * z^-4 ] T80.112 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^3 * y^-1 * z * y^-3 * z^12 ] T80.113 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y ] T80.114 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-7 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T80.115 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-14 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-7 ] T80.116 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-1 * x^6 * y^-4 * z * y^-2 ] T80.117 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^8 * z^-3 * x^8 * z^-1 * x^2 ] T80.118 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^4 * z^-4 * x^6 ] T80.119 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T80.120 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T80.121 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T80.122 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^23 * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 * x^2 ] T80.123 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^5 * z^-4 * x^6 ] T80.124 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^4 * y^-5 * x, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T80.125 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^9 * x^-6 * y * x^-1 * y^2 ] T80.126 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-11 * x^6 * y^-9 ] T80.127 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-6 * z * y^-3 * x^3 * y^-3 * z * y^-6 ] T80.128 : Triangle type {41,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-25 * y * x^-8 * z * x^-7 ] T80.129 : Triangle type {42,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^5 * z^-1 * y^4 * x^-1 * y * z^-2 * y^9 ] T80.130 : Triangle type {42,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^7 * z^-1 * x * z^-1, y^-4 * x^2 * y^-4 ] T80.131 : Triangle type {42,42,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-5 * y * z^-1 * y * z^-2 * x * z^-3 * x * z^-1 * y * z^-5 * y * z^-1 ] T80.132 : Triangle type {42,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^-4 * z * x^-7 * z^3 ] T80.133 : Triangle type {42,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, x * z^-5 * x^2 * z^-1 * x * z^-2 ] T80.134 : Triangle type {42,56,56} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^4 * z^-3, y * x^-4 * y * x^-1 * y^2 ] T80.135 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^81, y * z^-1 ] T80.136 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^15 * y^-3 * x^6 * z^-1 * x^4 ] T80.137 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T80.138 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-1 * x^6 * y^-4 * z * y^-2 ] T80.139 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T80.140 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-4 * x * z^-4 * x^2 * z^-4 ] T80.141 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y^6, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T80.142 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T80.143 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T80.144 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^6 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T80.145 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^5 * z^-2 * x^3 * y^-6 * x^3 ] T80.146 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^27 * x^-2 * y^-1 * z^12 ] T80.147 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-9 * y * z^-4 ] T80.148 : Triangle type {81,162,162} Group order 162 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T80.149 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^28 * y^-2 * z^12 ] T80.150 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * z^-7 ] T80.151 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T80.152 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-4 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T80.153 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T80.154 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, x^-1 * y^6 * x^-7 ] T80.155 : Triangle type {82,82,82} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^6 * z^-3 * x^2 * y^-6 * x * y^-1 * x^2 ] T80.156 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x^-2 * y^-1, y^-63 * x * y^-17, x * z^-1 ] T80.157 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-4 * y * x^-5 * y^2 ] T80.158 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T80.159 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T80.160 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-42 * x * y^-11 ] T80.161 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^3 * z^-1 * x^9 ] T80.162 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^-3 * y^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T80.163 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10 * y^-1, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T80.164 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * z, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T80.165 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y^3 * z^-2 * y^8 ] T80.166 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-22 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T80.167 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-5 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T80.168 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, x^-3 * z * x^-2 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T80.169 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^2 * z^-4, x^-3 * y^5 * x^-8 ] T80.170 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T80.171 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-9 * y^2 * z^-4 ] T80.172 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^11 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T80.173 : Triangle type {161,161,161} Group order 161 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^14 * x^-1 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] Genus 81 T81.1 : Triangle type {2,3,16} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z * y * x * z * y * x * z^2 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z^3 * y * x * z^2 * y^2 * z^-3 * x * y^-1 * z^-1, z^8 * y * z^-1 * x^2 * y^-1 * z^-1 * x * z^7 ] T81.2 : Triangle type {2,3,16} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * x * z^2 * y * x * z^2 * y^2 * z^-4 * x * z ] T81.3 : Triangle type {2,3,16} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z, z^-2 * x * z^3 * y * x * z^2 * y^2 * z^-3 * x * y^-1 * z^-1 ] T81.4 : Triangle type {2,3,16} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, z^3 * y * x * z * y * z^-2 * x * z * y * x * z^2 * y^2 * x * z^5 ] T81.5 : Triangle type {2,3,22} Group order 1320 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y^2 * z^-2 * x * z * y^-1 * z^-1, z * y * z^-2 * x * z^3 * y * x * z * y * z * y^-1 * z^-1 * x * z^2 ] T81.6 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z^-1 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T81.7 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y * x * y^-1 * z^-3 * x * z^2 ] T81.8 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z, z^-1 * y * x * z^2 * y * x * y * x * y^-1 * z^2 * y^-1 * z^-2 ] T81.9 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * x * z * y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y ] T81.10 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y ] T81.11 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T81.12 : Triangle type {2,4,8} Group order 1280 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * y * x * z ] T81.13 : Triangle type {2,4,9} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-4 * x * y * z^-4, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T81.14 : Triangle type {2,4,12} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, (y * z^-2)^4, z^12, y^-1 * z * y * z^-2 * x * z * y^-2 * z^-3 * x * z ] T81.15 : Triangle type {2,4,12} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, z * y^-1 * z * y^-1 * z * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x ] T81.16 : Triangle type {2,4,12} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-1)^6, (y * z^-3 * y * z^-1)^2 ] T81.17 : Triangle type {2,4,12} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^3 * y^-1 * z * y^-1 * z^-2 * x * z * y^-1 ] T81.18 : Triangle type {2,4,20} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2, z^-2 * x * z^7 * y * x * z^2 * y^-1 * z^-7 ] T81.19 : Triangle type {2,4,20} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-12 * x * y * z^-7 ] T81.20 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * z * y^2 * z^-4 * y, (y * z^-2)^4, x * z * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T81.21 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-2)^4, (y * z^-5)^2, z^2 * y * z^-1 * x * z^2 * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T81.22 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * z * y^2 * z^-4 * y, z^-6 * x * z^6 * y * z^-11 ] T81.23 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * z * y^2 * z^-2 * x * z * y^-1, z * y * z^-2 * y * x * y^-1 * z^-2 * x * y^-1 * z, (y * z^-2)^4, x * z * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T81.24 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T81.25 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T81.26 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x, z^-4 * x * z^5 * y^-1 * z^-2, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T81.27 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-4 * x * z^5 * y^-1 * z^-2, x * z * y^-1 * z * y * z^-1 * y * z^-3 * x * y^-1 * z^-2 ] T81.28 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-3 * x * z * y * z^-2 * x * z^7 * y * x * y^-1 * x * y^-1 * z^-7 ] T81.29 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^7 * y * z^-3 * x * z^5 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T81.30 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, z^-8 * x * z^4 * y * x * z^3 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-2 ] T81.31 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^-1 * z^-3 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T81.32 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^-1 * z^-3 * y * z^-1, z^2 * y * x * z^7 * y^-1 * z^-1 * x ] T81.33 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z * y^-1 * z^-3 * y * z^-1, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T81.34 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, z^-3 * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T81.35 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-2)^4, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T81.36 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * x * z * y^-1 * z * y * x * y^-1 * z^-2 * y, z^-1 * x * z^12 * y^-1 * z^-7 * x * y^-1 * z^-2 ] T81.37 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-2 * z^-4 * y, z^-3 * x * z^8 * y * z^-12 ] T81.38 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z^3 * y * x * z^3 * y * z^-2 * x * z^2 * y * z^-3 * x * z^5 * y^-1 * z^-2 * x ] T81.39 : Triangle type {2,4,24} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T81.40 : Triangle type {2,4,36} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-11 * x * z^12 * y * z^-1 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-3 ] T81.41 : Triangle type {2,4,44} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-25 * x * z^11 * y * x * z^2 * y^-1 * z^-4 ] T81.42 : Triangle type {2,4,68} Group order 680 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-13 * x * z^9 * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-1 ] T81.43 : Triangle type {2,4,84} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-67 * x * z^8 * y * x * z * y^-1 * z^-6 ] T81.44 : Triangle type {2,4,84} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-25 * x * z^7 * y^-1 * x * y^-1 * z^-8 ] T81.45 : Triangle type {2,4,84} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-68 * x * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T81.46 : Triangle type {2,4,164} Group order 656 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y * z^-126 ] T81.47 : Triangle type {2,4,324} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-36 * x * y^-1 * z^-125 ] T81.48 : Triangle type {2,5,6} Group order 1200 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T81.49 : Triangle type {2,5,10} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.50 : Triangle type {2,5,20} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y ] T81.51 : Triangle type {2,5,30} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z^2 * y^-1 * z^-3, x * y^-1 * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-2 * z^-1 * y ] T81.52 : Triangle type {2,5,30} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, y^-1 * z * y^2 * z^-3 * y * x * y^-1 * z^3 ] T81.53 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^3 * z^-1 * x * y^-1 * z^-1 * y, y * x * z * y * z^-1 * y^2 * x * y^-1 * z^-2 * y ] T81.54 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^8, z * y * x * z * y^2 * x * y^-1 * z^2, (y * z^-1 * y)^4, z^-2 * x * z^2 * y^2 * x * z * y^-2 * z^-1 ] T81.55 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, (y * z^-1 * y)^4 ] T81.56 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, y^-1 * z * y * z^-1 * x * y^-1 * z * y^-2 * z * y^-2 * z ] T81.57 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T81.58 : Triangle type {2,6,8} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T81.59 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-3 * y^2 ] T81.60 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, (y * z^-1 * y)^4 ] T81.61 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, z^-1 * y * z^-3 * y^2 * z^-3 * y * z^-1 ] T81.62 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z^8 ] T81.63 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-3 * z^-2 * y^2, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2 ] T81.64 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T81.65 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2 ] T81.66 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y, (z^-1 * y^2 * z^-1)^3 ] T81.67 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-1 * y)^4 ] T81.68 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, z * y * x * z * y^2 * z^-2 * y * x, (y * z^-1 * y)^4 ] T81.69 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^3 * z^-1 * x * y^-1 * z^-1 * y, (y * z^-1 * y)^4 ] T81.70 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z, (y * z^-1 * y)^4 ] T81.71 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, (y * z^-1 * y)^4 ] T81.72 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, y^-1 * z * y * z^-1 * x * y^-1 * z * y^-2 * z * y^-2 * z ] T81.73 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z, y^-1 * z * y * z^-1 * x * y^-1 * z * y^-2 * z * y^-2 * z ] T81.74 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, z * y * x * z * y^3 * z^-1 * x * z * y^-2, (y * z^-1 * y)^4 ] T81.75 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y^-2 * z^2 * y^-2 * z^-1 * x * y^-1 * z^2 ] T81.76 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^-2 * z^2 * y^-2 * z^-1 * x * y^-1 * z^2 ] T81.77 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.78 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.79 : Triangle type {2,6,8} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^8, (z * y^-1 * z)^3, y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * x * z ] T81.80 : Triangle type {2,6,11} Group order 660 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-5 * x * y * z^-5 ] T81.81 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^8, z^-1 * y * z^-1 * y^3 * z^-3 * y ] T81.82 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, z^-1 * y^2 * x * y^-2 * z^2 * y^-1 * z^-2 ] T81.83 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^8, z^-3 * y^3 * z^-2 * y^2 ] T81.84 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * z^-1 ] T81.85 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * x ] T81.86 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-2 * z^-1 * x ] T81.87 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T81.88 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-2 * x * y^-2 * z^-3 * y, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T81.89 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-2 * x * y^-2 * z^-3 * y, z^-1 * x * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-2 * z^-1 * y ] T81.90 : Triangle type {2,8,8} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z^2 * y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x ] T81.91 : Triangle type {2,8,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T81.92 : Triangle type {2,8,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T81.93 : Triangle type {2,8,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, x * z * y^-3 * z^-1 * y^2 * z^-1 ] T81.94 : Triangle type {2,8,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, x * z * y^-3 * z^-1 * y^2 * z^-1, x * z^3 * y^-1 * z^-4 ] T81.95 : Triangle type {2,8,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y^-1 * z * y^-2 * z^-2 * x * z ] T81.96 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, x * z^2 * y * z^-4 * x * z^5 * y^-1 * z^-3 ] T81.97 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-3 * x * z^2 * y * z^-3 * x * z^5 * y^-1 * z^-1 ] T81.98 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-4 * x * z^3 * y * z^-7 * x * y^-1 ] T81.99 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, z^-3 * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 ] T81.100 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^-2 * x * z^4 * y * z^-9 ] T81.101 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z^-3 * x * y^-1 * z^-3 ] T81.102 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, z^-3 * x * z * y * z^-7 * y^2 * z^-4 ] T81.103 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-2 * x * y^-2 * z^-3 * y, z^-16 ] T81.104 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-4 * z^-2 * y^3, z^-2 * x * z * y^3 * z^-1 * x * z * y^-1 * z^-1 ] T81.105 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * x * z * y * x * y^-1 * z^-4 ] T81.106 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * x * z * y^-2 * z^5 ] T81.107 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T81.108 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, x * z * y * x * z * y * x * y^-1 * z^-2 * y^2 * z^-1 ] T81.109 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-2 * x * y^-3 * z^-5 ] T81.110 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^3 * y^-3 * z^-3 * x * z ] T81.111 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-3 * z^-3 * x * z ] T81.112 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^3 * z^-2 * x * z^2 ] T81.113 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-2 * x * y^-3 * z^-5 ] T81.114 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.115 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, (y * z^-3)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z * y^-4 * z^-2 * y^3, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T81.116 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.117 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, x * z^3 * y^-1 * z^-4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T81.118 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T81.119 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, x * z^3 * y^-1 * z^-4 ] T81.120 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T81.121 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^3 * y^-1 * z^-4 ] T81.122 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z^3 * y^-1 * z^-4, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2 ] T81.123 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z * y * z^-2 * x * y^-1 * z^-3 * x, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.124 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-3 * z^-3 * x * z ] T81.125 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.126 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-2 * x * y^-3 * z^-5 ] T81.127 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-2 * z^-3 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.128 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-2 * z^-3 * y, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T81.129 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4, x * z * y * x * z * y * x * y^-1 * z^-2 * y^2 * z^-1 ] T81.130 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T81.131 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T81.132 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^-2 * x * y^-3 * z^-5, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.133 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-2 * x * y^-3 * z^-5, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.134 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, y * z^-1 * x * z * y^2 * x * y^-1 * z^-2, z^-2 * x * y^-3 * z^-5, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.135 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-2 * x * y^-3 * z^-5, x * z^3 * y^-2 * z^3 * y^-1 * z^-1 ] T81.136 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-1 * y * x * z * y^-2 * z^-5 ] T81.137 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, x * y^-1 * z * y^-1 * z^3 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T81.138 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T81.139 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z^2 * y^-2 * z^-5 ] T81.140 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, z^4 * y^-1 * z * y^2 * x * z * y^-1 * z * y^-1 ] T81.141 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2, x * y^-1 * z^2 * y^-2 * z^-5 ] T81.142 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T81.143 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-3)^2 ] T81.144 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T81.145 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-3)^2 ] T81.146 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 ] T81.147 : Triangle type {2,8,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, x * y^-1 * z * y^-1 * z^3 * y^2 * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-1 * y ] T81.148 : Triangle type {2,8,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-5 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T81.149 : Triangle type {2,8,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z^-5 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T81.150 : Triangle type {2,8,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-4 ] T81.151 : Triangle type {2,8,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z * y^2 * x * y^-1 * z^-2 ] T81.152 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^36 * y * z^-9 * x * z^10 ] T81.153 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-18 * x * z^21 * y * z^-2 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T81.154 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^5 * y * z^-8 * x * y^-1 * z^-12 ] T81.155 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^5 * y * x * z^6 * y * z^-2 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^2 ] T81.156 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^7 * y * z^-8 * x * y^-1 * z^-11 * x ] T81.157 : Triangle type {2,8,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, x * z^4 * y * z^-9 * x * y^-1 * x * y^-1 * z^-12 ] T81.158 : Triangle type {2,8,216} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^38 * y * z^-2 * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-3 * x * z ] T81.159 : Triangle type {2,8,216} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^40 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-3 * x * z ] T81.160 : Triangle type {2,9,9} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-9, (y^-2 * z)^3, (z * y^-1 * z)^3 ] T81.161 : Triangle type {2,10,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y^10, (y * z^-2 * y^2)^2, (y * z^-1 * y * z^-1 * y)^2, (y * z^-3 * y)^2, y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T81.162 : Triangle type {2,12,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * x * z * y^2 * x * z * y^-1 * z, x * z * y^-4 * z^-1 * y * z^-3, y^12 ] T81.163 : Triangle type {2,12,12} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, y^-1 * z * y^2 * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T81.164 : Triangle type {2,12,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-3 * z^-2 * y^2, y^-1 * z^2 * y^-2 * z^-3 * x ] T81.165 : Triangle type {2,12,12} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z * y^3 * x * y^-1 * z^-1 * y ] T81.166 : Triangle type {2,14,189} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-2 * z^4 * y^-1)^2, z^14 * y * z^-4 * x * y^-1 * z^-5 * x * z^2 ] T81.167 : Triangle type {2,16,48} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^-5 * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T81.168 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-2 * y * z^-1 * y^2 * z^-1 * y^4 * z^-1 * y * z^-1 * y ] T81.169 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, y^-2 * z * y^-3 * z^-1 * x * z^3 ] T81.170 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, (y * z^-1)^4 ] T81.171 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, x * y^-4 * z^-1 * y^3, x * z^2 * y^-2 * z^-3 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T81.172 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, y * x * z^11 * y * z^-4 * x * y * z^-5 * x * z ] T81.173 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-1 * x * z^3 * y * z^-1 * x * z^4 * y * z^-2 * x * y^-1 * z^-10 ] T81.174 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y * x * y^-1 * z * y * x * y^-10 * z^-1 * y, z^-4 * x * z * y * x * z * y * x * y^-1 * z^-9 * x * y^-1 * z^-5 ] T81.175 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-3 * x * z^2 * y * z^-1 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-4 * x * z * y^-1 * z^-3 ] T81.176 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * y^-4 * z^-1 * y^3, z^-5 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T81.177 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-5 * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T81.178 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * y^-4 * z^-1 * y^3, z^3 * y * z^-4 * x * z^2 * y^-1 * z^-1 * x ] T81.179 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * z^-4 * x * z^2 * y^-1 * z^-1 * x, y^2 * z^-2 * y^7 * z^-1 * y^2 * z^-1 * y ] T81.180 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^4 * y * z^-1 * x * z^6 ] T81.181 : Triangle type {2,16,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^2 * z^-2 * y^7 * z^-1 * y^2 * z^-1 * y ] T81.182 : Triangle type {2,20,20} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, y^9 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T81.183 : Triangle type {2,20,20} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-8 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^7 * y * z^-4 * x * z^2 * y^-1 * z^-4 ] T81.184 : Triangle type {2,20,20} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-2 * z * y^10 * x * y^-1 * z^-1 * y * x * y^-4, z^-2 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-2 ] T81.185 : Triangle type {2,20,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-7 * z^4 * y^-5 * z^4 ] T81.186 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, z^-1 * y^6 * z^-1 * y * z^-2 * y ] T81.187 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-1 * y * z^-2 * y, y^7 * z^-2 * y * z^-2 ] T81.188 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^-1 * z^3 * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-7 * z^3 ] T81.189 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * z^2 * y^-2 * z^-3 * y, y^7 * z^-2 * y * z^-2 ] T81.190 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * z^2 * y^-2 * z^-3 * y, z^-1 * y^6 * z^-5 ] T81.191 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-3 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z^2 * y^-1 ] T81.192 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * z^2 * y^-2 * z^-3 * y, y^8 * z^-1 * y^2 * z^-1 ] T81.193 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-6 * z^3 * y^-10 * z * y^-1 * z * y^-1 * z ] T81.194 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, y^-1 * z * y^-3 * z^-1 * x * z^2, z * y * x * y^-2 * z * y^-1 * z^2, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T81.195 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3, z^-1 * y^6 * z^-5 ] T81.196 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-1 * z * y^-4 * z^-1 * y * x * y^-2 ] T81.197 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T81.198 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^2 * z^-1 * y^4 * z^-3 * y * z^-1 ] T81.199 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-5, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T81.200 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-1 * y, y^-3 * z^3 * y^-1 * z * y^-1 * z^3 * y^-9 * z * y^-1 * z ] T81.201 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y * z^-2, z^-1 * y * x * y^-2 * z * y^-1 * z^-2, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T81.202 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^-2 * z * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-9 * z^3 * y^-1 ] T81.203 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, z^-1 * y^6 * z^-2 * y^2 * z^-1 ] T81.204 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z * y^-1 * z^2 * y^-3 * z * y^-1 * z * y^-1 * z^2 * y^-6 * z * y^-1 * z^2 * y^-1 ] T81.205 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-2 * y * z^-4 * y^3 * z^-1 * y^6 * z^-3 * y * z^-2 * y ] T81.206 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * y^-5 * z^-2 * y^2 * z^-1, y * z^-1 * y^5 * z^-2 * y * z^-1 * y ] T81.207 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * y^6 * z^-1 * y * z^-2 * y ] T81.208 : Triangle type {2,24,24} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 ] T81.209 : Triangle type {2,35,70} Group order 350 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y * z^-2 * y^13 * z^-1 * y * z^-15 * y^2 ] T81.210 : Triangle type {2,36,36} Group order 360 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^17 * z^-4 * y * z^-1 * y^9 * z^-1 * y * z^-2 ] T81.211 : Triangle type {2,38,171} Group order 342 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-6 * z^4 * y^-4 * z^5 ] T81.212 : Triangle type {2,44,44} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-27 * z^3 * y^-10 * z^2 ] T81.213 : Triangle type {2,56,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, z^4 * y^-10 * z^4 * y^-5 * z^3 * y^-1 * z ] T81.214 : Triangle type {2,56,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-23 * y * z^-2 * y^9 * z^-2 * y^18 * z^-1 ] T81.215 : Triangle type {2,68,68} Group order 340 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-1 * z^12 * y^-6 * z * y^-10 * z * y^-1 * z * y^-1 ] T81.216 : Triangle type {2,84,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-39 * z^3 ] T81.217 : Triangle type {2,84,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-80 * z * y^-1 ] T81.218 : Triangle type {2,84,84} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-50 * y^31 * z^-2 ] T81.219 : Triangle type {2,110,165} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-21 * y * z^-2 * y^9 * z^-2 * y^19 ] T81.220 : Triangle type {2,163,326} Group order 326 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^114 * y^-48 ] T81.221 : Triangle type {2,164,164} Group order 328 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^49 * z^-114 * y ] T81.222 : Triangle type {2,324,324} Group order 324 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^48 * z^-113 * y ] T81.223 : Triangle type {3,3,8} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^8, z^-1 * x^-1 * y * x^-1 * y^-1 * x * z^2 * y^-1 * z^-1 ] T81.224 : Triangle type {3,3,8} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, y^-1 * z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 * x, y^-1 * z^-2 * x^-1 * y * x^-1 * y * z^-1 * x * y^-1 * x ] T81.225 : Triangle type {3,3,8} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, z^3 * y * x^-1 * z^2 * y^-1 * x, x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * z^-2 ] T81.226 : Triangle type {3,3,8} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^8, z^3 * y * x^-1 * z^2 * y^-1 * x, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z ] T81.227 : Triangle type {3,3,8} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^8 ] T81.228 : Triangle type {3,3,11} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z * y^-1 * z^-1)^2, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x, z * y * x * z * y * x^-1 * y * z^-1 * x * z^2 ] T81.229 : Triangle type {3,3,35} Group order 525 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y * z^-3 * x * z^3 * y * x * z^5 ] T81.230 : Triangle type {3,3,163} Group order 489 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-5 * x * z^3 * y * z^-5 ] T81.231 : Triangle type {3,5,5} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T81.232 : Triangle type {3,6,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^6, y * z^-2 * x^-1 * y^-1 * z^-1 * y, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.233 : Triangle type {3,6,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T81.234 : Triangle type {3,6,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-3 * x^-1 * y^-1 * z * y, z^2 * y^2 * x^-1 * z * y^-1 * z * y^-1 ] T81.235 : Triangle type {3,6,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * z * y^-2 * z^-1 ] T81.236 : Triangle type {3,6,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T81.237 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y * z^-1 * x * y^-1 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2 ] T81.238 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y^-1 * z * y^-1, y^8 ] T81.239 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z^-2 * y * x^-1 * z * y^2, y * z^-1 * x * y^-1 * x * z * y^-1 * z^-1, z^8 ] T81.240 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y * z^-1 * x * y^-1 * x * z * y^-1 * z^-1, y^8 ] T81.241 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^8 ] T81.242 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^-2 * z^-1 * x^-1 * y^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^2 * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z * y^-1 * z^-1 * y * x^-1 * y^-3 * z ] T81.243 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8 ] T81.244 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T81.245 : Triangle type {3,8,8} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y ] T81.246 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, (z^-1 * y)^3, y^8, (x * z * y^2)^2, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T81.247 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2, y^8 ] T81.248 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-2 * x * z * y^-1 * z ] T81.249 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.250 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * y * x^-1 * z * y^-2, y^8, x * z * y^2 * x^-1 * y^-1 * z^-2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T81.251 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y^3 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.252 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, y * x * y^-2 * x * y^-2 * z^-1, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T81.253 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, (z^-1 * y)^3, y * x * y^-2 * x * y^-2 * z^-1 ] T81.254 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^8, y^2 * x^-1 * y * x^-1 * z * y * x * z^-1 ] T81.255 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-2 * y * x^-1 * z * y^-2, z^8, y * z^-1 * x^-1 * y * x^-1 * y * z^-1 * x^-1 * z ] T81.256 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T81.257 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z * y^2 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.258 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.259 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y ] T81.260 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, y^8, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y ] T81.261 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T81.262 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T81.263 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * y * x^-1 * z * y^2, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T81.264 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * y * x^-1 * z * y^2, y * z^-1 * x * y^-1 * x * z * y^-1 * z ] T81.265 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * x^-1 * z^2 * y, y^8, (x * z * y^2)^2 ] T81.266 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, y * z^-1 * y * z^-1 * y * z^-3, y^2 * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x^-1 ] T81.267 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, y * z^-1 * y * z^-1 * y * z^-3, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1 ] T81.268 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, y^8 ] T81.269 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2, z^8 ] T81.270 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^8, y^-1 * z * y^3 * x^-1 * y^-2 * z^2 * y^-1 ] T81.271 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^8 ] T81.272 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y^8, z^8 ] T81.273 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^8 ] T81.274 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8, z^2 * y^2 * x * z * y * x, x^-1 * y * x^-1 * y * x^-1 * z * y * z^-2 ] T81.275 : Triangle type {3,8,8} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^8 ] T81.276 : Triangle type {3,12,20} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y^3 * z^-3, z^-1 * y * z^-2 * x^-1 * z^2 * y * z^-1 ] T81.277 : Triangle type {3,22,66} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * z^-2 * y * z^-1 * y^5 * z^-1 * y * z^-3 * y^4 * z^-1 ] T81.278 : Triangle type {3,82,246} Group order 246 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^82 ] T81.279 : Triangle type {3,243,243} Group order 243 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-70 * z * y^-10 ] T81.280 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * z * y * x^-1, (x * y^-1)^4, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T81.281 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * y^-1 * z^-1 * y * x^-1 * y * x * z^2, y * x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * x * z^-1 ] T81.282 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T81.283 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z * y^-1 * z * y^-1 * x * z * x^-1 * y^-1 ] T81.284 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x^-1 * y^-1 * z^-1 * y * z^-1 * y * z^-1 * y * x * y * x * z * y^2 * z^-1 ] T81.285 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x^-1 * y^-1 * z^-1 * y * z^-1 * y * z^-1 * y * x * y * x^-1 * y^-1 * z^-1 * y * z^-1 ] T81.286 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 ] T81.287 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * y^-1)^4, (x * z^-1)^4, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T81.288 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * y^-1)^4, (x * z^-1)^4, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T81.289 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x * y^-1 * z^-1 * y * z^-1 * y * z^-1 * y * x * y * x^-1 * y^-1 * z^-1 * y * z^-1 ] T81.290 : Triangle type {4,4,4} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T81.291 : Triangle type {4,4,6} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, y * z^-1 * x^-2 * z^2 * x^-1, x * z * y^-2 * x * y^-1 * z^-1 * y ] T81.292 : Triangle type {4,4,6} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T81.293 : Triangle type {4,4,6} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^2 * y^-1 * z^-1 * y * x^-1 * y * x^2 * y^-1 * x * y^-1 * z ] T81.294 : Triangle type {4,4,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, (x * z * x^-1 * y^-1)^2 ] T81.295 : Triangle type {4,4,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T81.296 : Triangle type {4,4,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2 ] T81.297 : Triangle type {4,4,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^6, z^-1 * x * z^-1 * x^-2 * y^-1 * x^-1 * y * x * z^-1 * x * z^-1 ] T81.298 : Triangle type {4,4,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^6, z * x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z * x^-1 * z ] T81.299 : Triangle type {4,4,10} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-3 * x^-1 * z * y^-1 * z^-1, y * x * y^-1 * x * y^-1 * x * z * x^-1 * y^-1 * z^-1 ] T81.300 : Triangle type {4,4,10} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * x * z^-1 * x^-1 * y^-1 * z^-1, z^10 ] T81.301 : Triangle type {4,4,10} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^-3, z^10 ] T81.302 : Triangle type {4,4,10} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^10 ] T81.303 : Triangle type {4,4,10} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^10 ] T81.304 : Triangle type {4,4,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, (y^-1 * x)^3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T81.305 : Triangle type {4,4,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y * x * z^-1 * x^2 * z^3 ] T81.306 : Triangle type {4,4,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z * y * x * z * y * z^-1 ] T81.307 : Triangle type {4,4,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2, z^6 * y * z^-3 * x * z^2 ] T81.308 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * y * z^-1, z * y^-1 * z^-1 * y * x * z^2 * x^-1 ] T81.309 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z^-1 * y * x * z^2 * x^-1 ] T81.310 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y^-1 ] T81.311 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z, z * x^-1 * y * x^-2 * z * y^-1 * x * z ] T81.312 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^3 * x^-1 * z^2 * y^-1, (x * z^-1)^4, x^-1 * y * x^-1 * y * x^-1 * y * z^-3 ] T81.313 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, (x * z^-1)^4 ] T81.314 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z, (x * z^2 * y)^2 ] T81.315 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z, y^-2 * x * y^-1 * x * y^-1 * z^2 ] T81.316 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, (x * z^2 * y)^2 ] T81.317 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, z^-1 * x^-1 * z^3 * y^-1 * z^-2 * x^-1 * y^-1 * z^-4 ] T81.318 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, (x * z^-1)^4, y^-1 * z^-1 * x^-1 * y * x^2 * z^3 * x^-1, z^2 * y^-1 * z^-4 * x * z^5 ] T81.319 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z * y * z^-1 * x^-1 * z^3, (x * z^-1)^4, y^-1 * z^-1 * x^-1 * y * x^-1 * y * z^-2 * x^-1 ] T81.320 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, (x * z^-1)^4, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T81.321 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z * y * z^-1 * x^-1 * z^3, (x * z^-1)^4, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T81.322 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^-3 * x^-1 * z^4 * y * x * z * y^-1 * z^-2 ] T81.323 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-5 * x * y^-1 * x^-1 * z^4 ] T81.324 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z * y * z^-1 * x^-1 * y * z^-1 * x * y^-1 * z^-2 * x * z * y * x * z^2 ] T81.325 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, (x * z^-1)^4, z * y^-1 * z^-1 * x^-2 * z^3 * x^-1, z * y * z^-1 * x^-1 * z^3 * y^-1 * x^-1 * z^5 ] T81.326 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, y * x^-1 * y * x^2 * z^2 * x^-1, z^-5 * x * z^2 * y * x * z^2 * y * z^-1 ] T81.327 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T81.328 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * x^-1 * y^-1 * x * z * y * z^-1, (x * z^2 * y^-1)^2 ] T81.329 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T81.330 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * z^3 ] T81.331 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-3 * x^-1 * z^2 * y^-1 ] T81.332 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, (x * z^-1)^4, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T81.333 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T81.334 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T81.335 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, (x * z^-1)^4, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T81.336 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z^-2)^2, (y * z^-1)^4, (y * z^-3)^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-3 ] T81.337 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T81.338 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, (x * z^-1)^4 ] T81.339 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-2)^2, (x * z * x^-1 * y^-1)^2, y^-2 * x * y^-1 * x * y^-1 * z^2, z^-1 * x^-1 * z * y * x * z^2 * y^-1 ] T81.340 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y, y^-2 * x * y^-1 * x * y^-1 * z^2 ] T81.341 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y, (x * z^-1)^4, y * x^-1 * y * x^-2 * z^2 * y^-1 * z ] T81.342 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z^-2)^2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^4 * y^-1 * z^-2 * x * z^5 ] T81.343 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-2)^2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^-1 * x^-1 * z * y * x * z^2 * y^-1 ] T81.344 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, y * z^-2 * x^-2 * z^3 * x^-1, y^-1 * z^-1 * x * z^4 * y * z^-2 * x^-1 * z^3 ] T81.345 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, y * z^-2 * x^-2 * z^3 * x^-1, y^-1 * z^-2 * x^-1 * z^3 * y * z^-2 * x^-1 * z^3 ] T81.346 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, y^-1 * z^-2 * x^-2 * z^3 * x^-1, y^-1 * z^-1 * x * z^4 * y * z^-1 * x * z^4 ] T81.347 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, y^-1 * z^-2 * x^-2 * z^3 * x^-1, y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x * z^4 ] T81.348 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z^-2)^2, z^-2 * y * x^-1 * z * y^2, y * x^-1 * z^3 * y * z^-2 * x * z^5 ] T81.349 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, y * x^-1 * y * x^2 * z^2 * x^-1, z^2 * y^-1 * z^-2 * x^-1 * y^-1 * z^-2 * x^-1 * z^4 ] T81.350 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, (x * z^2 * y^-1)^2 ] T81.351 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T81.352 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T81.353 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T81.354 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^2 * z * y^-1 * z^-1 * x, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-2 * x^-1 * z ] T81.355 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2, z^6 * y * z^-3 * x * z^2 ] T81.356 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z^2 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-3 * x^-1 * z ] T81.357 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z * y * x * z^3 * y * z^-4 * x * z^2 ] T81.358 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^-2 * x * z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-3 ] T81.359 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * x * y^-1 * x * z^2 * y^-1 * x * y^-1 * x * z^5 ] T81.360 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z * y ] T81.361 : Triangle type {4,4,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * z^3 * y * z^-4 * x^-1 * z^3 * y ] T81.362 : Triangle type {4,4,18} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-2 * x * y^-1 * x * z^6 * y^-1 * x * z^7 * y ] T81.363 : Triangle type {4,4,22} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-7 * x^-1 * z^2 * y * x * z^4 * y^-1 * z^-1 * x * z * y * z^-4 ] T81.364 : Triangle type {4,4,34} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^2 * y * x * z^3 * y * x^-1 * y^-1 * x^-1 * z^9 ] T81.365 : Triangle type {4,4,42} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-42 ] T81.366 : Triangle type {4,4,42} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^8 * y^-1 * z^-2 * x * z^3 * y^-1 * z^-1 * x^-1 * z^5 ] T81.367 : Triangle type {4,4,42} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^5 * y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-1 * x^-1 * z^6 ] T81.368 : Triangle type {4,4,42} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-30 * x^-1 * z^3 * y * z^-1 * x * y^-1 * z^-6 ] T81.369 : Triangle type {4,4,82} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * z * x^-1 * z^5 ] T81.370 : Triangle type {4,4,82} Group order 328 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-65 * x * y^-1 * x * y^-1 * z^-15 ] T81.371 : Triangle type {4,4,162} Group order 324 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-64 * x * y^-1 * z^-16 ] T81.372 : Triangle type {4,5,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T81.373 : Triangle type {4,5,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, x^-1 * z * y * x * z * y, y * x^-1 * y^-1 * z * y^2 * x * y^-1 * z * y ] T81.374 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2 ] T81.375 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2, x^-1 * y^2 * x^2 * z * y * z^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T81.376 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y ] T81.377 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y^2 * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T81.378 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^6, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1 ] T81.379 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, y^-1 * z^2 * x^-1 * y^-1 * z * y^-1 ] T81.380 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y^2 * z^-1 * x^-1 * z * y^-1 * z, y * x^-1 * z * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 ] T81.381 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x * z^-1 * x^-1 * y^-1 * x * z^-2 * y, z * y * x * y^-1 * x * z * x^-1 * z ] T81.382 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y^-2 * x * y^-1 * x * y^-1 * z^2 ] T81.383 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y * x^-1 * y * x^2 * z^2 * x^-1, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T81.384 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y * z^-1 * x^-1 * y^-1 * x * y^-2 * z^-1 ] T81.385 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, y * z^-1 * x^-1 * y^-1 * x * y^-2 * z^-1, y * x^-1 * y^-2 * x * z * y * z^-1 ] T81.386 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (y * z^-2)^2, z^6, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y * x^-1 * y^-2 * x * y^-1 * z^-2 ] T81.387 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * x^-1 * y * x^2 * z^2 * x^-1, y * x^-1 * y^-2 * x * y^-1 * z^-2 ] T81.388 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2 ] T81.389 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T81.390 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, z^2 * y^2 * z^-1 * x * y^-2 * z^-1 * x ] T81.391 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * z * y, (z^-1 * y)^3, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.392 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, y^-2 * z * y * x^-1 * z^2 * y^-1 * z ] T81.393 : Triangle type {4,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * z * y, z^6, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T81.394 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T81.395 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y^-2 * x * y^-1 * x * y^-1 * z^2 ] T81.396 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T81.397 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, (z^-1 * x)^3, x^-1 * y^-1 * z * y^-1 * x * z * y^-1 * z ] T81.398 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.399 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2, x^-1 * y^2 * x^2 * z * y * z^-1 ] T81.400 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y * z^-1 * x^-1 * y^-1 * x * y^-2 * z^-1 ] T81.401 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, z^-3 * x^-1 * z^2 * y^-1 ] T81.402 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, z^-2 * y * x^-1 * y * z^-1 * y, x^-1 * y^-2 * z * y^-2 * z * y * x^-1 * z * y^-1 * z * y^2 ] T81.403 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z * y^2 * x^-2 * z^2 * y * x^-1 ] T81.404 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, x^-1 * z^2 * y^2 * x * y^-2 * z^-2 ] T81.405 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y * x^-1 * y^2 * z^-1, x^-1 * y^-1 * z * y * z^-1 * x * y^-2 * z^-2 ] T81.406 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, y^-3 * z^-1 * x^-1 * z^2 * y^-1 * z ] T81.407 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, y * x * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * z ] T81.408 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^-1 * z^-1 * x^2 * z * y^-1 * z, x * z^-1 * x^-1 * y^-1 * x * z^-2 * y, z^2 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 ] T81.409 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, z^-1 * y^2 * x^-1 * y^3 ] T81.410 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.411 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, z^6 ] T81.412 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y, y * x^-1 * y^-2 * x * z * y * z^-1 ] T81.413 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.414 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^6, x^-1 * y^2 * x^2 * z * x^-1 * z, y * z^-1 * x * y^-1 * x * y^-2 * z^-1 ] T81.415 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T81.416 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.417 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, x^-1 * z^2 * y^2 * x * y^-1 * z * y * z^-1 ] T81.418 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, x^-1 * z^2 * y^2 * x * y^-2 * z^-2 ] T81.419 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, x^-1 * z^2 * y^2 * x * y^-1 * z * y * z^-1 ] T81.420 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y^2 * x^-1 * z * y * z^-2, y^-2 * z * y * x^-1 * z^2 * y^-1 * z ] T81.421 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (z^-1 * y)^3, z^6, x^-1 * z^2 * y^2 * x * z * y^-1 * z^-1 * y ] T81.422 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (z^-1 * y)^3, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T81.423 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T81.424 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (z^-1 * y)^3, z^6, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.425 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^6, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T81.426 : Triangle type {4,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.427 : Triangle type {4,6,20} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-5 * x^-1 * y * z^-4 ] T81.428 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-1 * z^-1, y^2 * z^-1 * x^-1 * z * y^-1 * z, (x * y^-1)^4 ] T81.429 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * y^3 ] T81.430 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, x^-1 * z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 ] T81.431 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T81.432 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, z^-1 * y^3 * x^-1 * y^4, y * x^-1 * z * y * z^-1 * y * z^-1 * y * x^-1 * z ] T81.433 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^8, z^-1 * y^3 * x^-1 * y^4, y * x^-1 * z * y * z^-1 * y * x * y^-1 * z^-2 ] T81.434 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * x^-1 * z ] T81.435 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * y * z^-1 * y * x * z * y * x^-1 * z ] T81.436 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T81.437 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^8, x^-1 * z * y * z^-1 * y * x * y^-1 * z^2 * y ] T81.438 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, x^-1 * z * y * z^-1 * y * x * y^-1 * z^2 * y ] T81.439 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, x^-1 * z * y * z^-1 * y * x * z * y * z^-1 * y ] T81.440 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T81.441 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T81.442 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T81.443 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * y * z^-1 * y * x * z * y * x * z ] T81.444 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T81.445 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * x * z ] T81.446 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-2 * x^-1 * z ] T81.447 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * x^-1 * z ] T81.448 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * x^-1 * z ] T81.449 : Triangle type {4,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-2 * x^-1 * z ] T81.450 : Triangle type {4,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * z * y^-1 * z * y^-1 * z * y^-3 * x * y^-1 * z * y^-1 * z ] T81.451 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^2 * z^-1 * x^-1 * y^-1 * z^2, y^4 * x^-1 * y * z^-3 ] T81.452 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, (y * z^-2 * y)^2 ] T81.453 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^2 * z^-1 * x^-1 * y^-1 * z^2, z^-1 * y^4 * z^-3 ] T81.454 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1)^4 ] T81.455 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T81.456 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * z * y, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, (y * z^-1)^4 ] T81.457 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T81.458 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2 ] T81.459 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, y * z^-2 * x^-1 * y^-1 * z^-1 * y ] T81.460 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T81.461 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1 ] T81.462 : Triangle type {4,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T81.463 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T81.464 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T81.465 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^3 * y^-1, z * y^-4 * z * y^-4 * z^6 ] T81.466 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T81.467 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, x^-1 * z * y^4 * x^-1 * y^-2 * z ] T81.468 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z * y * x * y^-2 * z ] T81.469 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-2 * z^-1 * y, z * y^-1 * z^-2 * x^-1 * z^4 ] T81.470 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T81.471 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T81.472 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T81.473 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, z^2 * y^-2 * z^3 * y^-1 * z^6 * y^-1 * z ] T81.474 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T81.475 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T81.476 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T81.477 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-2 * y)^2 ] T81.478 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^4 * z^-3 ] T81.479 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^-2 * z^2 * y^-5 * z * y^-4 * x * z^2 ] T81.480 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y^3 * z^-2 * y ] T81.481 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y^4 * z^-3 ] T81.482 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T81.483 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y^3 * z^-2 * y ] T81.484 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z * y^-2 * z * x^-1 * y^-2 * z * y^-1 ] T81.485 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y^4 * z^-3 ] T81.486 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^4 * x^-1 * y^2 * z^-1 * y ] T81.487 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * y * z^-1 * y * z^-1 * x^-1 * z^-1 * x * z^-3 * y * z^-2 * y ] T81.488 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * z^-1 * x^-1 * y * z^-3 ] T81.489 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y * z^-1 * y^4 * z^-1 * y^7 * z^-2 ] T81.490 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y^3 * z^-2 * y ] T81.491 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y ] T81.492 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T81.493 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-2 * y * x^-1 * y * z^-1 * y^2, z^-4 * x^-1 * z^3 * y^-1 ] T81.494 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-4 * x^-1 * z^3 * y^-1, z * y^-4 * z * y^-4 * z^6 ] T81.495 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T81.496 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^5 * z^-1 * y^2 * z^-1 * y * z^-2 * y^4 ] T81.497 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^5 * z^-1 * y * z^-1 ] T81.498 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T81.499 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^2 * x^-2 * y^-1 * z * x^-1, y^5 * z^-1 * y * z^-1 ] T81.500 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^2 * x^-2 * y^-1 * z * x^-1, (y * z^-2 * y)^2 ] T81.501 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-1 * y^3 * z^-2 * y * x^-1 * z^-2 * y^2 * z^-2 * y^2 ] T81.502 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y^2 * x^-1 * y * z^-2 * y ] T81.503 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, z^2 * y^-3 * z^2 * y^-2 * z^3 * y^-1 * z^3 ] T81.504 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, y^5 * z^-1 * y * z^-1 ] T81.505 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T81.506 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T81.507 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T81.508 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3, (y * z^-1)^4 ] T81.509 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T81.510 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^4 * z^-3 * y^3 * z^-1 * y * z^-2 * y^2 ] T81.511 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y^2 * x^-1 * y^2 * z^-2 ] T81.512 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, z^-1 * y^4 * z^-3 ] T81.513 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^4 * z^-3 ] T81.514 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, (y * z^-2 * y)^2 ] T81.515 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, (y * z^-2 * y)^2 ] T81.516 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^4 * x^-1 * y * z^-3 ] T81.517 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-1 * z * y^-1 * z^9 * y^-1 * z * y^-1 * z ] T81.518 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (y * z^-2 * y)^2, y^4 * x^-1 * y^-3 * z, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T81.519 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (y * z^-2 * y)^2, (y * z^-1)^4, (y * z^-3)^2 ] T81.520 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4, (y * z^-3)^2, z^-1 * y^3 * x^-1 * y^4 ] T81.521 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^4 * x^-1 * y^-3 * z, z^-1 * y^3 * x^-1 * y^4, y^2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T81.522 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y^3 * x^-1 * y^-4 ] T81.523 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (y * z^-1 * y^2)^2, (y * z^-2 * y)^2, (y * z^-3)^2 ] T81.524 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, (y * z^-1 * y^2)^2, z^-1 * y^3 * x^-1 * y^-4, z^-4 * x^-1 * y * z^-3 ] T81.525 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, (y * z^-1)^4, y^4 * x^-1 * y^-3 * z, y * z^-3 * x^-1 * z^4 ] T81.526 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-3 * z, y * z^-3 * x^-1 * z^4 ] T81.527 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, (y * z^-1 * y^2)^2, z^-1 * y^3 * x^-1 * y^-4, z^-4 * x^-1 * y * z^-3 ] T81.528 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T81.529 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T81.530 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-2 * z * y^-2 * z * y^-7 * z^2 * y^-1 ] T81.531 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^4 * x^-1 * y * z^-3 ] T81.532 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^4 * x^-1 * y^-1 * z * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T81.533 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^-1 * z^-3 * x^-1 * z * y * x^-1 * y^-3 * z^-1 * x^-1 ] T81.534 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-1 * z * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T81.535 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y^-1 * z^-2 * x^-1 * y^-1 * x * z^4, x^-1 * z * y^4 * x^-1 * y^-2 * z ] T81.536 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-3 * z, z^2 * y * z^-1 * x^-1 * z^4 ] T81.537 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^-1 * x^-1 * z^2 * y * x^-1 * z * y * z^-1 * x * z * y * z^-7 ] T81.538 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^-1 * z^-3 * x^-1 * z * y * x^-1 * y^-3 * z^-1 * x ] T81.539 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z * y * x * y^-1 * z^-1 * y ] T81.540 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-1 * z * y^2, z * y^-1 * z^-2 * x^-1 * z^4 ] T81.541 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, y^6 * x^-1 * z * y * x^-1 * y^-2 * z^-1 * x * y^-1 * z^-1 * y^3 ] T81.542 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^4 * x^-1 * y^-2 * z^-1 * y, y * z^-3 * x^-1 * z^4 ] T81.543 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z * y)^2 ] T81.544 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1 ] T81.545 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1 ] T81.546 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x^-1 * z * y)^2 ] T81.547 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^3 * x^-1 * z^3 ] T81.548 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T81.549 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T81.550 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x * z^-2)^2, y^3 * x^-1 * z^3 ] T81.551 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * y * z^-3 ] T81.552 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-4 * x^-1 * y * z^-3 ] T81.553 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, (y * z^-1 * y^2)^2, z^-1 * y^3 * x^-1 * y^-4, z^-2 * x^-1 * z * y * x * z^3 * y ] T81.554 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^2 * y * x^-1 * z^4 * y^-1 * z^-3 * x^-1 * z^5 ] T81.555 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^5 * z^-1 * y * z^-1, y * z^-3 * x^-1 * z^4 ] T81.556 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * x^-1 * z^4, z * y^-4 * z^2 * y^-1 * z * y^-2 * z^3 * y^-1 * z ] T81.557 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, z^2 * y * x^-1 * z^5 * y * z^-2 * x^-1 * z^5 ] T81.558 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, (y * z^-1 * y^2)^2, z^-1 * y^3 * x^-1 * y^-4, z^-2 * x^-1 * z * y * x * z^2 * y^-1 * z^-1 ] T81.559 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y, y * z^-3 * x^-1 * z^4 ] T81.560 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-3 * x^-1 * z^4, z * y^-6 * z * y^-3 * z^3 * y^-1 * z ] T81.561 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * y * z^-3 ] T81.562 : Triangle type {4,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * y * z^-3 ] T81.563 : Triangle type {4,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y^4 * z^-4 ] T81.564 : Triangle type {4,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * z^2 * y^-1, y * z^-1 * y^2 * x * y^-1 * z^-1 * y, y^-1 * z^2 * y * x * z * y^-1 * z ] T81.565 : Triangle type {4,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T81.566 : Triangle type {4,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * y * z^-1 * x^-1 ] T81.567 : Triangle type {4,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x * z, z^-2 * y^4 * z^-4 ] T81.568 : Triangle type {4,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-2 * z * y^-1 * z ] T81.569 : Triangle type {4,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^-1 * z * y^-2 * z * y^-4 * z * y^-1 * z ] T81.570 : Triangle type {4,55,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^23 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T81.571 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-4 * y^2 * z^-5 * y^3 * z^-1 * y * z^-2 * y^7 * z^-2 ] T81.572 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^3 * z^-2 * y * z^-1 * y^5 * z^-1 * y^5 * z^-1 * y^8 * z^-1 ] T81.573 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^24 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T81.574 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^24 * z^-2 * y * z^-1 * y^7 * z^-1 * y^5 * z^-1 * y * z^-1 * y^12 ] T81.575 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-4 * y^2 * z^-5 * y^3 * z^-1 * y * z^-2 * y^9 ] T81.576 : Triangle type {4,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-4 * y^2 * z^-5 * y^6 * z^-1 * y^9 ] T81.577 : Triangle type {4,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^23 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T81.578 : Triangle type {4,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^23 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T81.579 : Triangle type {5,5,5} Group order 400 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, z^-1 * y * x^-2 * y^2 * z^-1 ] T81.580 : Triangle type {5,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z^-2 * x^-2 * y^-1 * z^-1 * y, y^-1 * x * z^-1 * x^-1 * y^-1 * z^2 ] T81.581 : Triangle type {5,5,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, y^-1 * z^-2 * x * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T81.582 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z * y^-2 * x * y^-1 * z ] T81.583 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, (z^-1 * x)^3, z^-1 * y * x^-2 * y^-1 * z * y^-1 ] T81.584 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^-5, z^-3 * x^-1 * z^2 * y^-1 ] T81.585 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y * x^-1 * y^-1 * x * z * y, y^-5 ] T81.586 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y^-5, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T81.587 : Triangle type {5,5,15} Group order 300 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, x^-5, (y^-1 * x)^5 ] T81.588 : Triangle type {5,5,55} Group order 275 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x * z^-2 ] T81.589 : Triangle type {5,5,55} Group order 275 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, x^-1 * z * y^-1 * x * z^-1 * y ] T81.590 : Triangle type {5,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^3 * x^-1 * y^-1 * z * y, z * y^2 * x^-1 * z^3 ] T81.591 : Triangle type {5,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, z^2 * y * x * z^-1 * x^-1 ] T81.592 : Triangle type {5,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3 ] T81.593 : Triangle type {5,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, y * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2 ] T81.594 : Triangle type {5,15,15} Group order 240 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^2 * z^2, z^-1 * y^2 * x^-1 * z * y ] T81.595 : Triangle type {5,15,15} Group order 240 Chiral action Defining relators: [ x * y * z, x^-5, (y * z^-1 * y)^2, (x * z * y)^2, (z^-1 * x)^3, y * z^-1 * x^-2 * y^-1 * z^-2 ] T81.596 : Triangle type {5,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, (x * z * y)^2, y^2 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * z * x^-1 * z, y^-1 * z * y * x^-1 * y^-1 * z * x^-1 ] T81.597 : Triangle type {5,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, (y * z^-1 * y)^2, (x * z * y)^2, z * y^-1 * z^-1 * x * z^2 ] T81.598 : Triangle type {5,20,44} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * x * y^-1 * x * y^-1 * z, y^-1 * z^-1 * y * x * z * x^-1 ] T81.599 : Triangle type {5,20,44} Group order 220 Chiral action Defining relators: [ x * y * z, x^-5, z * y^-1 * x^2 * y^-2, y^-1 * z^-1 * y * x * z * x^-1 ] T81.600 : Triangle type {6,8,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, y^8 ] T81.601 : Triangle type {6,8,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y * z^-1 * x^-1 * z * y^2 ] T81.602 : Triangle type {6,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * y^-1, x^6, y^-1 * z^-1 * y * x^-1 * y^-2 * z, z * y * x^3 * z^2 * x^-1 ] T81.603 : Triangle type {6,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, y * z^-1 * x^-1 * z * y * x * y^-1 * z^-1 * y * z^-1 ] T81.604 : Triangle type {6,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-2)^2, (x * z * y^-1)^2, (x * z^-1 * y)^2, (z^-1 * y)^3 ] T81.605 : Triangle type {6,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, z * y^2 * x^-1 * y^-3 ] T81.606 : Triangle type {7,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T81.607 : Triangle type {7,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^6 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T81.608 : Triangle type {7,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^6 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T81.609 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z * y^2 * x * z * x^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8 ] T81.610 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^8 ] T81.611 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T81.612 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * z^-1 * x^-1 * z^2 * y^-1, x^8, z^-1 * y * x * y^-1 * x * y^-2 * z^-1 ] T81.613 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z * y^-2 * x * z * x^-1, x^-1 * y * x^-2 * y * z^-1 * y, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3 ] T81.614 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.615 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1 ] T81.616 : Triangle type {8,8,8} Group order 256 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^2 * x * z * x^-1, z * x^-2 * y^-1 * x^-2 * z * y^-1, z^8 ] T81.617 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2, x^-1 * y * x^-2 * y^-2 * z, x^8 ] T81.618 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2, x^8 ] T81.619 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, y * x * y^-1 * x * z^2, x^8, y^8, y^2 * z^-1 * y^2 * z^-3 ] T81.620 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z * y^2 * x^-1 * z * y^-1 * z, y^-1 * z * y * x^-1 * z^2 * y^-1, x^8 ] T81.621 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (y * z^-2)^2, y^3 * x^-1 * z^3, x^8 ] T81.622 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * y^-1 * x)^2, y^2 * x^-2 * z * x^-1 * y, x^8 ] T81.623 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y, x^8 ] T81.624 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-2)^2, x^-1 * y * x^-2 * y^-2 * z, z^-1 * x^-1 * y * x^-1 * y * x * y^-1, x^8 ] T81.625 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * y^-1 * x)^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, x^8, z^8 ] T81.626 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, x^8, z^8 ] T81.627 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^8, z^8 ] T81.628 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (x * y^-1 * x)^2, (y * z^-2)^2, x^8, z^8 ] T81.629 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, x^-1 * z * x^-2 * z * y * z^-1, x^8 ] T81.630 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^2 * x^-2 * z * y^-1 * x, x^8 ] T81.631 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * x^-2 * z * y^-1 * x, x^8, y^8 ] T81.632 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, z^-2 * x^-2 * z * y^-1 * x, x^8 ] T81.633 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y^8, z^8 ] T81.634 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * z^2, z^-1 * y * x^-2 * y^-2 * x, x^8, y^8 ] T81.635 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^8, y^8, y^2 * z^-1 * y^2 * z^-3 ] T81.636 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, y^8 ] T81.637 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^-1 * z * y * x * y^-1 * z^-1, x^8, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T81.638 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8 ] T81.639 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2, x^8 ] T81.640 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2, x^8 ] T81.641 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T81.642 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, x^8, y^8 ] T81.643 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2, x^8 ] T81.644 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x, x^8, x^2 * y^-1 * x^2 * y^-3 ] T81.645 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^8, z^8 ] T81.646 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-2 * z * y^-1 * x, x * z * x^-2 * z^2 * y^-1, x^8 ] T81.647 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-2 * z * y^-1 * x, x^8, z * y * x^3 * y^-1 * z^-1 * x, z^-1 * x^-1 * y^-1 * x^2 * z^-1 * x * y^-1 ] T81.648 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8 ] T81.649 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z * x^-3 * y^-3, x * z * x^-2 * z^2 * y^-1, x^8 ] T81.650 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x^8 ] T81.651 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.652 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * z^2 * y, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.653 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, z^-1 * x^-3 * z^2 * y, z * x^-3 * y^-3, z^-2 * x^-2 * z * y^-1 * x ] T81.654 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T81.655 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * y * x^-1 * z * y^-2, y^8 ] T81.656 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * z * y^-1 * x, x * z * x^-2 * z^2 * y^-1 ] T81.657 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, z * x^-3 * y^-3, z^-2 * y * x^-1 * z * y^-2 ] T81.658 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, z * x^-3 * y^-3, z^-2 * x^-2 * z * y^-1 * x, x * z * x^-2 * z^2 * y^-1, z^-2 * y * x^-1 * z * y^2 ] T81.659 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T81.660 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, y^2 * z^-1 * y^2 * z^-3 ] T81.661 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T81.662 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y^2 * x^-2 * y^-1 * x * z^-1, z^-1 * y * x^-2 * y^2 * x, x * z * x^-2 * z^2 * y, z^2 * x^-2 * y^-1 * z^-1 * x^-1 ] T81.663 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * x * z^-1, z^-1 * y * x^-2 * y^2 * x, z^2 * x^-2 * z * y^-1 * x ] T81.664 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x^-1, y^3 * x^-1 * z^3 ] T81.665 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y^-1 * x * y^-1, x * z * x^-2 * z^2 * y ] T81.666 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T81.667 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * z^2 * y^-1, y^2 * x^-2 * y^-1 * x * z^-1, z^-2 * y * x^-1 * z * y^2 ] T81.668 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (y * z^-2)^2, x^8, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-2 ] T81.669 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, y^8, z^-1 * y^3 * x^-1 * y^4 ] T81.670 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * z^2 * y^-1, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y, z^2 * x^-2 * y * x * z ] T81.671 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y * z^-2, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y ] T81.672 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (x * z * y^-1)^2, (x * z * y)^2, y^8, z^8 ] T81.673 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-2)^2, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y, x * z * x^-2 * z^2 * y, z^2 * x^-2 * y^-1 * z^-1 * x^-1 ] T81.674 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-1 * x)^2, (x * z * y^-1)^2, (x * z * y)^2, y^2 * x^-2 * z * x^-1 * y, x * z * x^-2 * y^-1 * z^-2 ] T81.675 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-2)^2, x^-1 * y * x^-2 * y^-2 * z, x^8, x^-1 * y * x^3 * y^-1 * z^-2, z^-1 * x * y^-1 * x^2 * z^-1 * x^-1 * y ] T81.676 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, x^8 ] T81.677 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z * y)^2, z^-1 * x^-3 * y * z^-2, x^8 ] T81.678 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y * z^-2, x^8 ] T81.679 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (x * z * y^-1)^2, x * z * x^-2 * y^-1 * z^-2, x^8 ] T81.680 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z * y)^2, z^-2 * x^-2 * z * y^-1 * x, x^8 ] T81.681 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, x^8, y^8 ] T81.682 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, (x^-1 * z * y)^2, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, x^-1 * z * x^-2 * z * y * z^-1, y^3 * x^-1 * z^3 ] T81.683 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, x^-1 * z * x^-2 * z * y * z^-1 ] T81.684 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2, (x^-1 * z * y)^2, z * x^-3 * y^-3 ] T81.685 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1 ] T81.686 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y * x * y^-1 * x * z^2, x^8, y^8, z^8 ] T81.687 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * x * z^-1, x^8 ] T81.688 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y^-1)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * x * z^-1, z^-1 * y * x^-2 * y^2 * x, x * z * x^-2 * y^-1 * z^-2, x^8 ] T81.689 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * y * x^-1 * z * y^-2, y^2 * z^-1 * x^-1 * z * y^-1 * z^-1, x^8 ] T81.690 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, (x * z * y^-1)^2, (x^-1 * z * y)^2, y^3 * x^-1 * z^3 ] T81.691 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z * x^-2 * z * y * z^-1, z^-2 * y * x^-1 * z * y^2 ] T81.692 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y^-1)^2, (x^-1 * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, x * z * x^-2 * y^-1 * z^-2 ] T81.693 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^-2 * z^2 * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T81.694 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y^-1)^2, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, x * z * x^-2 * y^-1 * z^-2 ] T81.695 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, (x^-1 * z * y)^2, (x * z * y)^2, y^3 * x^-1 * z^3 ] T81.696 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, x^-1 * z * x^-2 * z * y * z^-1, y^8 ] T81.697 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, (x * z * y^-1)^2, (x * z * y)^2, y^3 * x^-1 * z^3 ] T81.698 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * x^-1 * z * y, x^8, y^8, z^-1 * y^3 * x^-1 * y^4 ] T81.699 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-1 * y^2 * x^-1 * z * y^-1 * z^-1, x^8 ] T81.700 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x^-3 * y * z^-2, y^2 * x^-2 * y^-1 * x * z^-1, x^8 ] T81.701 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * y * z^-2, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y, x^-1 * z * x^-2 * z * y * z^-1 ] T81.702 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * x^-1 * z * y, x^8, y^8, z^-1 * y^3 * x^2 * z^-1 * y^3 ] T81.703 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, y^8, z^-1 * y^3 * x^2 * z^-1 * y^3 ] T81.704 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, (x * z * y)^2, x^8, (x * z^-1)^4 ] T81.705 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, x^8, y * x^-4 * z * x^-3 ] T81.706 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, x^8, y * x^-4 * z * x^-3 ] T81.707 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^8, y^8, (x * z^-1)^4 ] T81.708 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, x^8, (x * z^-1)^4 ] T81.709 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, (x * z * y)^2, x^8, y * x^-4 * z * x^-3 ] T81.710 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, x^8, (x * z^-1)^4 ] T81.711 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^8, y^8, y * x^-4 * z * x^-3 ] T81.712 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^-1 * z * x^-2 * z * y * z^-1, x^8, z * y * x^3 * z * y * x^-1 ] T81.713 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * y * z^-2, x^-1 * z * x^-2 * z * y * z^-1 ] T81.714 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-3 * y * z^-2, x^8, y^-1 * z^-1 * x^3 * y^-1 * z^-1 * x^-1 ] T81.715 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z * x^-2 * y^-1 * z^-2, z^2 * x^-2 * z * y^-1 * x, x^8 ] T81.716 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2 ] T81.717 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y * z^-2, z^-1 * x * z^-1 * x^-2 * y * x * z^-1 * x ] T81.718 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3 ] T81.719 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, (x * z * y^-1)^2, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T81.720 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y * x^-1 * z^2 * y^-1 ] T81.721 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, y^8 ] T81.722 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * x^-3 * y * z^-2 ] T81.723 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, z^-1 * x * z^-1 * x^-2 * y * x * z^-1 * x ] T81.724 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * y^-1 * z * y, z^-1 * x^-3 * y * z^-2, z^-1 * y * x^-2 * y^-2 * x ] T81.725 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y * z^-2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1 ] T81.726 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y * z^-2, (x * z^-1)^4 ] T81.727 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z^-1)^4 ] T81.728 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2, y * x^-3 * y^-1 * z * y, y^8 ] T81.729 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3 ] T81.730 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2 ] T81.731 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y)^2, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1 ] T81.732 : Triangle type {8,8,8} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, y^8 ] T81.733 : Triangle type {8,8,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-1 * x * z * y^-1 * x * z^3 ] T81.734 : Triangle type {8,8,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, z * y * x^-2 * y^-1 * x * y^-1, x^8, y^-1 * x * z * y^-1 * x * z^3 ] T81.735 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-20 * x^-1 * y^-1 * z^-7 ] T81.736 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^-2 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-5 ] T81.737 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-10 * x * z * y^-1 * z^-1 * x * z^5 * y * x * z^5 * y^-1 * z^-3 ] T81.738 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y * x^-1 * z^3 * y^-1 * z^-1 * x * y * z^-1 * x^-1 * z^2 * y * x^-1 * z^2 ] T81.739 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-3 * x * y^-1 * x ] T81.740 : Triangle type {8,8,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, y * x^-1 * z^3 * y * z^-6 * x^-1 * z^3 ] T81.741 : Triangle type {8,8,108} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-6 * x^-1 * z^2 * y^-1 * z^-5 * x * z * y * z^-4 * x^-1 * z * y * z^-5 ] T81.742 : Triangle type {8,8,108} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-6 * x^-1 * z^2 * y^-1 * z^-5 * x * z * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z * y^-1 * z^-4 ] T81.743 : Triangle type {8,20,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z * x^-2 * y^-1 * z^-2, z^2 * x^-2 * z * y^-1 * z, x^8 ] T81.744 : Triangle type {8,20,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * y^-1 * x * z^2, x^8 ] T81.745 : Triangle type {8,20,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * z^-1 * y, x^8 ] T81.746 : Triangle type {8,20,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^2 * x^-2 * y^3, x^8 ] T81.747 : Triangle type {8,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, (y * z^-3)^2 ] T81.748 : Triangle type {8,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^5 * z^-1 * y * z^-1 ] T81.749 : Triangle type {8,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, z^-3 * y^2 * z^-3 ] T81.750 : Triangle type {8,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, y^5 * z^-1 * y * z^-1 ] T81.751 : Triangle type {8,48,48} Group order 192 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z * y^-1 * z^3 * y^-1 * z^2 * y^-1 * z^2 ] T81.752 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, y^3 * x^-1 * y * z^-2 ] T81.753 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * x^-1 * z^3, x^8 ] T81.754 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, (x^-1 * z * y)^2 ] T81.755 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3 ] T81.756 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T81.757 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-2 * x * y^-1 * x * z * y^-2 ] T81.758 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y^-2 * z * y^-1 * z^2)^2 ] T81.759 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-3 * x * y^-4 ] T81.760 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^2 * y^-1 * z^2 * y^-3 * z * y^-1 * z ] T81.761 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^2 * y^-1 * z^2 * y^-1 * z * y^-3 * z ] T81.762 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^3 * y^-2 * z * y^-1 * z * y^-3 * z ] T81.763 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-3 * z * y^-1 * z^2 ] T81.764 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^11 * y^-1 * z^2 * y^-6 * z^3 ] T81.765 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T81.766 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^14 * y^-1 * z * y^-4 * z^3 ] T81.767 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^8 * z^-1 * y ] T81.768 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-2 * x^-1 * z * x^-1 * z^4 ] T81.769 : Triangle type {8,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-2 * z^3 * y^-4 * z^3 ] T81.770 : Triangle type {9,9,15} Group order 225 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^-2 * x^-2 * y * z^-2 ] T81.771 : Triangle type {10,19,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T81.772 : Triangle type {10,20,20} Group order 200 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, z * x^-2 * y * x, y^-6 * z * y^-1 * z * y^-2 * z * y^-5 * z * y^-2 ] T81.773 : Triangle type {10,20,20} Group order 200 Chiral action Defining relators: [ x * y * z, x^-1 * z * y^-1 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2, y^-2 * x^3 * y^-1 * x * y^-1 ] T81.774 : Triangle type {10,20,20} Group order 200 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, x^10 ] T81.775 : Triangle type {10,20,20} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, z^-2 * y * x^-1 * y^-1 * z * y^-1, y^-1 * x^4 * y^-3 ] T81.776 : Triangle type {10,20,20} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^10 ] T81.777 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^10, z^3 * y^-1 * z^-1 * x^-1 * z^5 ] T81.778 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T81.779 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x^2 * z^-1 * x^2 * z^-3, x^10 ] T81.780 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x^3 * z^-2 * x, z^-3 * x^-1 * z^4 * y^-1 * z^-2 ] T81.781 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (x * y^-2)^2, z^-1 * x^4 * z^-3, x * y^-4 * z * y^5 ] T81.782 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^7 * z^-1 ] T81.783 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^10, z^-4 * x^-1 * z^3 * y * z^-2 ] T81.784 : Triangle type {10,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^10, x^4 * z^-1 * x^-5 * y^-1 ] T81.785 : Triangle type {10,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T81.786 : Triangle type {10,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T81.787 : Triangle type {12,16,48} Group order 192 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y * z^-1, y^-2 * x^2 * z^2, x^-1 * z * x^-1 * z^2 * x^-4 * z * x^-2 ] T81.788 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y^-1 * x * z^2, y * x^-3 * y^3 ] T81.789 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * y^3, z^-3 * y^2 * z^-3 ] T81.790 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^-1 * x^-1 * y^-1 * x * z * y, x^2 * y^-1 * x * z^-1 * x^3 * y^-1 * x * y^-1 * x * y^-2 ] T81.791 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x * y^-1 * x^2 * y^-1 * x * z ] T81.792 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T81.793 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * x^-1 * y^3 * z^-1, z^-1 * y * x * z^-2 * x^4 * z^-4 ] T81.794 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-3 * y^-1 * z^2, x^2 * y^-1 * x^3 * y^-1 * x * y^-2 ] T81.795 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, z^-1 * x^-4 * y^-1 * x^3, y^-1 * x^5 * y^-1 * x * y^-2 ] T81.796 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3, y^-1 * x * z^-1 * x * z^-2 * x^6 * y^-1 * x * y^-1 ] T81.797 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-1 * y^7 * z^-3 * y * z^-1 * y * z^-1 * y ] T81.798 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, x^3 * z^-2 * x^6 * y^-1 * x * y^-1 ] T81.799 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * y^-2 * z^-1, z^-2 * y * z^-1 * y * z^-3 ] T81.800 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, (y * z^-3)^2 ] T81.801 : Triangle type {12,16,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, (y * z^-3)^2 ] T81.802 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-4 * y * x^-1 * y, z^-1 * y^2 * x^-1 * y^-3 ] T81.803 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2, x^-7 * y^2 * x^-1 * z * x^-1 * z^2 * y ] T81.804 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, x * z^-1 * x * z^-1 * x^6 * z^-1 * x * z^-1 * x ] T81.805 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x * z * y)^2, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y * x * y^-1 ] T81.806 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z * y * x^-1 * y^-3 ] T81.807 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^4 * y^-2 * z^-1 ] T81.808 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^-1 * y^6 * x^-2 * z * x^-5 * y ] T81.809 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^2 * x^-1 * y^-3, x^2 * y^-1 * x^2 * y^-2 * z^-1 ] T81.810 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^-1 * y * x^-1 * z * y * x^-7 * z * x^-1 ] T81.811 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, y^-2 * x^3 * y^-2 * x, x^2 * z^-1 * x^2 * z^-3 ] T81.812 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^-2 * x^3 * y^-2 * x, z^-2 * x^3 * z^-2 * x ] T81.813 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^-12 ] T81.814 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x * y^-1 * x^3 * y^-1 * z^-2 ] T81.815 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^3 * y^-1 * z^-1 * x ] T81.816 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, z^-2 * y^3 * z^-2 * y ] T81.817 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * y * x^-1 * y^2 * x^-7 * y * x^-1 ] T81.818 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x * z^-2 * x^2 * z^-2 * x^7 ] T81.819 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, z * y * x^-1 * z * y * x^-5 * z^2 * x^-1 * z^2 * x^-1 ] T81.820 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z^-1 * x^3 * y^-1 * z^-1 * x ] T81.821 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T81.822 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * x^-2 * y^-2 * x, x * z^-1 * x^3 * y^-2 * z^-1 ] T81.823 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * z^-2 ] T81.824 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2, y^-2 * x^3 * y^-2 * x ] T81.825 : Triangle type {12,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^-2 * x^3 * y^-2 * x, z^-4 * x^-1 * z^3 * y^-1 ] T81.826 : Triangle type {12,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T81.827 : Triangle type {12,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^-5 * x * y^-1 * z^5 * y^-4 ] T81.828 : Triangle type {14,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-2, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T81.829 : Triangle type {16,16,24} Group order 192 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, y^-2 * x^3 * y^-2 * x, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T81.830 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-1 * z * y * x^-1 * z^2 * x^-1 ] T81.831 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, (y^-1 * x)^3, y^-1 * z * y^-1 * x * z^-1 * x, (x * z^-1 * y)^2 ] T81.832 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, (x * z^-1 * y)^2 ] T81.833 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, (y^-1 * x)^3, y^-1 * x^4 * y^-3, z^-2 * x^4 * z^-4 ] T81.834 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * x^-1 * y^-1 * z^-1, z * y^3 * z^-1 * x, (x * z^-1 * y)^2 ] T81.835 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z * y, x^-1 * y^-1 * x^2 * z^-2, z^-1 * y * x^-2 * y^-2 * x, y^3 * x^-1 * y * z^-1 * x^-1 ] T81.836 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^5 * y^-1 * z^-2, z^-1 * x^-1 * y^-1 * x^2 * z * y^-1 * x ] T81.837 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * x^3 * z^2, z^-1 * y * x^2 * z^-1 * y ] T81.838 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * x^3 * z^2, (y^-1 * x)^3, z * x^-1 * z^2 * x^-1 * z^4 ] T81.839 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, (y^-1 * x)^3, z^-1 * x^-1 * y^-1 * x^2 * z * y^-1 * x ] T81.840 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, y^-1 * x^4 * y^-3, z^-1 * x * z^-1 * x^-2 * z * x^-1 * y^-1 * x ] T81.841 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * y * x^2 * z^-1 * y ] T81.842 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z * y * x^-2 * z^2 * x^-1, z^-3 * x^-1 * z^2 * y^-1, y^-2 * x^3 * z^2 * y^-1 ] T81.843 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-2 * z^2 * x^-1, x * z * x^-2 * y^-1 * x * y^-1, y^-1 * x^4 * y^-3 ] T81.844 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3, y^-1 * x^4 * y^-3 ] T81.845 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, z^2 * y^-1 * z * x^-1 * z^4 ] T81.846 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, x * z^5 * y * z^-6 ] T81.847 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^3 * y^-1 * x * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x^3, y * x^-1 * z * y * z^-1 * x^-1 * z^4 * y * x^-1 * y * x^-1 * z^2 ] T81.848 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z^2 * y^-1 * z^-3 ] T81.849 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^-2 * x^-1 * z * y * z^-3 * x^-1 * y^-1 * x * z^3 * y^-1 ] T81.850 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z * y^-1 * x * y^-1 * x * z^3 ] T81.851 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x * y^-1 * x * z^2 * y^-1, z^4 * x^-1 * z^3 * y^-1 ] T81.852 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, y^-1 * x^4 * y^-3, z^-2 * x * y^-1 * x * z^2 * y^-1 ] T81.853 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, y^-1 * x^4 * y^-3, z * y^-1 * x * y^-1 * x * z^3 ] T81.854 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x^2 * y^-1 * x^2 * y^-3, z^-2 * x * y^-1 * x * z^2 * y^-1 ] T81.855 : Triangle type {16,16,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x^2 * y^-1 * x^2 * y^-3, z * y^-1 * x * y^-1 * x * z^3 ] T81.856 : Triangle type {16,44,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T81.857 : Triangle type {16,44,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^-4 * x^3 * y^-6 * x * y^-1 ] T81.858 : Triangle type {18,20,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T81.859 : Triangle type {18,36,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * y^2 * z^-1 * y, z^-1 * x^4 * z^-3 ] T81.860 : Triangle type {18,36,36} Group order 180 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^-6 * y^3 * x^-8 * z * y * x^-1 * z ] T81.861 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y ] T81.862 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T81.863 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^7 * x^-5 * y^2 ] T81.864 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, y^-2 * x^6 * y^-7 ] T81.865 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T81.866 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 ] T81.867 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T81.868 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^4 * x^-4 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T81.869 : Triangle type {19,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-2 * y * x^-1 * y * x^-1 * z^3 * x^-8 * y * x^-4 ] T81.870 : Triangle type {20,20,90} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * x * z^-3 * y * z^-1 * x * z^-2 * y * z^-1, z^-5 * y^2 * z^-4 ] T81.871 : Triangle type {20,20,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^6 * y^-2, z^4 * y * x^-1 * z^4 ] T81.872 : Triangle type {22,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-1 * z^2 * y^-1 * z * y^-1 * x * y^-2 * z * y^-2 * x * y^-1 ] T81.873 : Triangle type {22,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, x^-2 * y * x^-1 * y^3 * x^-1 * y * x^-1 * y^3 * z^-1 * y^3 ] T81.874 : Triangle type {22,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-4, z^-4 * x^2 * z^-4 ] T81.875 : Triangle type {22,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^2 * z^-2 * x^6 * z^-2 ] T81.876 : Triangle type {22,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-6 * z^2 * x^-2 * z * x^-8 * z * x^-4 ] T81.877 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T81.878 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T81.879 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T81.880 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T81.881 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-12 * y * x^-8 * z * x^-7 ] T81.882 : Triangle type {28,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T81.883 : Triangle type {35,35,35} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * z^-4 * y^6 * z^-1 * y^2 ] T81.884 : Triangle type {35,35,35} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-5 * y^6 ] T81.885 : Triangle type {42,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-20 * y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-2 ] T81.886 : Triangle type {42,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^7 * z^-3 * y^10 ] T81.887 : Triangle type {42,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^5 * z^-4 * x^6 ] T81.888 : Triangle type {42,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T81.889 : Triangle type {42,56,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-4 * x * z^-4 * x^2 * z^-4 ] T81.890 : Triangle type {42,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-6 * z^2 * y^-3 * x^4 * y^-9 ] T81.891 : Triangle type {42,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T81.892 : Triangle type {42,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-26 * z * x^-8 * y * x^-7 ] T81.893 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T81.894 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-23 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-6 ] T81.895 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^4 * z^-5 * y^6 ] T81.896 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-3 ] T81.897 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-5 * z * x^-6 * y * x^-6 * y^3 * x^-8 ] T81.898 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-13 * z * y^-3 * x^2 * y^-10 ] T81.899 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T81.900 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^3 * x^-5 * z^12 ] T81.901 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^41 * z^-2 * x^8 * z^-1 * x^4 ] T81.902 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T81.903 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T81.904 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, y * x^-1 * y^6 * x^-6 * y^2 ] T81.905 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, y^2 * z^-1 * y * z^-5 * y^2 * z^-4 ] T81.906 : Triangle type {55,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^10 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z^5 ] T81.907 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * y * x^-1 * z, z^-2 * y^4 * z^-4 ] T81.908 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-7 * z * y * x^-4 * z * x^-1 * z * x^-4 * y ] T81.909 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^5 * x^-1 * z^2 * x^-1 * z^6 ] T81.910 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x * y^-2 * x^9 ] T81.911 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x * z^-1 * x * z^-1 * x^4 * z^-3 ] T81.912 : Triangle type {56,56,84} Group order 168 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^11 * y^-1 * z^4 * x^-2 * z^5 * x^-1 * z^6 ] T81.913 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^7 * y^-1 * x^12 * y^-1 * x^62, y * z^-1 ] T81.914 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T81.915 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T81.916 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^3 * z^-3, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T81.917 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^3 * z^-2 * x^8 ] T81.918 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T81.919 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T81.920 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^9 * y^-1 * x^12 * y^-1 * x * y^-1 * x * y^-1 * x ] T81.921 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y^5 * z^-4 * y * x^-3 * y^4 ] T81.922 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-11 * x * y^-4 * z * y^-5 * x^2 * y^-11 ] T81.923 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^4 * z^-1 * x^4 * y^-5 * x^3 ] T81.924 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^-6 * x * y^-2 * z^3 * y^-5 ] T81.925 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^7 * y^-6 ] T81.926 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^5 * y^-1 * z^4 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z^5 ] T81.927 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-43 * x * y^-11 ] T81.928 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-6 * z * y^-6 * z^2 * y^-7 ] T81.929 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^2 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T81.930 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T81.931 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^6 * z^-3 * x^6 * y^-1 * x^2 ] T81.932 : Triangle type {82,164,164} Group order 164 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T81.933 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x^-2 * y^-1, y^-64 * x * y^-17, x * z^-1 ] T81.934 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-42 * x^2 * y^-11 ] T81.935 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-19 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T81.936 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T81.937 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^4 * y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T81.938 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T81.939 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-3 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-2 ] T81.940 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-2 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T81.941 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T81.942 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-5 * x^2 * y^-8 ] T81.943 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^7 * x^-5 * y^2 ] T81.944 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^7 * y^-4 * z * y^-2 ] T81.945 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * x^-5 * y, z^-4 * x * z^-4 * x * y * z^-4 ] T81.946 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-5 * x * z^-4 * x * y * z^-4 ] T81.947 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x^3 * z^-2 * x^8 ] T81.948 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T81.949 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T81.950 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^4 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z^5 ] T81.951 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^-4 * x^3 * y^-6 * x * y^-1 ] T81.952 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^7 * z^-4 * x^8 ] T81.953 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-1 * z^4 * y^-1 * z^4 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T81.954 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T81.955 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T81.956 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-16 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T81.957 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^11 * z^-3 * x^6 * z^-1 * x^4 ] T81.958 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-14 * x^2 * y^-3 ] T81.959 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, x * y^-1 * x^6 * y^-6 * x ] T81.960 : Triangle type {163,163,163} Group order 163 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^7 ] Genus 82 T82.1 : Triangle type {2,3,8} Group order 3888 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z^2 * y * x * z * y * z^-3 * x * z * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2, x * z^3 * y * z^-2 * x * z * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T82.2 : Triangle type {2,3,8} Group order 3888 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z^2 * y * x * z * y * z^-3 * x * z * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2, z * y * x * z^2 * y * x * z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T82.3 : Triangle type {2,3,12} Group order 1944 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * z^-2 * x * z * y * z^-2 * x * z^2 * y^-1 * z^-1, z^2 * y * x * z * y * z^-3 * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * z^2 ] T82.4 : Triangle type {2,3,12} Group order 1944 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3, z^2 * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 ] T82.5 : Triangle type {2,3,18} Group order 1458 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^5 * y^-1 * z^-6, z * y * x * z^3 * y * x * z * y^2 * x * y^-1 * z^-1 * x * z^2, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T82.6 : Triangle type {2,3,18} Group order 1458 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^2 * x * y^-1 * z^-1 * x * z^2, y * x * z * y * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z, z^7 * y * z^-1 * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z^4 * y^-1 * z^-2 * x * z^2 ] T82.7 : Triangle type {2,3,18} Group order 1458 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^2 * x * y^-1 * z^-1 * x * z^2, y * x * z^5 * y * x * z * y * z^-4 * x * z, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y * z^3 * y^-1 * z^-2 ] T82.8 : Triangle type {2,3,18} Group order 1458 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^2 * x * y^-1 * z^-1 * x * z^2, y * x * z^5 * y * x * z * y * z^-4 * x * z, z^2 * y * z^-1 * x * z * y * x * z^2 * y * x * z * y^2 * z^-4 * x * z ] T82.9 : Triangle type {2,3,24} Group order 1296 Chiral action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z^2 * y * x * z * y^2 * z^-2 * x * y^-1 * z^-2, x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T82.10 : Triangle type {2,3,24} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, z^2 * y * x * z^2 * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T82.11 : Triangle type {2,3,24} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * x * z * y * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z, z * y * z^-1 * x * z^5 * y * x * z * y * z^6 ] T82.12 : Triangle type {2,4,6} Group order 1944 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^-1 * z * y^2 * z^-1 * x * z * y^-1 * z * y^-1, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z ] T82.13 : Triangle type {2,4,6} Group order 1944 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^6, (y * z^-2)^4, x * z * y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T82.14 : Triangle type {2,4,8} Group order 1296 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y * z^-1 * y * x * z * y^-2 * z^-2 * y * z^-1 * y * z^-2 ] T82.15 : Triangle type {2,4,8} Group order 1296 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-1)^6, z^-1 * x * z * y * z^-2 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T82.16 : Triangle type {2,4,12} Group order 972 Chiral action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-3 * y ] T82.17 : Triangle type {2,4,12} Group order 972 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^-1 * y * z^-1 * x * z * y^-1 * z^-5 ] T82.18 : Triangle type {2,4,12} Group order 972 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3 * y * z^-1)^2, z^12, z^2 * y^-1 * z * y * z^-1 * y * z^-2 * x * z^2 * y^-1 ] T82.19 : Triangle type {2,4,12} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.20 : Triangle type {2,4,12} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^12, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2, z^3 * y * x * z * y * x * y^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T82.21 : Triangle type {2,4,12} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-4 * x ] T82.22 : Triangle type {2,4,12} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-2 * x * z * y^2 * z^-1 * x * z^3, (y * z^-3 * y * z^-1)^2 ] T82.23 : Triangle type {2,4,40} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z * y^-2 * z^-4 * y, z^7 * y * x * z^4 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x * z ] T82.24 : Triangle type {2,4,166} Group order 664 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-38 * x * y * z^-127 ] T82.25 : Triangle type {2,4,328} Group order 656 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y^-1 * z^-126 ] T82.26 : Triangle type {2,5,10} Group order 810 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2 ] T82.27 : Triangle type {2,6,6} Group order 972 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y^2 * x * y^-2 * z^2 * y^-1 * z^-2, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1 ] T82.28 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T82.29 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (z^-1 * y^2 * z^-1)^3 ] T82.30 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-2 * y * z^-1 * y)^2 ] T82.31 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z * y * x * z * y^3 * z^-1 * x * z * y^-2 ] T82.32 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T82.33 : Triangle type {2,6,6} Group order 972 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z * y^-2 * z * y^-2 * z * y^-2 * z * y^-3 * x * y^-2 * z * y^-2 * z^-1 * y * z^-1 * y^2 * z^-1 * y * x ] T82.34 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^3 * y^-1 * z^-4, (y * z^-1 * y)^4 ] T82.35 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * y * x * z ] T82.36 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * z^3 * y^-1 * z^-6 ] T82.37 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z * y^-2 * z * y^-2 * z^-1 * y * z^-1 * x * z ] T82.38 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-1 * y * z^-2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T82.39 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^-1 * z^-4, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y, y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z^-2 * x ] T82.40 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y, z^12 ] T82.41 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z^2 * y^-2 * z^-5 ] T82.42 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, (y * z^-1 * y * z^-1 * y)^2, z^-2 * x * z^3 * y^-1 * z^-6 ] T82.43 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-2 * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z^-2 ] T82.44 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.45 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.46 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.47 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * x ] T82.48 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z^-2 * x * y^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.49 : Triangle type {2,6,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^6, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.50 : Triangle type {2,6,30} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * z^-3 * x * y^-1 * z^-4 * x ] T82.51 : Triangle type {2,6,30} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^15 * y^-1 * x * z * y^-1 * z^-10 ] T82.52 : Triangle type {2,6,30} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-13 * x * z^3 * y * z^-7 * x * z^4 * y^-1 * z^-1 ] T82.53 : Triangle type {2,6,30} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-14 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T82.54 : Triangle type {2,6,84} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-12 * x * z * y * z^-1 * x * z * y * z^-4 * x * y * z^-6 ] T82.55 : Triangle type {2,6,84} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^61 * y * x * z * y^-1 * z^-9 * x * z^11 ] T82.56 : Triangle type {2,6,84} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-48 * x * z^21 * y^-1 * x * z^7 * y^-1 * z^-6 ] T82.57 : Triangle type {2,6,246} Group order 492 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^67 * y * z^-1 * x * z^7 * y^-1 * z^-3 * x * z^2 ] T82.58 : Triangle type {2,8,8} Group order 648 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y^2 * z^-1 * y^3 * x * y^-2 * z^-1 * x ] T82.59 : Triangle type {2,8,8} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y^3 * z^-1)^3 ] T82.60 : Triangle type {2,9,18} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z^3 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T82.61 : Triangle type {2,9,18} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-2 * y * z^-1, x * z^2 * y * z^-2 * x * y^-1 * z^4 * y^-1 * z^-2 ] T82.62 : Triangle type {2,9,18} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, z^-5 * y * x * z^4 * y^-1 * z^-2 ] T82.63 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T82.64 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.65 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T82.66 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T82.67 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y ] T82.68 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y^-1 * z * y^-1 * z * y^-2 * z^-2 * x * y^-1 * z ] T82.69 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.70 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.71 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-2 * z^-2 * x * y^-1 * z ] T82.72 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-2 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T82.73 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-2 * y^2, y^-1 * z * y^-1 * z * y^-2 * z^-2 * x * y^-1 * z, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y ] T82.74 : Triangle type {2,9,18} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^3 * y^2 * x * z^2, y^-9, x * z^2 * y * z^-1 * y * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T82.75 : Triangle type {2,9,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z^3 * y^-1 * z^-4 ] T82.76 : Triangle type {2,10,205} Group order 410 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-8 * x * z^20 * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T82.77 : Triangle type {2,12,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z^-1 * y * z^-1 * x * y^-1 * z^-3 * y ] T82.78 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, z * y^-4 * z * y^-1 * z^-1 * x ] T82.79 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^12, (y * z^-1 * y^4)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T82.80 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, z^-1 * x * y^-3 * z^-2 * y^2 ] T82.81 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T82.82 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^12, (y * z^-1 * y^4)^2, z^-3 * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T82.83 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12, z^3 * y * z^-2 * x * z^6 ] T82.84 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z * y^-3 * z * y^-1 * z^-1 * y, y^12, z * y * z^-4 * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T82.85 : Triangle type {2,12,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-3 * z^-1 * x * y^-2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T82.86 : Triangle type {2,18,63} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, z^10 * y * z^-4 * x * z^4 * y^-1 * z^-1 * x ] T82.87 : Triangle type {2,21,42} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z^2 * y^-3 * z^3 * y^-1 * z * y^-5 * z * y^-1 * z * y^-2 ] T82.88 : Triangle type {2,30,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-6 * z^-1 * y^5, y^-1 * z^10 * y^-1 * z^4 * y^-7 * z * y^-4 * z * y^-1 ] T82.89 : Triangle type {2,30,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-17 * z^4 * y^-5 * z^4 ] T82.90 : Triangle type {2,30,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^7 * z^-1 * y * z^-1, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T82.91 : Triangle type {2,40,40} Group order 360 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z^-1 * y * z^-2, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-2 * z * y^-4 * z * y^-2 * z * y^-2 ] T82.92 : Triangle type {2,57,114} Group order 342 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-24 * y^10 * z^-1 * y * z^-2 * y * z^-17 ] T82.93 : Triangle type {2,84,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-7 * y * z^-1 * y^10 * z^-4 * y^17 * z^-2 ] T82.94 : Triangle type {2,165,330} Group order 330 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^115 * y^-48 * z ] T82.95 : Triangle type {2,166,166} Group order 332 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^50 * z^-116 ] T82.96 : Triangle type {2,328,328} Group order 328 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^49 * z^-115 ] T82.97 : Triangle type {3,3,4} Group order 1944 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, y * x^-1 * y * x^-1 * z * y * x * z * y * x^-1 * z * y * z^-1 * x^-1 * y^-1 * x * z ] T82.98 : Triangle type {3,3,4} Group order 1944 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 ] T82.99 : Triangle type {3,3,4} Group order 1944 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, z^-1 * x * z * y * x * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y^-1 * x * y^-1 ] T82.100 : Triangle type {3,3,4} Group order 1944 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, z^2 * x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z * y * z^-1 * x ] T82.101 : Triangle type {3,3,4} Group order 1944 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, z * y^-1 * x * z * y * z^-1 * x^-1 * y * x * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x ] T82.102 : Triangle type {3,3,6} Group order 972 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, y^-1 * z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 * x, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 ] T82.103 : Triangle type {3,3,6} Group order 972 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, y^-1 * x * y^-1 * x * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * x ] T82.104 : Triangle type {3,3,9} Group order 729 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x, z^4 * y^-1 * x^-1 * z^4, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T82.105 : Triangle type {3,3,9} Group order 729 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, (z^-1 * x^-1 * y^-1)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1 ] T82.106 : Triangle type {3,3,9} Group order 729 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x * z^-1 * x ] T82.107 : Triangle type {3,3,9} Group order 729 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x, z^4 * y^-1 * x^-1 * z^4, z^-1 * x * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 ] T82.108 : Triangle type {3,3,9} Group order 729 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x * z * y * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z^-1 * x ] T82.109 : Triangle type {3,3,12} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-4 * x^-1 * z^3 * y^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * z * y * x * y^-1 ] T82.110 : Triangle type {3,3,12} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-4 * x^-1 * z^3 * y^-1, z * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * x^-1 ] T82.111 : Triangle type {3,3,12} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^-1 * x * y^-1 * x * z^2 * y^-1 * z^-2 * x * z^-1 * x^-1 * z^2 * y ] T82.112 : Triangle type {3,3,12} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, z^-4 * x^-1 * z^3 * y^-1, y * x^-1 * y * z^-1 * x^-1 * y * x * z * y * z^-2 * x^-1 ] T82.113 : Triangle type {3,3,12} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1, x^-1 * z * y * x^-1 * y * x^-1 * y * x * y^-1 * x * z ] T82.114 : Triangle type {3,3,21} Group order 567 Chiral action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x, z * y^-1 * z^-3 * x^-1 * z^4, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T82.115 : Triangle type {3,3,57} Group order 513 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y * z^-3 * x * z^3 * y * x * z^4 * y * x ] T82.116 : Triangle type {3,3,84} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^3 * y * x * y^-1 * x^-1 * z^4 * y * x ] T82.117 : Triangle type {3,4,4} Group order 972 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (y * x^-1 * z)^3, (z^-1 * x^-1 * y^-1)^3 ] T82.118 : Triangle type {3,4,4} Group order 972 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-2 * y * z^-1 * y * x^-1 * z * y * x * y^-1, y^-1 * z^-1 * x^-1 * z * y^2 * z^-1 * x^-1 * z * y^-1 ] T82.119 : Triangle type {3,4,6} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z * y^-2 * x * z * y * x^-1 ] T82.120 : Triangle type {3,4,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, x^-1 * y * z^-1 * y * x^-1 * z * y * z^-2, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T82.121 : Triangle type {3,4,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T82.122 : Triangle type {3,4,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, (x * y^-1 * z^-1 * y)^2, (x * z^2 * y)^2 ] T82.123 : Triangle type {3,4,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T82.124 : Triangle type {3,4,6} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-1 ] T82.125 : Triangle type {3,4,24} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-6 * x * y^-1 * z^-5 ] T82.126 : Triangle type {3,6,6} Group order 486 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^-2, z * y * x^-1 * y * x^-1 * y^-1 * z * y * x ] T82.127 : Triangle type {3,6,6} Group order 486 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2, z^2 * y^2 * x^-1 * y^-1 * z^-1 * x^-1, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1 ] T82.128 : Triangle type {3,6,6} Group order 486 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y^-1 * z * x^-1 * y^-1 * x * z^2 * y^-1, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2 ] T82.129 : Triangle type {3,6,6} Group order 486 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-2 * x^-1 * y^-1 * x * y^-2 * z^-1, (y * x^-1 * z)^3, y^-3 * z^-1 * x^-1 * z^2 * y^-1 * z ] T82.130 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, (z^-1 * x^-1 * y^-1)^3 ] T82.131 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T82.132 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, (z^-1 * x^-1 * y^-1)^3 ] T82.133 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T82.134 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-1 * x^-1 * y^-1 * x * z^2 * y^-1 * z^-1 * x * y^-1 * x^-1 * z * y * z^-1 * x * z^-2 ] T82.135 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1, (z^-1 * x^-1 * y^-1)^3 ] T82.136 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, x^-1 * z * y^-2 * x * z * y^-1 * z ] T82.137 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1, y * z^-1 * y^2 * x^-1 * y^-1 * z^3 ] T82.138 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^-2 * z * y^-2 * z^-1 * y * x^-1 * y^-1 * z^3 * y * x ] T82.139 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T82.140 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (y * z^-2)^2, z^6, y^2 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z ] T82.141 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T82.142 : Triangle type {3,6,6} Group order 486 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * x * y^-1 * x * z * y * x * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 * x^-1 * z ] T82.143 : Triangle type {3,6,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, x^-1 * z * y^-2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y^-1 * x * z^3 ] T82.144 : Triangle type {3,6,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, x^-1 * z * y^-2 * x * y^-1 * z^-1 * y, x * z^2 * y^-1 * x * z^2 * y ] T82.145 : Triangle type {3,6,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, x^-1 * z * y^-2 * x * y^-1 * z^-1 * y, (x * z^2 * y)^2 ] T82.146 : Triangle type {3,6,8} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1 ] T82.147 : Triangle type {3,6,14} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, y^-1 * z^-2 * x^-1 * z^3, y^2 * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x^-1 ] T82.148 : Triangle type {3,6,38} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, y * x * y^-2 * x * z^3 ] T82.149 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-1 * x^-1 * z^4, z * y^-4 * z * y^-1 * z * y^-1 ] T82.150 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^2 * x^-1 * z^3 ] T82.151 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x * y^-1 * z^-1, z^2 * x^-1 * y^-1 * x * z * y^-2, z^2 * y^2 * x^-1 * z^3 ] T82.152 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^2 * x^-1 * z^3 ] T82.153 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * y * x * y^-1 * z^-1, z^2 * x^-1 * y^-1 * x * z * y^-2, x * z * y^-1 * z^-1 * x^-1 * z^3 * y ] T82.154 : Triangle type {3,9,18} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x * z * y * x^-1 * y^-1 * z^-3 ] T82.155 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * y^4 * z^-3 ] T82.156 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T82.157 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * y^-1 ] T82.158 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^-1 * z * y * x^-1 * y^-1 * z^2, y * z^-1 * x^-1 * y^-1 * x * z^2 * y ] T82.159 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-3 * z^3 * y^-1 * z * x * y^-2 * z * y^-1 ] T82.160 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-2 * x^-1 * y * x^-1 * z * y * x * z^-1 ] T82.161 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x * y^-1 * x * y^-2 * z ] T82.162 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * z * y^-2 ] T82.163 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y, y^-2 * z^2 * y^-1 * z^2 * y^-1 * x * y^-2 * z^2 ] T82.164 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, y * z^-3 * y * z^-1 * y^2 * z^-1 * y^2 * z^-1 ] T82.165 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-1 * z^-2, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T82.166 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^2 * y^-3 * z * x^-1 * z * y^-1 * z^4 ] T82.167 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^2 * x^-1 * y * x^-1 * y^2 * x^-1 * z, z^-2 * x^-1 * y * x^-1 * y * z^-1 * x * y^-1 ] T82.168 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * y^-2, z * y^-4 * z * y^-1 * x * z * y^-3 * z ] T82.169 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^-1 * z^4 * y^-1 * z^2 * x^-2 * y^-3 * z ] T82.170 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, z^-3 * y^3 * z^-1 * y^2 * z^-1 * y * z^-1 ] T82.171 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * z^-2 * x^-1 * y^-2 * z, y^-3 * z * y^-4 * x^-1 * y^-3 * z ] T82.172 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, y^-2 * z^2 * y^-1 * z * x^-1 * z * x * y^-1 * z * y^-1 * z * y^-1 ] T82.173 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^-1 * x * z * y^-1 * z^2 * y * x * y^2 * z^-1 * y^2 * z^-1 ] T82.174 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, y * z^-2 * x^-1 * z^3, y * z^-1 * y * z^-1 * y^3 * z^-1 * y^2 * z^-2 ] T82.175 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * x^-1 * z)^3, y^-1 * z * y^-4 * z * x^-1 * y^-4 * z ] T82.176 : Triangle type {3,12,12} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^-2 * z * y^-8 * z ] T82.177 : Triangle type {3,30,30} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-9 * y * z^-3 * y^8 * z^-2 * y^3 * z^-1 * y^2 ] T82.178 : Triangle type {3,30,30} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-12 * y * z^-2 * y^7 * z^-3 * y^4 * z^-1 ] T82.179 : Triangle type {3,30,30} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y * z^-8 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y^4 * z^-1 * y^4 * z^-2 * y * z^-1 * y ] T82.180 : Triangle type {3,30,30} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, (y * z^-1 * y^3)^2 ] T82.181 : Triangle type {3,33,44} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-3 * z * y^-1 ] T82.182 : Triangle type {3,83,249} Group order 249 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-71 * z * y^-9 * z^2 ] T82.183 : Triangle type {3,84,84} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y * z^-1 * y^10 * z^-1 * y^70 * z^-1 ] T82.184 : Triangle type {3,84,84} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-10 * y * z^-2 * y^7 * z^-3 * y * x^-1 * y^3 ] T82.185 : Triangle type {3,84,84} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^14 * z^-70 ] T82.186 : Triangle type {3,246,246} Group order 246 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^11 * z^-1 * y^69 * z^-1 ] T82.187 : Triangle type {4,4,4} Group order 648 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x^-1 * z * x^-1 * y * x^-2 * z * y^2 * z^-1 * x^-1, x * z^-2 * y * x^-2 * y^-1 * z^2 * y * z^-1 ] T82.188 : Triangle type {4,4,4} Group order 648 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y * z^-1 * x^-1 * y * x^-2 * y^-1 * x * z^-1 * x * z^-1, x * y^-1 * z^-1 * y * x^-2 * y^-1 * z * y^2 * z^-1 ] T82.189 : Triangle type {4,4,4} Group order 648 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x * z * x^-1 * y * x^-2 * y^-1 * z^-1 * x * z * y^-1, x^-1 * y^-2 * z^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z ] T82.190 : Triangle type {4,4,4} Group order 648 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y * z^-1 * x^-1 * y * x^-2 * z * x^-1 * y^-1 * z * x^-1, y^-2 * z^-1 * y * x^-2 * y^-1 * z^2 * y * x^-1 ] T82.191 : Triangle type {4,4,4} Group order 648 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, (y * x^-1 * z)^3, (z^-1 * x^-1 * y)^3 ] T82.192 : Triangle type {4,4,20} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * z * x^-1 * z, y^-1 * z^-3 * x^-1 * z * y * x^-1 * z^4 ] T82.193 : Triangle type {4,4,20} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, z^-1 * x^-1 * y * x^2 * z * y * x, z * y^-1 * z^-3 * x^-1 * y^-1 * z^-3 * x * z ] T82.194 : Triangle type {4,4,83} Group order 332 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-66 * x * y^-1 * x * y^-1 * z^-15 ] T82.195 : Triangle type {4,4,164} Group order 328 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-65 * x * y^-1 * z^-16 ] T82.196 : Triangle type {4,6,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, (z^-1 * x)^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T82.197 : Triangle type {4,6,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, x * z * y * x^2 * z * y^-1 * z^-1 ] T82.198 : Triangle type {4,6,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * x)^3, y^2 * x^-2 * y^-1 * z * x^-1 ] T82.199 : Triangle type {4,6,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, (z^-1 * x)^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T82.200 : Triangle type {4,6,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z^2 * y * z^-1 * x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x^-1 ] T82.201 : Triangle type {4,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^-2, y * z^-3 * x^-1 * z^4 ] T82.202 : Triangle type {4,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-5 * x * z^2 * y^-1 * z^-3 * x * y^-1 * z^-4 * x * z * y^-1 * z^-6 ] T82.203 : Triangle type {4,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-6 * x * z^3 * y^-1 * z^-1 * x^-1 * z^7 * y^-1 * z^-5 ] T82.204 : Triangle type {4,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y * z^-1 * y * x^-1 * y^2 * z^-1, y^-7 ] T82.205 : Triangle type {4,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, (z^-1 * y)^3, y^-7 ] T82.206 : Triangle type {4,8,34} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x * z * y^-1 * z^-6 * x^-1 * y^-1 * z^-10 * x^-1 ] T82.207 : Triangle type {4,10,14} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, z^-3 * x * z^2 * y * x^-1 * z * y * x^-1 * y * x * z * y * z^-3 ] T82.208 : Triangle type {4,12,42} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^-1 * z^7 * y * x * z^8 * y * z^-4 ] T82.209 : Triangle type {4,14,28} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-1 * x * z^-2 * y ] T82.210 : Triangle type {4,24,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, x^-1 * z * y^-1 * z^-8 ] T82.211 : Triangle type {4,110,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^24 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.212 : Triangle type {5,5,5} Group order 405 Reflexible action Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, (z^-1 * x)^3, z^-1 * y * x^-2 * y^2 * z^-1 ] T82.213 : Triangle type {5,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-14 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T82.214 : Triangle type {5,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.215 : Triangle type {5,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^11 * z^-1 * y^3 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.216 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, y^6, z^6, y^2 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T82.217 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^6, z^-2 * x^-2 * z * y^-1 * x ] T82.218 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T82.219 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z^6, z^-1 * y * x^-2 * y^-2 * x ] T82.220 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, z^6, z^-2 * y * x^-1 * z * y^-2 ] T82.221 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, x^-1 * y * x^-2 * z * y^2, z^-1 * y * x^-2 * y^-2 * x ] T82.222 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^6, (x * z * y^-1 * x)^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T82.223 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T82.224 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z^6, z * y * x^-2 * y^-2 * x ] T82.225 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1 ] T82.226 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2 ] T82.227 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y * x^-3 * z * x^-2, z^-2 * y * x^-1 * z * y^-2 ] T82.228 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y * x^-3 * z * x^-2, y * z^-2 * x^-1 * y^-2 * z ] T82.229 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T82.230 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, z^6 ] T82.231 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z^-1 * y, y^6, z^6, z^-2 * x^-2 * y^-1 * z^-1 * x ] T82.232 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, (z^-1 * x^-1 * y^-1)^3 ] T82.233 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T82.234 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * y^-1 * z, z * y^-2 * x * z^-1 * x, y^6 ] T82.235 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^6, z^-2 * x^-2 * z * x^-1 * y, y * z^-1 * y * x^-1 * z^2 * y ] T82.236 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * z * y^-1 * x, z^-2 * y * x^-1 * z * y^-2, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T82.237 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^6, z^-2 * x^-2 * z * x^-1 * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T82.238 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^6, y^6, x^2 * z^-2 * x^2 * z^-1 * x * z^-2 * x * z^-1 ] T82.239 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * z^-1 * x)^2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (y * z^-1 * y)^2 ] T82.240 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T82.241 : Triangle type {6,6,6} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^6, z^-2 * x^-2 * z * x^-1 * y, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T82.242 : Triangle type {6,6,15} Group order 270 Reflexible action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^2 * y * x^-1 * z * y^-1 * x ] T82.243 : Triangle type {6,6,15} Group order 270 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-1 * x * y^-1 * x * z^4 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-3 ] T82.244 : Triangle type {6,6,15} Group order 270 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^15 ] T82.245 : Triangle type {6,6,15} Group order 270 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^6 * y * x * z^6 * y * z^-1 * x ] T82.246 : Triangle type {6,6,42} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, z^3 * x^-1 * y^-1 * z^2 ] T82.247 : Triangle type {6,6,42} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * z * y^2, z^-3 * x^-1 * z * y^-1 * z^-1 ] T82.248 : Triangle type {6,6,42} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * z * y^-1 * x * z^-1 * y, y^6, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * x^-1 * z^3 ] T82.249 : Triangle type {6,6,42} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z * y^-1 * z^-1 * x^-1 * z^3, z^-1 * y * z^-1 * x^2 * z^-1 * y * z^-1 ] T82.250 : Triangle type {6,6,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-9 * x^-1 * y^-1 * z^-4 ] T82.251 : Triangle type {6,6,42} Group order 252 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, x * z^3 * y^-1 * z^-3 * x^-1 * y * z^-1 * x^-1 * y * z^-4 ] T82.252 : Triangle type {6,6,42} Group order 252 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * y * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 * z^-4 ] T82.253 : Triangle type {6,6,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-42 ] T82.254 : Triangle type {6,6,42} Group order 252 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^22 * y^-1 * z^-12 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T82.255 : Triangle type {6,6,123} Group order 246 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^23 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^7 * y * z^-5 * x^-1 ] T82.256 : Triangle type {6,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, z^-2 * x * z^2 * y^-1 * x * y^-1 * z^-4 ] T82.257 : Triangle type {6,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * y * x^-1 * y^3 ] T82.258 : Triangle type {6,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * z^2 * y^-1 ] T82.259 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-1 * y^4 * x^-1 * y * z^-1 * y * z^-4 * y * z^-1 * y^3 ] T82.260 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-3 * x^2 * y^-3 ] T82.261 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z * x^-1 * y^-3 ] T82.262 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, y^-1 * x * z^3 * y * z^-1 * x^-1 * z * y * z^-3 * x * z ] T82.263 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y^2 * z^-2 ] T82.264 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-5 * y * z^-1 * y * x * z^-1 * y * z^-2 * y * x^-1 * y * z^-1 * y^2 ] T82.265 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^-2 * x^-1 * z^2 * y * x * z^3 * y^-1 * z^-3 ] T82.266 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * x * z^-1 * x * z^-3 ] T82.267 : Triangle type {6,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-3 * z^4 ] T82.268 : Triangle type {6,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^2 * x^-1 * z * y^2 ] T82.269 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, (y^-2 * z * y^-1)^3 ] T82.270 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y * x^-1 * y * x^-1 * y^-1 * x * z ] T82.271 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T82.272 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, x^-1 * z * y^-1 * x * z^2 ] T82.273 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^3 * x^-1 * z^3 ] T82.274 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^4 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T82.275 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^3 * y^-1 * z * y^-1 * z * y^-1 * z^4 ] T82.276 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, x * y^-2 * x * z * y^-1, z^-2 * y * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z ] T82.277 : Triangle type {6,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-1 * y^7 * z^-1 ] T82.278 : Triangle type {6,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x * z^-2, y * x^-3 * z * x^-2 ] T82.279 : Triangle type {6,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2 ] T82.280 : Triangle type {6,30,35} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^3 * y * x * z^3 ] T82.281 : Triangle type {6,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.282 : Triangle type {6,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T82.283 : Triangle type {6,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^12 * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T82.284 : Triangle type {8,9,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-1 * z * y^-3 * x * y^-4 ] T82.285 : Triangle type {8,12,24} Group order 216 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^2 * z^-1 * y, y^2 * x^2 * z^2, x^8 ] T82.286 : Triangle type {8,12,24} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * z * y^-1, (z^-1 * x)^3, (y * z^-2)^2, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T82.287 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, (z^-1 * x)^3, z * y^-1 * z * x^-1 * y^-1 * z * y^-1 ] T82.288 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, (z^-1 * x)^3, x * z * x^-2 * y^-1 * z^-2 ] T82.289 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, (z^-1 * x)^3, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * z * y^-1 * z^2 ] T82.290 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x * z^-1 * x^-2 * y * x * z^-1 ] T82.291 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x * z^-1 * x^-2 * y * x * z^-1, x^8 ] T82.292 : Triangle type {8,12,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, x^8, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T82.293 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, y^2 * x^-1 * z^2, x^-1 * y * x^-2 * y * z^-1 * x^-1, z^-1 * x * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T82.294 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T82.295 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, (y^-1 * x)^3, (z^-1 * y)^3, x^-1 * y^-1 * x^3 * y^-1 * z * x^-1 ] T82.296 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, (y^-1 * x)^3, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y^-2 * x^3 * z * x^-2 ] T82.297 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, x^-1 * y^-1 * x^3 * y^-1 * z * x^-1 ] T82.298 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, z^-1 * y^3 * z^-2, y * z^-1 * y * x * y^-1 * z^-1, z^-1 * x * z^-1 * x * z * y^-1, y^-2 * x^3 * z * x^-2 ] T82.299 : Triangle type {9,9,9} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * z^-1 * y * x * y^-1 * z^-1, y^-2 * x^3 * z * x^-2 ] T82.300 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-9, y^-9 ] T82.301 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * y^-1 * z^-1, y^-9 ] T82.302 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^-1 * z^-1, y^-9 ] T82.303 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x * z^-1 * x * z * y^-1, y^9 ] T82.304 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, y^-9 ] T82.305 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^9 ] T82.306 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, (z^-1 * x^-1 * y^-1)^3 ] T82.307 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T82.308 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, (y^-1 * x)^3, x^-1 * z * y^-1 * x * z^-1 * y, (z^-1 * x)^3 ] T82.309 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, (y^-1 * x)^3, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2 ] T82.310 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x^-3 * y^-1 * x^2, z^-1 * x * y^-1 * x^2 * y^-1 * z * y^-1, x * y^-1 * z^-1 * x^2 * z^-2 * y ] T82.311 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, (y^-1 * x)^3, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^-3 ] T82.312 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y^-1 * z^-1 * x * z * y^-1, z^-1 * y^2 * x^-1 * y^-3 ] T82.313 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-1 * y^-1 * x * z * x^-1, z^-1 * y^2 * x^-1 * y^-3 ] T82.314 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, y * z^-1 * y * x * y^-1 * z^-1 ] T82.315 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, y^-1 * z^-1 * x^-2 * z * y^-1 * z ] T82.316 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, (y^-1 * x)^3, (z^-1 * x)^3, (z^-1 * y)^3, z^-1 * x^-3 * y^-1 * x^2, y^-1 * z^-1 * x^-2 * z * y * x^-1 ] T82.317 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^-1 * z^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2 ] T82.318 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-1 * x^-2 * z * y * x^-1 ] T82.319 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^-1 * y * x^-2 * z * y^-1 * z^-1 ] T82.320 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * y^3 * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^-1 * z^-1, z^-1 * y * x^-2 * y^-1 * z^-1 * y ] T82.321 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y * x * y^-1 * x * y^-1 * z^-1 ] T82.322 : Triangle type {9,9,9} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, x^-1 * y^2 * x^-1 * z * y^2, (z^-1 * x^-1 * y^-1)^3 ] T82.323 : Triangle type {9,9,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-2 * x^2 * z * y^-1 ] T82.324 : Triangle type {9,9,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T82.325 : Triangle type {9,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, x * y^-2 * x * z^-1 * y ] T82.326 : Triangle type {9,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^2 * x^2 * z^-1 * y, x^-1 * z * y * x^-1 * z * x^-1 * z, z * y^-2 * x^2 * y^-1 * z * y^-1 ] T82.327 : Triangle type {9,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-1 * y^2 * x^2 * z^-1 * x^2 ] T82.328 : Triangle type {9,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * x^-1 * y^-1 * x * y^-1 * x, x^-9 ] T82.329 : Triangle type {9,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, z^-9 * y^8 * z^-1 * y * z^-2 ] T82.330 : Triangle type {9,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-9 * z^5 * y^-1 * z * y^-5 ] T82.331 : Triangle type {12,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^-2 * y^2 * z^-1, y^2 * x^-2 * y^-1 * x * z, z * y * x^-2 * z^2 * x^-1 ] T82.332 : Triangle type {12,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * z * y^-1, x * z * y^-1 * x * y^-1 * z^-1, (x * z * y)^2 ] T82.333 : Triangle type {12,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, z * y * x^2 * y^-1 * z, y * z^-1 * x^2 * z * y ] T82.334 : Triangle type {12,12,12} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, (x * z * y)^2, y^-1 * x^4 * y^-3 ] T82.335 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-1 * x^-3 * y * z^-1 * y * z^-1 ] T82.336 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^-4 * y^-1 * x * z, y^-1 * z * y * x^-1 * y^-3 ] T82.337 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x ] T82.338 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * z^2, z^-1 * x^-3 * y * x^2, y^3 * x^-1 * y^-2 * z ] T82.339 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^-4 * y^-1 * x * z, y^-1 * z * y * x^-1 * y^-3 ] T82.340 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, y * z^-1 * x^-3 * y * z^-1 * y * z^-1 ] T82.341 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * x^-3 * y * z^-1 * y * z^-1 ] T82.342 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-4 * y * x * z^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^-1 * z * y * x^-1 * y^-3 ] T82.343 : Triangle type {12,12,12} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^3 ] T82.344 : Triangle type {12,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^-9 * z^2 * y^-4 ] T82.345 : Triangle type {12,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^2 * z^-1 * y * z^-5 * y^2 * z^-4 ] T82.346 : Triangle type {15,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T82.347 : Triangle type {15,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T82.348 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T82.349 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T82.350 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x^2 * z^-3, y^4 * x^-1 * y * z^-1 * y * z^-1 ] T82.351 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-2 * x * y^-1 * x^8 * y^-1 * x^2 ] T82.352 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, z^-3 * y^8 * z^-1 ] T82.353 : Triangle type {15,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, z^-3 * y^6 * z^-3 ] T82.354 : Triangle type {16,88,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-2, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T82.355 : Triangle type {16,88,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x^2 * z^-4, y^-4 * x^2 * y^-7 ] T82.356 : Triangle type {16,88,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, z^2 * x^-5 * z^4 * x^-1 * z * x^-1 * z^4 ] T82.357 : Triangle type {16,88,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, y^-3 * x^6 * y^-8 ] T82.358 : Triangle type {18,30,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-2 ] T82.359 : Triangle type {18,30,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^-3 * x^5 * y^-6 * x * y^-1 ] T82.360 : Triangle type {20,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3, x^-1 * y^3 * x^-1 * y^6 ] T82.361 : Triangle type {20,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^5 * y^-1 * x * y^-1 * z^-1 * x^6 * y^-1 * x * y^-1 * z^-1 * x * y^-1 * x^2 ] T82.362 : Triangle type {20,30,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^2 * z^-3, x^-6 * y^3 ] T82.363 : Triangle type {20,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-4 * y * x^-1 * z^3 * x^-8 * y * x^-1 * y * x^-3 ] T82.364 : Triangle type {21,21,21} Group order 189 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^2 * y^-6 * z * y^-2 ] T82.365 : Triangle type {21,21,21} Group order 189 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-6 * y^3, z^2 * x^-3 * z^4 ] T82.366 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y * x^-1 * y^3 * x^-1 * y * x^-1 * y^3 * z^-1 * y ] T82.367 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, x^-1 * y * x^-1 * y * x^-1 * y^3 * z^-1 ] T82.368 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x * z^-1 * x * z^-3 ] T82.369 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2, x^-5 * z^3 * y ] T82.370 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-1 * x * z^-3 * x * z^-1 * x * y * z^-4 ] T82.371 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * z^3, y^5 * z^-1 * y * z^-1 ] T82.372 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, (y * z^-3)^2 ] T82.373 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^-1 * y * x^-3 * y * x^-1 * z * y ] T82.374 : Triangle type {22,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^-3 * y * x^-5 * y * x^-1 * z * y ] T82.375 : Triangle type {25,35,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * x^-5 * y, z^-5 * x * z^-4 * x * y * z^-4 ] T82.376 : Triangle type {25,35,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T82.377 : Triangle type {25,35,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * z * x^-10 * y * x^-1 * y * x^-1 * y * x^-2 ] T82.378 : Triangle type {25,35,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^5 * z^-1 * y^4 * x^-6 * y^4 ] T82.379 : Triangle type {30,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x * z^-2 * y * z^-4 ] T82.380 : Triangle type {30,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1, y^5 * z^-1 * y * z^-1 ] T82.381 : Triangle type {30,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, z^-1 * y^2 * x^-1 * y^-3, x^3 * y^-2 * x^6 * y^-3 * x^2 * y^-1 * x ] T82.382 : Triangle type {30,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y * z^-6 * y * z^-1 * x * z^-4 * y ] T82.383 : Triangle type {30,30,30} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T82.384 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-2 * z * y^-6 * z^5 * y^-6 ] T82.385 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, x^-1 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T82.386 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T82.387 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-17 * z * x^-8 * y * x^-8 ] T82.388 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-3 * x^4 * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T82.389 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^-4 * y^6 * x^-4 * z * x^-5 ] T82.390 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z^6 ] T82.391 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^-9 * z^2 * y^-4 ] T82.392 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-7 ] T82.393 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T82.394 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, x^-2 * y^6 * x^-4 * z * x^-3 ] T82.395 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^16 * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T82.396 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-3 * x * y^-1 * x * y^-1 * z^2 * y^-9 * x * y^-1 * x * y^-3 ] T82.397 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, y^2 * z^-1 * y * z^-5 * y^2 * z^-4 ] T82.398 : Triangle type {34,85,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-3 ] T82.399 : Triangle type {42,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T82.400 : Triangle type {42,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-13 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-7 ] T82.401 : Triangle type {42,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-5 * y * x^-5 * y^4 * x^-1 * z * x^-7 ] T82.402 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T82.403 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^-2 * y^5 * x^-3 * z^2 * x^-3 ] T82.404 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^9 * y^-6 * x^3 ] T82.405 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-6 * y * z^-5 * y^6 * z^-3 ] T82.406 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 ] T82.407 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-17 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T82.408 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^-9 * z^2 * y^-4 ] T82.409 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-13 * z^2 * y^-6 * z^2 * y^-7 ] T82.410 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-35 * y * x^-1 * y * x^-1 * y * x^-17 ] T82.411 : Triangle type {56,84,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-4 * y * x^-7 * z * x^-10 * y * x^-1 * y * x^-1 * y * x^-2 ] T82.412 : Triangle type {57,57,57} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-8 * x * z^-13 * x^2 * z^-6 ] T82.413 : Triangle type {57,57,57} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^3 * y^-1 * z * y^-4 * z^5 * y^-1 * z^6 ] T82.414 : Triangle type {57,57,57} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, z^-3 * y * z^-5 * y^2 * z^-4 ] T82.415 : Triangle type {57,57,57} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^3 * z^-3 ] T82.416 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-27 * z * y^-14 ] T82.417 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-43 * x^2 * y^-11 ] T82.418 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^4 * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T82.419 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T82.420 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x * y^-1 * x^6 * y^-7 ] T82.421 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-7 * x^5 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T82.422 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-4 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T82.423 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^5 * z^-1 * y^4 * x^-6 * y^4 ] T82.424 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-11 * y^6 * z^-1 * y * z^-1 ] T82.425 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^8 * y^-6 * x^2 ] T82.426 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T82.427 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^5 * z^-4 * x^4 * y^-2 * x ] T82.428 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^7 * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T82.429 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T82.430 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-4 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-6 ] T82.431 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^3 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T82.432 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T82.433 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T82.434 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T82.435 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, y^-3 * x^4 * y^-7 ] T82.436 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T82.437 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T82.438 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-1 * x * y^-7 * z^2 * y^-3 * x^4 * y^-9 ] T82.439 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T82.440 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T82.441 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T82.442 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^8 * y^-4 * x ] T82.443 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^7 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * y^-2 * x^9 * z^-1 * x^2 ] T82.444 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-10 * z * y^-5 * x * y^-5 * z * y^-6 ] T82.445 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^6 * z^-4 * x^7 ] T82.446 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T82.447 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^-1 * y^6 * x^-7 ] T82.448 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T82.449 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^8, y^5 * z^-4 * y * x^-3 * y^4 ] T82.450 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^20 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 * x^2 ] T82.451 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-11 * z^2 * y^-2 * z * y^-1 * z * y^-5 * x^2 * y^-11 ] T82.452 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T82.453 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^6 * z^-3 * x^6 * y^-1 * x^2 ] T82.454 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^-5 * x * y^-2 * z^3 * y^-4 ] T82.455 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T82.456 : Triangle type {83,166,166} Group order 166 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^83, y * z^-1 ] T82.457 : Triangle type {84,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^3 * x^-1 * y * x^-1 * y^4 * x^-1 * y^3 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T82.458 : Triangle type {84,84,84} Group order 168 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^7 * z^-1 * x * z^-1, y^-3 * x * y^-1 * x * y^-4 ] T82.459 : Triangle type {165,165,165} Group order 165 Reflexible action Defining relators: [ x^-2 * y^-1, y^-64 * x * y^-18, x * z^-1 ] T82.460 : Triangle type {165,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^2 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T82.461 : Triangle type {165,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^2 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T82.462 : Triangle type {165,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-1 * y * z^-2 ] T82.463 : Triangle type {165,165,165} Group order 165 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^-3 * y^5 * x^-1 * z^4 * x^-5 ] Genus 83 T83.1 : Triangle type {2,4,8} Group order 1312 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y^-1 * z * y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * x * z ] T83.2 : Triangle type {2,4,8} Group order 1312 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y^-1 * z * y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T83.3 : Triangle type {2,4,12} Group order 984 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, z^-1 * y * z^-1 * y * x * z * y * z^-1 * y * x * y^2 * z^-1 * y * z^-1 * y * z^-1 * x * z^2 * y ] T83.4 : Triangle type {2,4,168} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y * z^-128 ] T83.5 : Triangle type {2,4,168} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-76 * x * z * y^-1 * z^-6 ] T83.6 : Triangle type {2,4,332} Group order 664 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-38 * x * y^-1 * z^-127 ] T83.7 : Triangle type {2,6,44} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^9 * y * z^-2 * x * z * y^-1 * z^-3 * x * y^-1 * z^-4 * x ] T83.8 : Triangle type {2,6,249} Group order 498 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^68 * y * z^-1 * x * y^-1 * z^-8 * x * z^4 ] T83.9 : Triangle type {2,8,8} Group order 656 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * y^-1 * z * y^-1 * z^-2 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T83.10 : Triangle type {2,8,8} Group order 656 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 ] T83.11 : Triangle type {2,8,8} Group order 656 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y^2 * x * y^-2 * z^-1 * x * y^-1 * z^-1 * x, z^-3 * y * x * y^-1 * z^3 * y^-1 * z^-1 ] T83.12 : Triangle type {2,8,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-11 * x * z^5 * y * z^-3 * x * z^3 * y^-1 * x * z^3 * y^-1 * z^-2 ] T83.13 : Triangle type {2,8,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-11 * x * z^7 * y * z^-2 * x * z * y^-1 * z^-7 ] T83.14 : Triangle type {2,8,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^36 * y * x * y^-1 * z^-7 * x * z^11 ] T83.15 : Triangle type {2,8,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-22 * x * z^19 * y * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T83.16 : Triangle type {2,12,12} Group order 492 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-2 * y * x ] T83.17 : Triangle type {2,12,68} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^21 * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^3 ] T83.18 : Triangle type {2,24,32} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x ] T83.19 : Triangle type {2,24,32} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-10 * z^-1 * y * x, z^-7 * x * z * y^-1 * z^-7 ] T83.20 : Triangle type {2,44,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-6 * y^12 * z^-4 * y^19 * z^-1 ] T83.21 : Triangle type {2,44,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^2 * z^-7 * y * z^-1 * y^11 * z^-3 * y * z^-17 * y ] T83.22 : Triangle type {2,167,334} Group order 334 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^116 * y^-50 ] T83.23 : Triangle type {2,168,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-50 * y^33 ] T83.24 : Triangle type {2,168,168} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^51 * z^-116 * y ] T83.25 : Triangle type {2,332,332} Group order 332 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^50 * z^-115 * y ] T83.26 : Triangle type {3,33,66} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-4 * z * y^-2 * z ] T83.27 : Triangle type {3,44,44} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y * z^-1 * y * z^-2 * y * z^-2 * y^2 * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y ] T83.28 : Triangle type {3,249,249} Group order 249 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-71 * z * y^-11 ] T83.29 : Triangle type {4,4,4} Group order 656 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * x * y^2 * x * y^-1 * z * y^-1 * z ] T83.30 : Triangle type {4,4,4} Group order 656 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z ] T83.31 : Triangle type {4,4,6} Group order 492 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y^-1 * z^-1 * y * x * z^-1 * x^-1 * y * x^-1 * y^-1 * z * x^-1 * y^-1 * z * x^-1 ] T83.32 : Triangle type {4,4,84} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^74 * y * x^-1 * y * x^-1 * z^8 ] T83.33 : Triangle type {4,4,84} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-29 * x^-1 * z^4 * y * z^-1 * x * y^-1 * z^-6 ] T83.34 : Triangle type {4,4,84} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-29 * x * z^4 * y * z^-1 * x * y^-1 * z^-6 ] T83.35 : Triangle type {4,4,166} Group order 332 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-66 * x * y^-1 * z^-16 ] T83.36 : Triangle type {4,8,8} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y^-2 * z^-1 * x^-1 * z * y * x * y^-1 * z^-1 * x * y^-1 ] T83.37 : Triangle type {4,8,8} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * z^2 * x^-1 ] T83.38 : Triangle type {4,8,8} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, z * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1, z * x^-1 * y * x^-2 * z * x^-1 * y^-1 * x ] T83.39 : Triangle type {4,8,8} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, x^-1 * y * x^-2 * y^-1 * z^2 ] T83.40 : Triangle type {4,8,8} Group order 328 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x^-1 * z * y^-2 * z^-1 * x^-1 * z * y * z^-1 * y * z^-1 * y * x * y^-1 ] T83.41 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * y * x^2 * z * y * x, z^2 * y * x^-1 * y * x^-1 * z^5 ] T83.42 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, z^4 * y * x^-1 * z * y^-1 * z^-1 * x * z ] T83.43 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, z^2 * y * z^-2 * x^-1 * z^4 ] T83.44 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^5 * y * x^-1 * z^2 * y * z^-2 * x^-1 * z^2 * y^-1 * z^-4 * x ] T83.45 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^5 * y * x^-1 * z * y^-1 * z^-3 * x^-1 * y * z^-6 * x^-1 ] T83.46 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^8, x^-1 * z * y^2 * x * z * y^2, z^4 * y * x^-1 * z * y^-1 * z^-1 * x^-1 * z ] T83.47 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^2 * y * x * z * y * z^-7 * x * y^-1 * z^-1 * x * z * y * z^-1 * x^-1 * z ] T83.48 : Triangle type {4,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^8 * y^-1 * z^-4 * x^-1 * z^5 ] T83.49 : Triangle type {4,12,22} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-5 * x^-1 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-8 ] T83.50 : Triangle type {4,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x * z, y^7 * z^-1 * y * z^-1 ] T83.51 : Triangle type {4,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-8 * z * y^-1 * z * y^-1 * z^2 * y^-2 * z^4 ] T83.52 : Triangle type {4,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-8 * z * y^-2 * z * y^-5 * z^2 * y^-1 ] T83.53 : Triangle type {4,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x * z, z^-3 * y * z^-1 * y * z^-4 ] T83.54 : Triangle type {4,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-5 * x^-1 * y^-1 * z^-1 * x^-1 * z ] T83.55 : Triangle type {4,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-5 * x^-1 * y^-1 * z^-1 * x * z ] T83.56 : Triangle type {4,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^15 * y^-5 * z^2 * y^-6 * z ] T83.57 : Triangle type {4,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * y^-1 * z^2 * y^-2 * z^3 * y^-1 * z * y^-1 * z ] T83.58 : Triangle type {4,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-3 * z * y^-1 * z * y^-3 * z * y^-1 ] T83.59 : Triangle type {4,57,76} Group order 228 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^2 * z^-1 * y^3 * x^-1 * y^2 * z^-7 * y^2 ] T83.60 : Triangle type {4,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-1 * y^22 * z^-2 * y * z^-1 * y^7 * z^-1 * y^5 * z^-1 * y * z^-1 * y^11 * z^-1 ] T83.61 : Triangle type {4,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^25 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T83.62 : Triangle type {6,6,22} Group order 264 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, x * z * y * z^-4 * x^-1 * y^-1 * z^-4 ] T83.63 : Triangle type {6,8,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^4 * y^-1 * z^-1 * x * z^4 ] T83.64 : Triangle type {6,8,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^4 * y^-1 * z^-3 * x * z^2 ] T83.65 : Triangle type {6,10,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, y^10 ] T83.66 : Triangle type {6,35,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-4 * x * z * y^-2 ] T83.67 : Triangle type {6,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-1 * z * y^-5 * z * y^-10 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-6 ] T83.68 : Triangle type {8,8,15} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-1 * x^-1 * z^3 * y^-1 * x * y^-1 * x * z * y * z^-7 ] T83.69 : Triangle type {8,8,15} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^-3 * x * z * y * z^-4 * x * z^2 * y^-1 * z^-3 ] T83.70 : Triangle type {8,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-7 * x^-1 * z^2 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x^-1 * z^4 * y * x * z^8 * y ] T83.71 : Triangle type {8,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-20 * x^-1 * y * x^-1 * y * z^-6 ] T83.72 : Triangle type {8,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^5 * y * x^-1 * y^-1 * z^-5 ] T83.73 : Triangle type {8,8,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * z^5 * y * x^-1 * y * z^-4 * x^-1 * y^-1 ] T83.74 : Triangle type {8,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^11 * y^-1 * z^2 * y^-4 * z^5 ] T83.75 : Triangle type {8,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^4 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T83.76 : Triangle type {10,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^6 * z^-5 * y^8 ] T83.77 : Triangle type {12,12,34} Group order 204 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^3 * y^-1 * x * y^-1 * x * y^-1 * x * z^11 ] T83.78 : Triangle type {12,24,48} Group order 192 Chiral action Defining relators: [ x * y * z, x * z * y^-1 * x * y^-1 * z^-1, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * y^-1 * z^2 ] T83.79 : Triangle type {12,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y^-2 * x^3 * y^-2 * x, z^-4 * x^-1 * z^2 * y * z^-1 ] T83.80 : Triangle type {12,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^2 * z^-4 ] T83.81 : Triangle type {12,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-12, z * y^-1 * z * y^-3 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 ] T83.82 : Triangle type {12,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^2 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-2 * y^3 ] T83.83 : Triangle type {16,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * x * z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T83.84 : Triangle type {16,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * y^-1 * z^-1, y^-2 * z * y^-1 * z * y^-2 * z * y^-1 * z^3 ] T83.85 : Triangle type {20,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3, y^7 * x^-5 * y^2 ] T83.86 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-1 * z^3 * y^-2 * x * y^-2 * z * y^-2 * x * y^-1 ] T83.87 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^-1 * y * x^-1 * y^3 * x^-1 * y^6 * x^-1 * y ] T83.88 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^5 * y^-1 * x * y^-2, z^-4 * x^2 * z^-4 ] T83.89 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^2 * z^-2 * x^5 * z^-1 * x * z^-1 ] T83.90 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-4 * y * x^-2 * y * x^-1 * y * x^-6 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T83.91 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-5 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T83.92 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-2 ] T83.93 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^3 * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T83.94 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^4 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T83.95 : Triangle type {22,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-6 * y * x^-8 * z * x^-7 ] T83.96 : Triangle type {30,36,36} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, y * z^-1 * y * x^2 * z^-1 * y * z^-1 ] T83.97 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-1 * z^3 * y^-2 * x * y^-2 * z * y^-2 * x * y^-1 ] T83.98 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, x^-2 * y * x^-1 * y^3 * x^-1 * y * x^-1 * y^3 * z^-1 * y^3 ] T83.99 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^5 * y^-1 * x * y^-2, z^-3 * x * z^-1 * x * z^-4 ] T83.100 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^2 * z^-2 * x^6 * z^-2 ] T83.101 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * z * x^-4 * y * x^-1 * y * x^-7 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T83.102 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * z^-2 * y^6 * z^-2 * y^5 ] T83.103 : Triangle type {44,44,44} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^-4 * x^4 * y^-8 ] T83.104 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T83.105 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x * y^-1 * x^6 * y^-5 * x^2 ] T83.106 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-7 * x^2 * y^-6 * x * y^-1 * x * y^-2 ] T83.107 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T83.108 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^8 * y^-1 * x^12 * y^-1 * x^63, y * z^-1 ] T83.109 : Triangle type {84,168,168} Group order 168 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-26 * z * x^-8 * z * x^-7 ] T83.110 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x^-2 * y^-1, y^-65 * x * y^-18, x * z^-1 ] T83.111 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-44 * x * y^-11 ] T83.112 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^24 * y^-2 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T83.113 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^10 * y^-2 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T83.114 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^7 * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T83.115 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^4 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T83.116 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^2 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T83.117 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-4 * y^6 * x^-6 * y * x^-3 ] T83.118 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^6 * z^-4 * y * x^-6 * y * x^-1 * y^2 ] T83.119 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y^6 * x^-6 * y * x^-1 ] T83.120 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^5 * z^-4 * y * x^-5 * y^3 ] T83.121 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-4 * x^2 * y^-7 ] T83.122 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y^-7 * z^5 * y^-1 * z * y^-1 * z * y^-1 ] T83.123 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T83.124 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^3 * z^-5 * y^6 ] T83.125 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T83.126 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T83.127 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T83.128 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^6 * z^-4 * x^7 ] T83.129 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T83.130 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^-3 * y^5 * x^-8 ] T83.131 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T83.132 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^20 * x^-1 * z^13 ] T83.133 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T83.134 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T83.135 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-8 * z^3 * x^-5 * z^2 * x^-8 ] T83.136 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T83.137 : Triangle type {167,167,167} Group order 167 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^2 * z^-4, x^-3 * y^6 * x^-2 * z^3 * x^-5 ] Genus 84 T84.1 : Triangle type {2,4,87} Group order 696 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-68 * x * z^11 * y^-1 * z^-7 ] T84.2 : Triangle type {2,4,170} Group order 680 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-40 * x * y * z^-129 ] T84.3 : Triangle type {2,4,336} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y^-1 * z^-128 ] T84.4 : Triangle type {2,6,86} Group order 516 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^63 * y * x * z * y^-1 * z^-9 * x * z^11 ] T84.5 : Triangle type {2,8,58} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-24 * x * z^11 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-17 ] T84.6 : Triangle type {2,10,44} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^22 * y * x * z * y * z^-9 * x * y^-1 * z^-3 * x * z^6 ] T84.7 : Triangle type {2,10,210} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^27 * y * z^-1 * x * y^-1 * z^-9 * x * z^3 ] T84.8 : Triangle type {2,12,102} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, x * z^16 * y * z^-4 * x * y^-1 * z^-9 * x * z^2 * y^-1 ] T84.9 : Triangle type {2,14,30} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^-7 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-7 ] T84.10 : Triangle type {2,16,26} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y * x * y^-1 * z * y * x * y^-10 * z^-1 * y, z^-5 * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-5 ] T84.11 : Triangle type {2,26,182} Group order 364 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-13 * z^4 * y^-5 * z^4 ] T84.12 : Triangle type {2,36,90} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-4 * z^4 * y^-4 * z^4 ] T84.13 : Triangle type {2,44,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-9 * z^4 * y^-4 * z^4 * y^-1 ] T84.14 : Triangle type {2,50,175} Group order 350 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-12 * z^4 * y^-6 * z^3 ] T84.15 : Triangle type {2,58,174} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-24 * y * z^-2 * y^9 * z^-2 * y^20 ] T84.16 : Triangle type {2,86,172} Group order 344 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-52 * y^33 ] T84.17 : Triangle type {2,87,87} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-83 * z * y^-1 ] T84.18 : Triangle type {2,169,338} Group order 338 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^117 * y^-50 * z ] T84.19 : Triangle type {2,170,170} Group order 340 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^52 * z^-118 ] T84.20 : Triangle type {2,336,336} Group order 336 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^51 * z^-117 ] T84.21 : Triangle type {3,3,86} Group order 516 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z * y^-1 * z^-9 ] T84.22 : Triangle type {3,3,169} Group order 507 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-5 * x * z^3 * y * x * z^4 * y * z^-1 ] T84.23 : Triangle type {3,21,91} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z^2 * y^-1 * x * z^3 ] T84.24 : Triangle type {3,44,66} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^3 * y^-1 * z^6 ] T84.25 : Triangle type {3,85,255} Group order 255 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-72 * z * y^-10 * z^2 ] T84.26 : Triangle type {3,86,86} Group order 258 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^71 * y^-12 * z * y^-1 ] T84.27 : Triangle type {3,252,252} Group order 252 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y * z^-1 * y^82 ] T84.28 : Triangle type {4,4,85} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-4 * x^-1 * y * z^-3 * x * z^2 * y^-1 * x * z * y^-1 * z^-3 * x^-1 * y ] T84.29 : Triangle type {4,4,85} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^2 ] T84.30 : Triangle type {4,4,85} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * y * z^-5 * x * z^-4 ] T84.31 : Triangle type {4,4,85} Group order 340 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z * y^-2 * z^-4 * x * z^-1 * x * z^3 ] T84.32 : Triangle type {4,4,85} Group order 340 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^68 * y * x * z^16 ] T84.33 : Triangle type {4,4,168} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^74 * y * x^-1 * z^9 ] T84.34 : Triangle type {4,8,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x * z * y^-1 * z^-6 * x^-1 * y^-1 * z^-10 * x ] T84.35 : Triangle type {4,20,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * z^-5 * x^-1 * z, y^7 * z^-1 * y * z^-1 ] T84.36 : Triangle type {4,24,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, x * z * y^-1 * z^-8 ] T84.37 : Triangle type {4,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * y, z^3 * y * x^-1 * z^2 * y^-1 ] T84.38 : Triangle type {4,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, x^-1 * y^-4 * z^-1 * y^2 * x^-1 * y^-2 * z^-1 * y^2, z^-1 * y^5 * z^-2 * y * z^-1 ] T84.39 : Triangle type {4,57,228} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^25 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T84.40 : Triangle type {4,58,58} Group order 232 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-1 * y^23 * z^-2 * y * z^-1 * y^10 * z^-1 * y^6 * z^-1 * y^11 ] T84.41 : Triangle type {4,76,114} Group order 228 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-8 * z * y^-1 * z^2 * y^-4 * z^2 * y^-1 ] T84.42 : Triangle type {4,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^25 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T84.43 : Triangle type {5,43,215} Group order 215 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-11 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T84.44 : Triangle type {5,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^29 * z^-1 * y * z^-1 * y^12 ] T84.45 : Triangle type {5,44,44} Group order 220 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z^-1 * y * z^-10 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^12 ] T84.46 : Triangle type {5,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-13 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T84.47 : Triangle type {5,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-13 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T84.48 : Triangle type {6,6,43} Group order 258 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^-2 * x * z^-1 * y * z^-3 ] T84.49 : Triangle type {6,6,43} Group order 258 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^3 * y * x * z^3 ] T84.50 : Triangle type {6,6,43} Group order 258 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-43 ] T84.51 : Triangle type {6,8,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z^-3 ] T84.52 : Triangle type {6,10,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, z^2 * y * z^-1 * x^-1 * z^4, y^10 ] T84.53 : Triangle type {6,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^3 * y * x^-1 * z^3 ] T84.54 : Triangle type {6,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T84.55 : Triangle type {6,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^2 * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T84.56 : Triangle type {7,29,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-3 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T84.57 : Triangle type {7,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-2 * y^5 * z^-2 * y * z^-1 ] T84.58 : Triangle type {7,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, z * x^-2 * y * x, z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 * z^4 * y^-7 * z * y^-1 ] T84.59 : Triangle type {7,30,30} Group order 210 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-1 * z^2 * y^-1 * z * y^-9 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-6 ] T84.60 : Triangle type {7,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^7 * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T84.61 : Triangle type {7,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-5 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T84.62 : Triangle type {7,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-6 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T84.63 : Triangle type {8,8,29} Group order 232 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^2 * y * z^-1 * x * z^3 ] T84.64 : Triangle type {8,8,29} Group order 232 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-13 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-6 ] T84.65 : Triangle type {8,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y * z^-1 * x^-1 * y^-1 * x * z^3, y^10 ] T84.66 : Triangle type {8,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y^3 * x^-1 * y^-1 * z, y * x^-3 * y^2 * z^-1, z * x^-3 * z * y^-1 * z, x * z^-1 * x^-2 * y * x * z^-1 ] T84.67 : Triangle type {8,10,12} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, y^3 * x * y^-1 * z^-1, y * z^-2 * x^-1 * z^3 ] T84.68 : Triangle type {8,25,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-10 ] T84.69 : Triangle type {8,26,26} Group order 208 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^-11 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * z ] T84.70 : Triangle type {8,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-7 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T84.71 : Triangle type {8,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y ] T84.72 : Triangle type {9,22,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T84.73 : Triangle type {9,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^5 * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T84.74 : Triangle type {9,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^3 * y^-6 * z^5 * y^-1 * z * y^-1 * z^4 ] T84.75 : Triangle type {9,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T84.76 : Triangle type {10,10,22} Group order 220 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y * z^-1 * x^2 * z^-1 * y, y^-3 * x^3 * y^-2 * x * y^-1 ] T84.77 : Triangle type {10,10,22} Group order 220 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z * y, x^-10 ] T84.78 : Triangle type {10,10,22} Group order 220 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, y * x^-1 * y^-1 * x * z^2, x^-10 ] T84.79 : Triangle type {10,10,22} Group order 220 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^-2, y * z^-1 * x^2 * z * y, x^-10 ] T84.80 : Triangle type {10,10,22} Group order 220 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-14 * x * y * z^-7 ] T84.81 : Triangle type {10,10,105} Group order 210 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-5 * x * z^4 * y^-1 * z^-6 * x * y^-1 * z^-4 ] T84.82 : Triangle type {10,10,105} Group order 210 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^5 * y * z^-4 * x^-1 * z^4 * y * x^-1 * z * y^-1 * z^-3 * x^-1 * z ] T84.83 : Triangle type {12,12,51} Group order 204 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y * x * z^2 ] T84.84 : Triangle type {12,12,51} Group order 204 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x * z * y^-1 * z^-2 * x^-1 * z^5 ] T84.85 : Triangle type {13,15,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^2 * y^-4 * x^2, z^-9 * y^2 * z^-4 ] T84.86 : Triangle type {13,16,16} Group order 208 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * x^3 * z * x^-1, z^-1 * y^2 * z^-2 * y^5 * z^-3 * y^2 * z^-1 ] T84.87 : Triangle type {13,16,16} Group order 208 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^-6 * z * y^-1 * z * y^-4 * z * y^-1 * z, x^-5 * y^-1 * z * y^-1 * z * x^-2 * y * z^-1 * y * z^-1 * x^-2 ] T84.88 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^2 * y^-4 * x^2, y^-5 * x * y^-2 * z^3 * y^-4 ] T84.89 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-2, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T84.90 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T84.91 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T84.92 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T84.93 : Triangle type {13,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T84.94 : Triangle type {14,14,15} Group order 210 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, (x^-1 * y * x^-1 * y * x^-1 * y * x^-1)^2, z^15 ] T84.95 : Triangle type {14,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^8, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T84.96 : Triangle type {14,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-4 * y^6, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T84.97 : Triangle type {14,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T84.98 : Triangle type {14,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-5 * y^2 * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T84.99 : Triangle type {14,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * y * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T84.100 : Triangle type {15,15,65} Group order 195 Chiral action Defining relators: [ x * y * z, z^2 * y^-1 * x * z^-1 * x, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * x)^3 ] T84.101 : Triangle type {15,15,65} Group order 195 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, z^-1 * x * z^-1 * y * z^-2, z^-1 * y * z^-1 * x^-1 * z * y * z^-1 ] T84.102 : Triangle type {15,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, (y^-5 * x * y^-1)^2 ] T84.103 : Triangle type {15,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T84.104 : Triangle type {15,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T84.105 : Triangle type {18,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T84.106 : Triangle type {18,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T84.107 : Triangle type {18,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T84.108 : Triangle type {18,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-3 * x^4 * y^-7 ] T84.109 : Triangle type {20,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T84.110 : Triangle type {20,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T84.111 : Triangle type {20,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T84.112 : Triangle type {21,27,27} Group order 189 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y^-1 * x^3 * z^-1 * x^-1, z^2 * y^-3 * x^-1 * y^-2 * z * y^-1 ] T84.113 : Triangle type {22,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * z^2 * x^-7 * z * x^-7 ] T84.114 : Triangle type {22,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^9 ] T84.115 : Triangle type {22,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T84.116 : Triangle type {22,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 ] T84.117 : Triangle type {22,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2, x * y^-1 * x^6 * y^-7 ] T84.118 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, y^10 * x^-6 * y * x^-1 * y^3 ] T84.119 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-3 * y^7 ] T84.120 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T84.121 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-8 * y^3 * x^-8 ] T84.122 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * z * y^-2, z^-9 * y * z^-4 ] T84.123 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T84.124 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^-1 * z^4 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T84.125 : Triangle type {25,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^-2 * y^6 * x^-6 * y * x^-1 ] T84.126 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x * z^3 * y^-1 * x * y^-1 * x * z * y^-1 ] T84.127 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-2 * x^-1 * y * x^-1 * z * y * z^-2 ] T84.128 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6 * y^-2, z^3 * y^-1 * x * z^3, y^5 * z^-1 * y * z^-1 ] T84.129 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^2 * y^-1 * z^-1 * x * z^3 ] T84.130 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-2 * x * z^3, x^8 * y^-2 ] T84.131 : Triangle type {26,26,91} Group order 182 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, z^4 * x^-3 * z^2 * x^-1 * z^5 ] T84.132 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T84.133 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T84.134 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T84.135 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-4 * x * z^-4 * x^2 * z^-4 ] T84.136 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-2 ] T84.137 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^9 * x^-6 * y * x^-1 * y^2 ] T84.138 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T84.139 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^3 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T84.140 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-3 * z^4 * x^-6 * y * x^-7 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T84.141 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T84.142 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x * y^-1 * x^6 * y^-5 * x^2 ] T84.143 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T84.144 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^9 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T84.145 : Triangle type {29,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-14 * y^3 * x^-4 * y^3 * x^-8 ] T84.146 : Triangle type {30,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x * z^-1 * x^7 * z^-1 * x * z^-1 * x^4 ] T84.147 : Triangle type {30,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * z^3, y^-2 * x * y^-1 * x * z * y^-2 ] T84.148 : Triangle type {30,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * x^-1 * y^6 ] T84.149 : Triangle type {36,36,45} Group order 180 Chiral action Defining relators: [ x * y * z, y^-3 * x * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * x^3 * z^-1 * x * z^-1 ] T84.150 : Triangle type {36,36,45} Group order 180 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^3 * x^-1 * z^5 ] T84.151 : Triangle type {36,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * y * z^-2, z^-2 * x^3 * z^-2 * x ] T84.152 : Triangle type {36,36,45} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * y * z^-1 * x * z^-4 ] T84.153 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * z^-3 * y^5 * z^-2 * y^5 ] T84.154 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^8 * y^-6 * x * y^-11 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T84.155 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T84.156 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^16 * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T84.157 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T84.158 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T84.159 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^9 * z^-3 * x^8 * z^-1 * x^2 ] T84.160 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-4 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T84.161 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-4 * x^6, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T84.162 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T84.163 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^25 * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 * x^2 ] T84.164 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^4 * y^-5 * x, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T84.165 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^3 * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T84.166 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^5 * z^-4 * x^6 ] T84.167 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, (y^-3 * z * y^-6)^2 ] T84.168 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^6 * z^-4 * y * x^-3 * y^5 ] T84.169 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T84.170 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-6 ] T84.171 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T84.172 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x * y^-1 * x^6 * y^-7 ] T84.173 : Triangle type {43,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-27 * y * x^-8 * z * x^-7 ] T84.174 : Triangle type {44,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^2 * x^-1 * y^3 * x^-1 * y^2 * x^-1 * y * z^-1 * y ] T84.175 : Triangle type {44,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, y^-3 * x^2 * y^-3 ] T84.176 : Triangle type {44,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, z^-2 * x * z^-1 * x * z^-3 ] T84.177 : Triangle type {44,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^-1 * y * x^-3 * z^3 * x^-1 ] T84.178 : Triangle type {44,44,88} Group order 176 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, z^-2 * x^2 * z^-3 * x^3 * z^-2 * x * z^-1 ] T84.179 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-57 ] T84.180 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-16 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T84.181 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-14 * x^3 * z^-3 * y * z^-1 * y * z^-1 ] T84.182 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T84.183 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-2 * y^6 * x^-2 * z^3 * x^-4 ] T84.184 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T84.185 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T84.186 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^4 * x^-4 * y^2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T84.187 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^6 * z^-4 * y * x^-5 * y^4 ] T84.188 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^3 * y^-3 * x * y^-1 * x * y^-1 * x * y^-1 * x^12 * y^-1 * x * y^-1 * x * y^-1 * x ] T84.189 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T84.190 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T84.191 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y ] T84.192 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T84.193 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^6 * z^-3 * y^9 ] T84.194 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-6 * z * y^-1 * z * y^-5 * x^3 * y^-10 ] T84.195 : Triangle type {57,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^24 * y^-2 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T84.196 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^5 * z^-1 * y^4 * x^-1 * y^3 * z^-1 * y ] T84.197 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, x * z * y^-3 * x * y^-5 ] T84.198 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-3 ] T84.199 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, z^-3 * x * z^-1 * x * z^-4 ] T84.200 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * y^-1 * z^-2, y^-4 * x^2 * y^-4 ] T84.201 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x * z^2, x^2 * z^-1 * x^7 * z^-1 * x ] T84.202 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * z * y, z^-5 * y^3 * z^-2 * y^3 * z^-3 ] T84.203 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^-4 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 ] T84.204 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x * z^-2 * x * z^-2 * x^2 * z^-3 ] T84.205 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1, y^2 * x^-1 * y * x^-1 * y^3 * z^-1 ] T84.206 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3, x^7 * y^-1 * z^-2 ] T84.207 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^3 * z^-1 * x * y^-1 * x^5 * y^-1 * x ] T84.208 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z^-2 * x^2 * z^-1 * x * y^-1 * x^5 * y^-1 * x^5 ] T84.209 : Triangle type {58,58,87} Group order 174 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^18 * x^-1 * y^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T84.210 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-31 * x * y^-11 ] T84.211 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^8 * y^-4 * x ] T84.212 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T84.213 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, x^-1 * y^6 * x^-7 ] T84.214 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-45 * x * y^-11 ] T84.215 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T84.216 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-9 * y * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T84.217 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T84.218 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^11 * x^-6 * y * x^-1 * y^4 ] T84.219 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T84.220 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T84.221 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^5 * z^-3 * y^8 ] T84.222 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^11 * z^-1 * x * z^-1 * x * z^-1 * x * y^-2 * x^9 * z^-1 * x^2 ] T84.223 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-4 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T84.224 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-1 * x^2 * y^-7 * z^2 * y^-3 * x^4 * y^-9 ] T84.225 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-2, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T84.226 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^4 * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T84.227 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-7 * z * y^-1 * z * y^-1 * z * y^-5 * x * y^-5 * z * y^-1 * z * y^-1 * z * y^-3 ] T84.228 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^7 * z^-4 * y^6 * z^-1 * y^2 ] T84.229 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^21 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 * x^2 ] T84.230 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-8 * y^2 * z^-4 ] T84.231 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^7 * z^-4 * x^2 * z^-4 * x^4 ] T84.232 : Triangle type {85,170,170} Group order 170 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^85, y * z^-1 ] T84.233 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^33 * x^-2 * y^9 ] T84.234 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^5 * y^-6 * x * y^-11 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T84.235 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-4 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T84.236 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-6 * x^2 * y^-6 * x * y^-1 * x * y^-1 ] T84.237 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^8 * y^-6 * x^2 ] T84.238 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^5 * z^-4 * x * y^-6 * x^2 ] T84.239 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T84.240 : Triangle type {86,86,86} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^4 * z^-4 * x^6 ] T84.241 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T84.242 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x^-2 * y^-1, y^-65 * x * y^-19, x * z^-1 ] T84.243 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^9 * z^-4 * x^7 * z^-1 * x^2 ] T84.244 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11 * y^-1, y^-5 * x * y^-1 * z^5 * y^-4 ] T84.245 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-5 * y * z^-5 * y^6 * z^-2 ] T84.246 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-12 * x^5 * z^-2 * y * z^-2 ] T84.247 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y^-7 * z^5 * y^-1 * z * y^-1 * z^2 ] T84.248 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-14 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T84.249 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-44 * x^2 * y^-11 ] T84.250 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-2 * y * x^-2 * y * x^-1 * y * x^-10 * z * x^-7 ] T84.251 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T84.252 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-7 * z^5 * y^-1 * z * y^-3 ] T84.253 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y^4 * z^-1 * y * z^-1 * y * z^-5 * y^9 ] T84.254 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T84.255 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * x^-1 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T84.256 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T84.257 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T84.258 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, x^-2 * y^6 * x^-6 * y * x^-1 ] T84.259 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T84.260 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-11 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * y^-1 * x^10 * z^-1 * x^2 ] T84.261 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^22 * y^-2 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T84.262 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 * x^2 ] T84.263 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-4, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T84.264 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T84.265 : Triangle type {169,169,169} Group order 169 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y ] Genus 85 T85.1 : Triangle type {2,3,8} Group order 4032 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z * y * z^-1 * x * z^3 * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-3 * x * z, z * y * x * z^2 * y * z^-2 * x * z * y * x * z * y * x * z * y^-1 * z^3 * y^-1 * z^-2 * x, x * z^2 * y * z^-1 * x * z * y * z^-1 * x * z * y * z^-1 * x * z * y * x * z * y^-1 * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 ] T85.2 : Triangle type {2,3,8} Group order 4032 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^8, y * z^-2 * x * z^2 * y * x * z^3 * y * x * z * y^-1 * z^-3 * x * z^3, z * y * x * z^2 * y * x * z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T85.3 : Triangle type {2,3,12} Group order 2016 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3, z^-1 * x * z^2 * y * z^-1 * x * z * y * x * z * y * x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T85.4 : Triangle type {2,3,20} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, y * z^-1 * x * z^4 * y * x * z * y * z^6, x * z * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-3 ] T85.5 : Triangle type {2,3,48} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-6 * x * z^6 * y * z^-7 * x * z^3 * y * z^-1 * x * y^-1 * x * z^3 * y^-1 * z^-4 ] T85.6 : Triangle type {2,3,48} Group order 1152 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z * y * x * z * y * x * z^2 * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z^3 * y * x * z^2 * y^-1 * z^-3 * x * y^-1 * z^-1, y * z^-7 * x * z^2 * y^-1 * x * z^5 ] T85.7 : Triangle type {2,4,6} Group order 2016 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, y^-1 * z * y * x * z^2 * y * x * y^-1 * z * y^-1 * z^-2 * x * z, y * z^-1 * y * z^-1 * y * z^-1 * x * y^2 * z^-1 * y * z^-1 * y * z^-2 ] T85.8 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-1)^6, x * z^2 * y^-1 * z * y^-2 * z^-3 * y * z^-1 * y, z^-1 * x * z * y * z^-2 * x * y^-1 * z^-3 * x * y^-1 * z^-2 ] T85.9 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2 * y * z^-1)^2 ] T85.10 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-1)^6, x * z^2 * y^-1 * z * y^-2 * z^-3 * y * z^-1 * y, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T85.11 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T85.12 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y * x * z * y^-1 * z^3 * y^-1 * z^-2, y^-1 * z * y * z^-1 * x * z^2 * y^-2 * z^-2 * x * z^2, y * z^-1 * y * z^-1 * y * z^-1 * x * y^2 * z^-1 * y * z^-1 * y * z^-2 ] T85.13 : Triangle type {2,4,8} Group order 1344 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y * z^-1 * x * z^2 * y^-2 * z^-2 * x * z^2 ] T85.14 : Triangle type {2,4,25} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^-7 * x * z^10 * y^-1 * x * z^3 * y^-1 * z^-3 ] T85.15 : Triangle type {2,4,28} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-2 * x * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^7 * y^-1 * z * y^-2 * z^-7 * y ] T85.16 : Triangle type {2,4,60} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y * z^-1)^6, z^7 * y * z^-2 * x * z^3 * y^-1 * z^-3 * x * z^3 ] T85.17 : Triangle type {2,4,88} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-70 * x * z^8 * y * x * y * z^-8 ] T85.18 : Triangle type {2,4,88} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-25 * x * z^11 * y * z^-1 * x * y^-1 * z^-5 ] T85.19 : Triangle type {2,4,172} Group order 688 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y * z^-130 ] T85.20 : Triangle type {2,4,340} Group order 680 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-40 * x * y^-1 * z^-129 ] T85.21 : Triangle type {2,6,6} Group order 1008 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2, y^-1 * z * y^2 * z^-1 * y^2 * x * y^-2 * z^-1 * y * x * y^-2 * z ] T85.22 : Triangle type {2,6,6} Group order 1008 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z * y * x * z * y^-4 * z^-1 * y * x * y^-1 * z^-1 * x * z * y * x * y^-2 * z^-1 * y ] T85.23 : Triangle type {2,6,6} Group order 1008 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-2 ] T85.24 : Triangle type {2,6,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^10, z^2 * y^-1 * z^2 * y * x * z * y^-1 * z^-2 * y * z^-1 * x ] T85.25 : Triangle type {2,6,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3 * y)^2, z^10 ] T85.26 : Triangle type {2,6,12} Group order 672 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z * y * z^-2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * y ] T85.27 : Triangle type {2,6,12} Group order 672 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T85.28 : Triangle type {2,6,12} Group order 672 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-1 * x * y^-2 * z^-2 * y * z^-1 * y, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T85.29 : Triangle type {2,6,12} Group order 672 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T85.30 : Triangle type {2,6,15} Group order 630 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-2 * z^-1 * y, z^-1 * x * z^6 * y^-1 * x * z * y^-1 * z^-5 ] T85.31 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^6 * y^2 * x * z^5 ] T85.32 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-1 * x * z^2 * y^-2 * z^-1 * x * z * y^-1 * z^-1, z^6 * y^2 * x * z^5 ] T85.33 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T85.34 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2 ] T85.35 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-2 * y * z^-1, z^-2 * x * z^4 * y * z^-3 * x * z^3 * y^-1 * z^-2 ] T85.36 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^4 * y * z^-5 * x * z^3 * y^-1 * z^-2 ] T85.37 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y, z^4 * y^-2 * z^-2 * x * y^-1 * z ] T85.38 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z^3 * y^-1 * z^-4 ] T85.39 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2 ] T85.40 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^4 * y * z^-1 * x * z^6 * y * x * y^-1 * x * z * y^-1 * z^-6 * x * z^2 ] T85.41 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^3 * y * z^-2 * x * z^6 ] T85.42 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * x * y^-1 * z * y^-1 * z * y^-1 * z ] T85.43 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-1 * x * y^-1 * z * y^-2 * z^-5 ] T85.44 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-7 * x * z^7 * y^-1 * z^-9 ] T85.45 : Triangle type {2,6,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, x * z^5 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T85.46 : Triangle type {2,6,39} Group order 546 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-2 * z^-1 * y, x * z^5 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T85.47 : Triangle type {2,6,66} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z * y * x * z^9 * y^-1 * x * z * y^-1 * z^-6 * x * y^-1 * z^-1 * x ] T85.48 : Triangle type {2,6,87} Group order 522 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^71 * y * z^-8 * x * z^7 ] T85.49 : Triangle type {2,6,255} Group order 510 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-49 * x * z^21 * y^-1 * x * y^-1 * z^-13 ] T85.50 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8 ] T85.51 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z * y^3 * x * y^-1 * z^-2, (y^3 * z^-1)^3 ] T85.52 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z * y^3 * x * y^-1 * z^-2, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T85.53 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, (y * z^-2 * y^2)^2, (y * z^-3 * y)^2 ] T85.54 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, z^2 * y^-4 * z^-2 * y * x * y^-1, y * z^-1 * x * y^-3 * z^2 * y^-2 * z^-1, x * z^2 * y^-3 * z^-1 * y^2 * z^-2, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-2 ] T85.55 : Triangle type {2,8,8} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, z^8, x * z^2 * y^-3 * z^-1 * y^2 * z^-2 ] T85.56 : Triangle type {2,8,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^12 ] T85.57 : Triangle type {2,8,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, z^12 ] T85.58 : Triangle type {2,9,18} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T85.59 : Triangle type {2,10,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z * y * z^-1 * x * y^-1 * z^-2 * x, y^10, (y * z^-1 * y^3)^2, y * z^-1 * x * y^-3 * z^-2 * y * z^-2 ] T85.60 : Triangle type {2,10,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, y * x * z * y^2 * x * y^-1 * z^-1, y^10 ] T85.61 : Triangle type {2,12,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y^12, z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T85.62 : Triangle type {2,12,12} Group order 504 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^2 * x * y^-1 * z^-1, x * y^-5 * z^-5, y^12 ] T85.63 : Triangle type {2,12,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z * y^-4 * z^4, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^3 * z^-1 * y^2 * x ] T85.64 : Triangle type {2,12,36} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T85.65 : Triangle type {2,12,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^8 * y * x * z * y * x * z^2 * y * x * z * y * x * y^-1 * x * z^19 ] T85.66 : Triangle type {2,12,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^21 * y * z^-1 * x * z^4 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 * x * z ] T85.67 : Triangle type {2,12,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-2 * x * z^14 * y * z^-4 * x * y * z^-7 * x * z^2 * y^-1 * z^-2 ] T85.68 : Triangle type {2,18,18} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-2 * y * z^-1, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-2 * z * y^-1 * z ] T85.69 : Triangle type {2,22,187} Group order 374 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^9 * y * z^-1 * x * z^4 * y^-1 * z^-1 * x ] T85.70 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-2 * y^2 * z^-1 * y^2 * z^-5 ] T85.71 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^9 * z^-1 * y * z^-1, x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-6 ] T85.72 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-4 * z^-1 * y^4 * x * y^-4 * z^-1 * y^2 * x, y^-3 * z^2 * y^-1 * z^4 * y^-7 * z * y^-4 * z * y^-1 ] T85.73 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^-2 * z * y^3 * x * y^-1 * z^-1 * x, z^4 * y^-15 * z^2 * y^-1 * z^2 ] T85.74 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-3 * y^4 * z^-5 ] T85.75 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, z^-1 * y^6 * z^-1 * y * z^-2 * y ] T85.76 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-11 * z^4 * y^-5 * z^4 ] T85.77 : Triangle type {2,24,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^-2 * z * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-9 * z^3 * y^-1 ] T85.78 : Triangle type {2,25,25} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^-1 * z * y^-1 * z^7 * y^-1 * z^3 * y^-8 * z * y^-1 * z ] T85.79 : Triangle type {2,27,54} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y * x * y^-1 * z^-2 * x, y^-2 * z^3 * y^-2 * z * y^-5 * z * y^-1 * z * y^-7 * z^4 ] T85.80 : Triangle type {2,28,28} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y * x * y^-4 * z * y^5 * x * y^-1 * z * y, y^-5 * z^4 * y^-1 * z^4 * y^-4 * z * y^-2 * z * y^-6 ] T85.81 : Triangle type {2,28,28} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z^3 * y * x * z * y * x * y^-3 * z^-1 * x * y^-1 * z^-1 * x ] T85.82 : Triangle type {2,36,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, z^-2 * y^10 * z^-4 * y^16 * z^-4 ] T85.83 : Triangle type {2,45,90} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-45 ] T85.84 : Triangle type {2,60,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-25 * y^13 * z^-2 * y^19 * z^-1 ] T85.85 : Triangle type {2,60,60} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-5 * z^4 * y^-5 * z^4 * y^-2 ] T85.86 : Triangle type {2,88,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-27 * z^3 * y^-9 * z^2 * y^-1 ] T85.87 : Triangle type {2,88,88} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-53 * y^33 * z^-1 ] T85.88 : Triangle type {2,171,342} Group order 342 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^118 * y^-52 ] T85.89 : Triangle type {2,172,172} Group order 344 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^53 * z^-118 * y ] T85.90 : Triangle type {2,340,340} Group order 340 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^52 * z^-117 * y ] T85.91 : Triangle type {3,3,4} Group order 2016 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, (y^-1 * z^-1 * x * z)^3, z^2 * y * z^-1 * x^-1 * y * z^-1 * x^-1 * z * y * x^-1 * z * y * z^-1 * x ] T85.92 : Triangle type {3,3,4} Group order 2016 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^4, z^2 * x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z^-1 * x * z^-1 * x, x^-1 * z * y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 * z * y * x * z, x^-1 * z * y * x * z * y * x^-1 * y^-1 * x * z * y * x * z * y^-1 * z^-2 ] T85.93 : Triangle type {3,3,6} Group order 1008 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, y^-1 * x * y^-1 * z^-1 * x^-1 * y * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x^-1 ] T85.94 : Triangle type {3,3,10} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z^2 * y)^2, (x^-1 * z * y^-1 * z^-1)^2, z^10 ] T85.95 : Triangle type {3,3,24} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-4 * x^-1 * y^-1 * z^-4 * x^-1 * z^4 ] T85.96 : Triangle type {3,3,24} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-4 * x^-1 * z^3 * y^-1, y^-1 * z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T85.97 : Triangle type {3,4,4} Group order 1008 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z, x^-1 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-1 * x * z ] T85.98 : Triangle type {3,4,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x^-1 * z * x^-1 * z^2 * y^-1 * z^-2 * x * z^-1 * x * z^2 * y * z^-2 ] T85.99 : Triangle type {3,4,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x^-1 * z * x^-1 * z^2 * y^-1 * z^-2 * x^2 * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T85.100 : Triangle type {3,4,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x^-1 * z * x^-1 * z^2 * y^-1 * z^-2 * x * z^-1 * x * z^2 * y^-1 * z^-2 ] T85.101 : Triangle type {3,4,6} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x^-1 * z * x^-1 * z^2 * y^-1 * z^-2 * x * z^-2 * x^-1 * z * y^-1 * z^-2 ] T85.102 : Triangle type {3,4,8} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * y^-1, (y * z^-1)^4 ] T85.103 : Triangle type {3,4,8} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^8, x^-1 * y * x^-1 * y * z^-1 * x * y^-1 * z^-2 * x^-1 * z * y^2 * z^-1 * x * z^2 * y^-1 * z^-1 ] T85.104 : Triangle type {3,4,8} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (y * z^-1)^4, (z^-1 * x^-1 * y^-1)^3 ] T85.105 : Triangle type {3,4,8} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T85.106 : Triangle type {3,4,12} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x * z * y^-1 * z^-1 * x^-1 * z * x^-1 * z^2 * y * z^-2 * x ] T85.107 : Triangle type {3,4,12} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T85.108 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y * z^-2, y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T85.109 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T85.110 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^-2, y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x * z ] T85.111 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-1 * x^-1 * y^-1 * x * z^2 * y^-1 * z^-1 * x * y^-1 * x * z^-2 * x^-1 * z * y * z^-1 ] T85.112 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2, z^2 * y^2 * x^-1 * z * y * x ] T85.113 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^-2 * z * y^-2 * z^-1 * y * x^-1 * y^-1 * z^-2 * y * z^-1 * x ] T85.114 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (x^-1 * y^-1 * x * y^-1 * x * z * y * x * z)^2 ] T85.115 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z ] T85.116 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 ] T85.117 : Triangle type {3,6,6} Group order 504 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^2 * y^2 * x * z^2 * y^-1, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T85.118 : Triangle type {3,6,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, x * z^3 * y^-1 * x * z^3 * y ] T85.119 : Triangle type {3,6,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, (x * z^3 * y^-1)^2 ] T85.120 : Triangle type {3,6,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3 ] T85.121 : Triangle type {3,6,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T85.122 : Triangle type {3,6,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * z * y^-1 * z^-1, (z^-1 * x^-1 * y^-1)^3 ] T85.123 : Triangle type {3,6,114} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T85.124 : Triangle type {3,10,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^10, y * z^-1 * y^2 * z^-1 * x^-1 * z^-2 * y^2 * z^-1 ] T85.125 : Triangle type {3,10,10} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, x^-1 * y^-3 * x * y^-2 * z, x^-1 * z^2 * y^-1 * x * z^3, (x * z * y^2)^2 ] T85.126 : Triangle type {3,12,12} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * y^2 * x * z^2 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z ] T85.127 : Triangle type {3,12,12} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y * x * z * y * x * z * y^-1 * z * y^-1 ] T85.128 : Triangle type {3,12,12} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^2 * y^-2 * z^2 * y^-2 * z * y^-1 * z * y^-1 ] T85.129 : Triangle type {3,12,12} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-2 * y * z^-2 * x * y * z^-1 * y * z^-2, y^2 * z^-1 * y^2 * z^-2 * x * z * y^-2 * z^2 ] T85.130 : Triangle type {3,14,42} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^3 * x^-1 * z * y^-1 * z, y * z^-1 * y * z^-1 * y^7 * z^-1 * y^2 ] T85.131 : Triangle type {3,14,42} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * x * z^2 * y, y^-4 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 ] T85.132 : Triangle type {3,15,15} Group order 315 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^2 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 * z^-1 ] T85.133 : Triangle type {3,15,95} Group order 285 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z^-1 * x * z^3 ] T85.134 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y^4 * z^-1 * y * z^-3 * y^7 * z^-2 * y^2 * z^-2 ] T85.135 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * z^-1 * y^2 * z^-1 * x^-1 * y * z^-4 ] T85.136 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, y * z^-5 * y * z^-3 * y * z^-1 * y^2 * z^-1 * y^5 * z^-1 * y^2 * z^-1 ] T85.137 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z^2 * y^-1 * z * y^-1 * z^2 * y^-2 * z ] T85.138 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^3 * z^-7 * y^7 * z^-4 * y * z^-1 * y ] T85.139 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, (z * y * x^-1)^4 ] T85.140 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, y^-2 * z * y * x^-1 * y^-4 ] T85.141 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, y * z^-2 * y^6 * z^-2 * y ] T85.142 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, z^-5 * y * z^-2 * y * z^-1 * y * z^-2 * y^4 * z^-3 * y * z^-1 * y * z^-1 ] T85.143 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y^4 * z^-3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T85.144 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y * x * z^-1, y^4 * x^-1 * y^-2 * z * y ] T85.145 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-3 * y^6 * z^-1 * x^-1 * y^-3 * z^-1 * y * z^-1 ] T85.146 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, z^-1 * y^4 * z^-3 ] T85.147 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T85.148 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z * y * x^-1 * y^-3, z^-3 * x^-1 * z * y * z^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T85.149 : Triangle type {3,24,24} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T85.150 : Triangle type {3,39,39} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y * x^-1 * y * x^-1 * y * x * z * y^-1, y^-5 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z ] T85.151 : Triangle type {3,66,66} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, z^-1 * y * z^-5 * y * z^-2 * y^3 * z^-1 * y^2 * z^-2 * y^4 ] T85.152 : Triangle type {3,86,258} Group order 258 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-73 * z * y^-10 * z^2 ] T85.153 : Triangle type {3,87,87} Group order 261 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^10 * z^-1 * y^72 * z^-1 ] T85.154 : Triangle type {3,255,255} Group order 255 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-72 * z * y^-10 * z * y^-1 ] T85.155 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (z^-1 * x)^3, x * z * y * x^-2 * y^-1 * z^-1 * y * z^-1 ] T85.156 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, x * z * y * x^-1 * y^-1 * z^-1 * y ] T85.157 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, x * z * y * x^-2 * y^-1 * z^-1 * y * z^-1, x^-1 * y^-1 * z^-1 * x^-2 * z * y * z^-1 * y, (x * z * y^-1 * x * y^-1)^2 ] T85.158 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * z^-1 * y * x^-2 * z * y^-1 * z * x^-1, (y * x^-1 * z)^3, (z^-1 * x^-1 * y)^3 ] T85.159 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x, y * z^-1 * y * x^-2 * z * y^-1 * z * x^-1 ] T85.160 : Triangle type {4,4,4} Group order 672 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z * x^-1 * z * x^-1 * y^-1 * z * y^-1 ] T85.161 : Triangle type {4,4,14} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-2 * y * z^-5 * x * z^-1 * x * z * y * z^-3 ] T85.162 : Triangle type {4,4,30} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^5 * y^-2 * z^-2 * x * z^-2 * x * z ] T85.163 : Triangle type {4,4,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z^3 ] T85.164 : Triangle type {4,4,44} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-6 * x^-1 * z^9 * y * x * y^-1 * z^-5 ] T85.165 : Triangle type {4,4,44} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-33 * x * z^3 * y * z^-1 * x * z * y * z^-4 ] T85.166 : Triangle type {4,4,44} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^30 * y^-1 * z^-4 * x * z^2 * y^-1 * z^-6 * x ] T85.167 : Triangle type {4,4,86} Group order 344 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^69 * y * x * z^16 ] T85.168 : Triangle type {4,4,170} Group order 340 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^68 * y * x * y^-1 * z^-4 * x * z^11 ] T85.169 : Triangle type {4,6,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z * y * x^-1 * z * y * x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x^-1 ] T85.170 : Triangle type {4,6,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y^2 * x^-1 * z * y^3, y^2 * z^-1 * y * x^-1 * z^4, z^-3 * y * x^-1 * y^-1 * z^2 * y^-1 ] T85.171 : Triangle type {4,6,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, y * z^-1 * y^2 * x^-1 * z * y * z^-1 * y ] T85.172 : Triangle type {4,8,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (z^-1 * y)^3, z^8 ] T85.173 : Triangle type {4,8,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * z^2 * x^-1, z^2 * x^-1 * y^-1 * x * y^-2 * z, y^8 ] T85.174 : Triangle type {4,8,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T85.175 : Triangle type {4,8,10} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, y^-1 * z^-2 * x^-1 * z^3, y^8 ] T85.176 : Triangle type {4,8,10} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^3, (x * y^-1)^4 ] T85.177 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^2 * y^-1 * x * z^2, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T85.178 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^2 * y^-1 * x * z^2, (y * z^-1)^4 ] T85.179 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, z * y^-1 * z^-1 * x * z^2, x^-1 * y * x^-2 * y^-2 * z ] T85.180 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^8, z * y^3 * x^-1 * z^3 ] T85.181 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^2 ] T85.182 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, x * z * y * x^-1 * y^-1 * z^-2 ] T85.183 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, z^10 ] T85.184 : Triangle type {4,8,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^10 ] T85.185 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, z^6 * y^-1 * x * z^5, x^-1 * z^5 * y^-1 * x * y * z^-5 ] T85.186 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * z^5 * y^-1 * x^2 * z^5 ] T85.187 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T85.188 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z * y^-1 * z^-1 * x^2 * z * y^-1 * z ] T85.189 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^8, z^-3 * y^2 * z^-3 ] T85.190 : Triangle type {4,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^2 * y * x^-1 * z^3 ] T85.191 : Triangle type {4,8,136} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^14 * y^-1 * z^-5 * x * y^-1 * x * z^13 ] T85.192 : Triangle type {4,8,136} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^14 * y^-1 * z^-5 * x * y^-1 * x * y^-1 * z^-4 * x * z^8 ] T85.193 : Triangle type {4,9,18} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y * x^-1 * y * x^2 * z^2 * x^-1, y^-9 ] T85.194 : Triangle type {4,9,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y * x^-1 * y * x^2 * z^2 * x^-1, y^-9 ] T85.195 : Triangle type {4,9,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * x * z^-1 * x * z * y^-1, y^-9 ] T85.196 : Triangle type {4,9,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, (x * z * y)^2, z^-1 * y^2 * x^-1 * y^-3, y * z^-2 * x^-1 * z^3, y^-9 ] T85.197 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 ] T85.198 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T85.199 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T85.200 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T85.201 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * x * z, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z^5 * y^-3 * z * y^-1 ] T85.202 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y^-1 * z * y^2 * x * z * y * x^-1 ] T85.203 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y^2 * x^-1 * y^-2 * z^-1 ] T85.204 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-2 * y * x^-1 * y^2 * z^-1 ] T85.205 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3, y^5 * x^-1 * y^-6 * z^-1 ] T85.206 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * y^-2 * z^2 * x * y^-1 * z * y^-2 * z ] T85.207 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (z^-1 * x)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T85.208 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * y * x^-1 * y^-1 * z^-1, x * z * y^2 * z^-2 ] T85.209 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-1 * z^3 * y^-4 * z * y^-3, y^-12 ] T85.210 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, y^-12 ] T85.211 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^4 * x * z^-1 * x * z^-1 ] T85.212 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^-1 * z^3 * y^-4 * z * y^-3, y^-12 ] T85.213 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^4 * x * z^-1 * x * z^-1, y^-1 * z^-3 * x^-1 * z^2 * y * z^-2 * x * z^3 ] T85.214 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, (y * x^-1 * z)^3 ] T85.215 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3, y^4 * x * z^-1 * x * z^-1 ] T85.216 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3, z * y^3 * x * z^-1 * x * y^-1 ] T85.217 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1, x * z^-1 * y^2 * x^-1 * z * x^-1 * z * y ] T85.218 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, (y * x^-1 * z)^3 ] T85.219 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z^2 * y, (y * z^-1)^4 ] T85.220 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z^2 * y, (y * z^-1)^4 ] T85.221 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-12, x^-1 * z^3 * y * x^-1 * z * y * x^-1 * y * x^-1 * y^-3 * z^-4 ] T85.222 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^4 * x * z^-1 * x * z^-1, z^3 * y * z^-3 * x * z^5 ] T85.223 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^6 * x * y^-2 * z^-1 * x * y^-2 * z^-1, y^-1 * z^-5 * x^-1 * y * x^-1 * z^5 ] T85.224 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y^2 * z^-1 * y^2 * z^-3 ] T85.225 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z * y^2 * x * z^-1 * x, y^-2 * z * y * z^-1 * y^2 * x * z * y^-4 ] T85.226 : Triangle type {4,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x * z * y)^2, (y * z^-2)^2, (x * y^-1)^4 ] T85.227 : Triangle type {4,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, (y * z^-1)^4, y^4 * x^-1 * y^-3 * z, z^-2 * x^-1 * z * y * x * z^2 * y^-1 * z^-1 ] T85.228 : Triangle type {4,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^4 * x^-1 * y^-1 * z * y^2, z * y * x^-1 * z * y * x * z^4 ] T85.229 : Triangle type {4,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x * z^-2)^2, y * x * z^-1 * y^2 * x * y^-1 * z * y^2, z * y * x^-1 * z * y * x * z^4 ] T85.230 : Triangle type {4,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^4 * x^-1 * y^-2 * z * x^-1, z * y * x^-1 * z * y * x * z^4 ] T85.231 : Triangle type {4,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^4 * x^-1 * y^-2 * z^-1 * y, z * y * x^-1 * z * y * x * z^4 ] T85.232 : Triangle type {4,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^-1 * x^-1 * z^2 * y * x^-1 * z * y * z^-1 * x * y^-1 * z^-8 ] T85.233 : Triangle type {4,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^4 * x^-1 * y^-3 * z, z^9 * y * x^-1 * y * x^-1 * z^5 ] T85.234 : Triangle type {4,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^2 * y * x * z^4 * y^-1 * z^-3 * x^-1 * z^5 ] T85.235 : Triangle type {4,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, z^2 * y * x * z^5 * y * z^-2 * x^-1 * z^5 ] T85.236 : Triangle type {4,18,36} Group order 252 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1, y^-5 * z * y^-2 * z ] T85.237 : Triangle type {4,21,28} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x^-1 * z^3 ] T85.238 : Triangle type {4,24,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x * z, y^-1 * z^10 * y^-1 ] T85.239 : Triangle type {4,24,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z, z^7 * x^-1 * y^-1 * z^4 ] T85.240 : Triangle type {4,30,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * z * y^-1 * z * y^-1 * z * y^-4 * z^3 ] T85.241 : Triangle type {4,30,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-5 * y^2 * z^-2 * y^6 * z^-1 * y * z^-2 * y * z^-1 * y^6 * z^-1 * y ] T85.242 : Triangle type {4,58,116} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-26 * z * y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-2 ] T85.243 : Triangle type {4,114,228} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^26 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T85.244 : Triangle type {5,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T85.245 : Triangle type {5,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, y^6, (x * z * y * x)^2 ] T85.246 : Triangle type {5,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T85.247 : Triangle type {5,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^6, (x^-1 * z * y)^2, z^6, y^2 * x^-2 * z^2 * x^-1 ] T85.248 : Triangle type {5,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, (y * z^-1 * y)^2, y^2 * x * y^-1 * x * y^-1 * z^-1 * y ] T85.249 : Triangle type {5,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, (x * y^-2)^2 ] T85.250 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^6, x * z^-1 * x^-2 * y^-1 * z^-1 * y ] T85.251 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * x * y^-1 * x * z^-1 * x ] T85.252 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * y^-1, y^6, z^6, x^-1 * z * x^-2 * z * y^-1 * z^-1, y * x * y^-1 * x^2 * y^-2 * z^-1 ] T85.253 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * y^-1, y^6, z^6, x^-1 * z * x^-2 * z * y^-1 * z^-1, x^2 * y^-1 * x^2 * z * y^2 ] T85.254 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, y * x * y^-1 * x * y^-1 * x * z * y * x * z ] T85.255 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^6, y * x^-3 * z * x^-2, y * x * y^-1 * x * y^-1 * x * z * y * x * z ] T85.256 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, y^-1 * z * y^-1 * z * y^-1 * z^2 * x * y^-1 * z * y^-1 * z^2 ] T85.257 : Triangle type {6,6,6} Group order 336 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^6, y * z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-2 * y ] T85.258 : Triangle type {6,6,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, x * z^-1 * y * x^-1 * y^-1 * z^-2, x * z * y * x^-1 * z^2 * y^-1 ] T85.259 : Triangle type {6,6,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-1 * x^-2 * y^-1 * z^2, y^-1 * z * x^-2 * z^2 * y^-1 ] T85.260 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * x)^3, y^-1 * z^-1 * x^-2 * y^-1 * z^2 ] T85.261 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y * z^-1 * y * x * y^-1 * z^-1, (z^-1 * x)^3, z * y * x^-2 * y * x * z ] T85.262 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1 ] T85.263 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^3 * x^-1 * z^2 * y^-1 ] T85.264 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, (x * z * y)^2, z^2 * y^-1 * x^2 * z^3 ] T85.265 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * y * x^-2 * z * y * x, z^2 * y^-1 * x^2 * z^3 ] T85.266 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x * z * y)^2, y^-1 * z^-1 * x^-2 * y * x * y^-1, x * z * x^-2 * y^-1 * z^-2 ] T85.267 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T85.268 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^-4 * x^-1 * z^3 * y^-1 ] T85.269 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 ] T85.270 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, z * y^-2 * x^2 * y^-1 * z * y^-1 ] T85.271 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^3 ] T85.272 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-1 * x^-2 * z^2 * y^-1, z^-2 * y * x^-1 * y^-1 * x * z^-1 ] T85.273 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x^-1 * z * y)^2, z^2 * y * x * z^-1 * x^-1 ] T85.274 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^6, (y * z^-1 * y)^2, y * z^-2 * x^-1 * z^3 ] T85.275 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2 ] T85.276 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x^-1 * y^-1 * x^2 * z * y * x ] T85.277 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T85.278 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T85.279 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^6, y^6, z^-1 * x^-1 * y^-1 * x^2 * z * y^-1 * x ] T85.280 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * y * z^-1 * x^-1 * z^3, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T85.281 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^12 ] T85.282 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * x^-2 * y^-2 * z^-1, x * z^-1 * y * x^-1 * z^2 * y^-1 ] T85.283 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^4 * x^-1 * z^3 * y^-1 ] T85.284 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, y^-1 * z^-1 * x * z^4 * y * x^-1 * z^5 ] T85.285 : Triangle type {6,6,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z * y * x^-2 * y^-1 * x * y^-1, z * x^-1 * y * x^-1 * y^-2 * x, y * x * z * y * x * z^3 ] T85.286 : Triangle type {6,6,33} Group order 264 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, x * z^2 * y^-1 * z^-1 * x^-1 * y * x * z * y * z^-4 ] T85.287 : Triangle type {6,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z * y^2 * x * z * x^-1, y^8 ] T85.288 : Triangle type {6,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8 ] T85.289 : Triangle type {6,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x^-1 * z * y)^2, (x * z * y)^2 ] T85.290 : Triangle type {6,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T85.291 : Triangle type {6,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y^8 ] T85.292 : Triangle type {6,8,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^-4 * x^-1 * z * y * z^-4 ] T85.293 : Triangle type {6,8,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^2 * y * z^-2 * x^-1 * z^5 ] T85.294 : Triangle type {6,10,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^10 ] T85.295 : Triangle type {6,12,12} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T85.296 : Triangle type {6,12,12} Group order 252 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, x^6, y * x^-3 * z * x^-2 ] T85.297 : Triangle type {6,12,12} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, (z^-1 * y)^3, z^2 * y^-1 * x^2 * z^3, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 ] T85.298 : Triangle type {6,12,12} Group order 252 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-2 * y ] T85.299 : Triangle type {6,12,12} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, z^-2 * y^2 * z^-1 * y, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T85.300 : Triangle type {6,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * z * y^-1 * x * z^2, (y * z^-2)^2 ] T85.301 : Triangle type {6,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y * x^-3 * z * x^-2, z * y^2 * x^-1 * z^3 ] T85.302 : Triangle type {6,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z * y^-1 * x * y^-1 * x * z^5 * y^-1 * z^-1 * x * y * x * z^9 ] T85.303 : Triangle type {6,12,76} Group order 228 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * y)^3, z^-2 * y * x^-1 * z^2 * y ] T85.304 : Triangle type {6,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^3, z^2 * x^-2 * z^3 ] T85.305 : Triangle type {6,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^-4 * z^2 * y^-1 ] T85.306 : Triangle type {6,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^-3 * x * y^-1 * z * y^-2 ] T85.307 : Triangle type {6,35,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T85.308 : Triangle type {6,36,36} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z * y^-1 * z^2 * y^-4 * z * y^-1 * z^2 ] T85.309 : Triangle type {6,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T85.310 : Triangle type {6,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^-1 * z^2 * y^-1 * z * y^-2 * z^5 ] T85.311 : Triangle type {6,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^11 * z^-1 ] T85.312 : Triangle type {6,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z * y^-6 * z ] T85.313 : Triangle type {6,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z * y^-3 * z^4 ] T85.314 : Triangle type {6,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-3 * x^-1 * z^3 ] T85.315 : Triangle type {6,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^10 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T85.316 : Triangle type {8,18,24} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T85.317 : Triangle type {8,18,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x^8, x^-1 * y^-1 * z * x^-1 * z * y^6 ] T85.318 : Triangle type {9,9,9} Group order 252 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * y * z^-1 ] T85.319 : Triangle type {9,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^-1 * y, x^-1 * y * x^-2 * z^3, z * y * x^-2 * y * z^-1 * x^-1 ] T85.320 : Triangle type {9,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-2, y * x^-3 * y^3, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T85.321 : Triangle type {9,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, z * y * x^-2 * z * y * x ] T85.322 : Triangle type {9,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, x * y^-2 * x * z^-1 * y, (z^-1 * y)^3 ] T85.323 : Triangle type {9,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3, x^-9 ] T85.324 : Triangle type {9,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x * z^-1 * y * x * z^-2, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^-3 ] T85.325 : Triangle type {9,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x^-9 ] T85.326 : Triangle type {9,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2, x^-9 ] T85.327 : Triangle type {10,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1 * x)^2, (x * z^-1 * x)^2, (x * y^-2)^2, z * y * z^-1 * x^-2 * y^-1 * z * y * x ] T85.328 : Triangle type {10,10,10} Group order 240 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, y^-1 * z^-2 * x * z^2 ] T85.329 : Triangle type {10,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, (z^-1 * x)^3, z * y^-1 * x * y^-1 * x * z^3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T85.330 : Triangle type {10,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1, x^10 ] T85.331 : Triangle type {10,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3, z^-3 * x^2 * z^-3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T85.332 : Triangle type {10,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-5 * y * z^-5 * y^6 * z^-2 ] T85.333 : Triangle type {10,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-8 * z^5 * y^-1 * z * y^-4 ] T85.334 : Triangle type {10,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T85.335 : Triangle type {11,18,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T85.336 : Triangle type {11,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T85.337 : Triangle type {11,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z * y^-6 * z^5 * y^-1 * z * y^-1 * z^2 ] T85.338 : Triangle type {11,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-3 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T85.339 : Triangle type {11,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^-7 * z^5 * y^-1 * z * y^-1 * z * y^-1 ] T85.340 : Triangle type {11,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^6 * z^-4 * y * x^-1 * y^6 ] T85.341 : Triangle type {12,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^2 * z * y, z * y^-1 * z^-1 * x^-1 * z^3, y^-1 * x * y^-3 * x^4 * z * y^-1 * x^2 ] T85.342 : Triangle type {12,12,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^3 * x^-1 * z^2 * y^-1, z^-2 * x * y^-1 * x * z^2 * y^-1 ] T85.343 : Triangle type {12,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^-4 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-4 ] T85.344 : Triangle type {12,12,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z^6 * y^-1 * z^-4 ] T85.345 : Triangle type {12,12,102} Group order 204 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y * z^-1 * x^-1 * z * y * z^-1 * x * z * y^-1 * z^-2 * x^-1 * z^5 ] T85.346 : Triangle type {12,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^8 * z^-3 * y * z^-1 * y * z^-2 ] T85.347 : Triangle type {12,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T85.348 : Triangle type {12,48,48} Group order 192 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, y^-2 * x^3 * y^-1 * x * y^-1, x * z^-1 * x^3 * z^-3 ] T85.349 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2, x^-2 * z^2 * x^-1 * z * x^-2 * z * x^-2 ] T85.350 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z^-2, x * y^-2 * x * z * y^-1 ] T85.351 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T85.352 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x^-1 * y * x^-1 * z * y * x^-7 * z * x^-1 ] T85.353 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T85.354 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * x^2 * y^-4, z^-4 * x^2 * z^-4 ] T85.355 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x * y^-1 * x^3 * y^-1 * z^-2, z^-2 * y^3 * z^-2 * y ] T85.356 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1, x^-1 * y * x^-1 * z * x^-2 * z * x^-6 * y ] T85.357 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-4 * y^-1 * x^3, x^-1 * y * x^-4 * z * x^-6 ] T85.358 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x * y^-1 * x * y^-4, z^-3 * x * z^-1 * x * z^-4 ] T85.359 : Triangle type {12,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-3 * y^4 * z^-3 * y * z^-1 * y^2 * z^-1 ] T85.360 : Triangle type {14,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, (z * y^-1)^7 ] T85.361 : Triangle type {14,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^5 * z * x^-1 * y^-1, x^2 * z^-1 * x^2 * z^-3 ] T85.362 : Triangle type {14,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^4 * z^-1 * x^-2, y^-3 * x * y^-1 * x * y^-4 ] T85.363 : Triangle type {14,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * y^-1 * x^3 * z * x^-2, x * z^-3 * x^10 * y^-1 * x ] T85.364 : Triangle type {14,28,28} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T85.365 : Triangle type {16,24,48} Group order 192 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x^-1, z^-2 * x^2 * y^-2, y * z^-2 * y^3 * z^-1 * y^3 * z^-1 * y ] T85.366 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3, x^-6 * y^3 ] T85.367 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * z * y * x^-8 * z * y * x^-5 ] T85.368 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * z^2 * y^-1, z^-1 * x^5 * y^-1 * z^-1 * x * y^-1 ] T85.369 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * y * x * z * y^-1, x^-6 * y^3 ] T85.370 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^2 * z^-2 * x^4 * z^-3 ] T85.371 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, (y * z^-2)^2 ] T85.372 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3, y^-1 * z * y^-5 * z * y^-1 ] T85.373 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (z^-1 * x)^3, (y * z^-2)^2 ] T85.374 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y^4 * x^-1 * y^-1 * z^-1 * y^2, x^-1 * z * x^-1 * z * x^-1 * y^-1 * z^3 ] T85.375 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, z^-3 * x^2 * z^-3 ] T85.376 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-1 * z * y * x^-1 * y * x^-1 * z * y * x^-6 * z^2 * x^-1 * y * x^-2 ] T85.377 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x^3 * y^-4, x^2 * z^-2 * x^4 * z^-4 ] T85.378 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^-2 * z^3 * y^-2 * z * x^-1 * z^3 * y^-1 ] T85.379 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T85.380 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-6 * z * x^-1 * y ] T85.381 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-3 * y * x^-1 * z * y * x^-7 * z * x^-3 ] T85.382 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-4 * x^-1 * z * y * z^-2, y^-1 * x^5 * y^-1 * z^-2 * x ] T85.383 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, (y * z^-2)^2, x^-6 * z * x^-1 * y ] T85.384 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, y^-1 * x^5 * y^-1 * z^-2 * x ] T85.385 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^4 * y^-4, z^-1 * x * z^-2 * x^4 * z^-1 * x * z^-2 ] T85.386 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, x^-6 * z * x^-1 * y ] T85.387 : Triangle type {16,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-2, z^-2 * x^-2 * z * y^-1 * x, x^-6 * z * x^-1 * y ] T85.388 : Triangle type {18,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T85.389 : Triangle type {18,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^7 * z^-3 * x^4 * y^-3 * x^4 ] T85.390 : Triangle type {20,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T85.391 : Triangle type {20,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T85.392 : Triangle type {20,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-4 ] T85.393 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-7 * x * y^-2 * z * y^-2 ] T85.394 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^6 * x^-6 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T85.395 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, z^-1 * x^4 * z^-3, y^4 * x^-1 * y^-1 * z^-1 * y^2 ] T85.396 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, z^-1 * x^4 * z^-3 ] T85.397 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, y^3 * x^-1 * y^-4 * z^-1, y^-2 * z * y^-1 * x * y^-3 * x * y^-4 * z ] T85.398 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * y^-1 * z^-1, x^-2 * y^2 * x^-1 * y^2 * x^-1 * y^3 * x^-1 * y * z^-1 * y ] T85.399 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T85.400 : Triangle type {24,24,24} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T85.401 : Triangle type {27,27,27} Group order 189 Chiral action Defining relators: [ x * y * z, x * z^-1 * x^-1 * y^-1 * z^-1, z^-1 * x^3 * z^-2, y^8 * x^-3 * y^4 ] T85.402 : Triangle type {27,27,27} Group order 189 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, y^-1 * x * y^-1 * x * z * y^-1 ] T85.403 : Triangle type {30,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-7 * y * x^-1 * y * x^-1 * y * x^-12 * y * x^-1 * y * x^-1 * y * x^-2 ] T85.404 : Triangle type {30,36,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-3 ] T85.405 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T85.406 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-8 * y^2 * x^-6 * y^3 * x^-6 * y * x^-7 ] T85.407 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x^2 * z^-3, y^2 * x^-3 * y^4 ] T85.408 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^18 * y^-1 * x^10 * y^-1 * x ] T85.409 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-2 * y * x^2 * z^-3, y^2 * x^-3 * y^4 ] T85.410 : Triangle type {30,60,60} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-1 * z * x^-1 * y * x^-7 ] T85.411 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-5 ] T85.412 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^-13 * x * y^-1 * x * y^-1 ] T85.413 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, z^-9 * y^2 * z^-4 ] T85.414 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z^10 * x^-4 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T85.415 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-5 * y^5 * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y * x^-2 ] T85.416 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-18 * y^2 * x^-7 * z^2 * x^-8 ] T85.417 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T85.418 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-3 * y^6 * x^-4 * z * x^-4 ] T85.419 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^2 * x^-1 * y * x^-1 * y * x^-1 * y^9 * z^-2 * y * x^-1 * y * x^-1 * y^3 ] T85.420 : Triangle type {35,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^-5 * x * y^-1 * z^5 * y^-4 ] T85.421 : Triangle type {36,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^3 * z^-2 * x, x * y^-1 * x * y^-1 * x * z * y^-1 * z^-1 ] T85.422 : Triangle type {36,36,90} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z * y^-1 * z * x^-1 * z^3 * x^-3 * z * y^-1 * z^2 * x^-1 * z * x^-1 * z^2 * y^-1 * z * y^-1 * z ] T85.423 : Triangle type {36,45,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^-4 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T85.424 : Triangle type {36,45,60} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^9 * z^-2 * y * x^-1 * y * x^-1 * y^3 ] T85.425 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-1 * z^2 * y^-1 * z * y^-1 * x * y^-2 * z * y^-2 * x * y^-1 ] T85.426 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y^3 * x^-1 * y^2 * x^-1 * y^5 ] T85.427 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-4, z^-3 * x * z^-1 * x * z^-4 ] T85.428 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^2 * z^-2 * x^5 * z^-1 * x * z^-1 ] T85.429 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-6 * z^2 * x^-2 * z * x^-9 * z * x^-3 ] T85.430 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T85.431 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^2 * x^-6 * y^18 * x^-1 * y * x^-1 * y^3 ] T85.432 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^3 * y^-6 * z^11 ] T85.433 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^3 * z^-1 * x^4 * y^-5 * x^2 ] T85.434 : Triangle type {44,88,88} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-28 * z * x^-8 * y * x^-7 ] T85.435 : Triangle type {45,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-13 * x^3 * y^-2 * x * y^-4 * x * y^-1 ] T85.436 : Triangle type {45,45,45} Group order 180 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, y^2 * x^2 * z^2, (x * z * y)^2, z^2 * y^-1 * z * x^-1 * y^-1 * z^3 ] T85.437 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^16 * z^-2 * y^12 ] T85.438 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-2, x^-2 * y^5 * x^-3 * z^2 * x^-3 ] T85.439 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^24 * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^3 ] T85.440 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^5 * z^-1 * x * z^-1 * x * z^-4 * x^9 ] T85.441 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T85.442 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T85.443 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T85.444 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^2 * z^-1 * y * z^-5 * y^6 ] T85.445 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-4 * x^5 * y^-6 * x * y^-2 ] T85.446 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-3 * x^7, y^-9 * z^2 * y^-4 ] T85.447 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-15 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T85.448 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-13 * x * z^-4 * x^2 * z^-5 * y * z^-1 ] T85.449 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^7 * x^-6 * y * x^-7 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T85.450 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-10 * y * z^-4 ] T85.451 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^3 * z^-1 * x * z^-1 * x * z^-4 * x^7 ] T85.452 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-6 * x^3 * y^-6 * x * y^-3 ] T85.453 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-2 * z * y^-9 * z * y^-5 ] T85.454 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^9 * z^-4 * y^6 * z^-1 * y * z^-1 * y^2 ] T85.455 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-12 * x * y^5 * z^-1 * y * z^-2 ] T85.456 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^10 * y^-6 * x^4 ] T85.457 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T85.458 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T85.459 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^-3 * y^5 * x^-3 * z^2 * x^-4 ] T85.460 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^7, z^-3 * y * z^-5 * y^2 * z^-4 ] T85.461 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, x^8 * y^-6 * x^2 ] T85.462 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-37 * y * x^-1 * y * x^-1 * y * x^-17 ] T85.463 : Triangle type {58,87,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^-3 * y^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T85.464 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * z^-3 * y^2 * x^-2 * y^8 ] T85.465 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-45 * x^2 * y^-11 ] T85.466 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T85.467 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T85.468 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^-6 * x * y^-2 * z^3 * y^-5 ] T85.469 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-7 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T85.470 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T85.471 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x^3 * z^-2 * x^8 ] T85.472 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^11 * z^-5 * y^10 ] T85.473 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T85.474 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^7 * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T85.475 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^4 * y^-5 * x, z^-5 * x * z^-4 * x * y * z^-4 ] T85.476 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^11 * z^-1 * y^8 * z^-1 * y^10 * z^-1 * y * z^-1 * y^2 ] T85.477 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 ] T85.478 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T85.479 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T85.480 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^5 * z^-3 * x^6 * y^-1 * x ] T85.481 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^-1 * y^6 * x^-5 * y^2 ] T85.482 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, z^-9 * y * z^-4 ] T85.483 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-9 * z^4 * y^-7 ] T85.484 : Triangle type {86,172,172} Group order 172 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^9 * y^-1 * x^12 * y^-1 * x^64, y * z^-1 ] T85.485 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-10 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-7 ] T85.486 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x^-2 * y^-1, y^-66 * x * y^-19, x * z^-1 ] T85.487 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-13 * y^2 * x^-5 * y^3 * x^-8 ] T85.488 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, x^6 * z^-4 * x^7 ] T85.489 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^9, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T85.490 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-10 * y * z^-5 * y * x^2 * z^-4 * y * z^-1 * y * z^-1 ] T85.491 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^-2 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T85.492 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, z^-3 * y * z^-5 * y^2 * z^-4 ] T85.493 : Triangle type {171,171,171} Group order 171 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-2 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] Genus 86 T86.1 : Triangle type {2,3,40} Group order 1200 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1, z^10 * y * z^-3 * x * y^-1 * z^-4 * x * z^5 ] T86.2 : Triangle type {2,4,174} Group order 696 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-174 ] T86.3 : Triangle type {2,4,344} Group order 688 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y^-1 * z^-130 ] T86.4 : Triangle type {2,6,20} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T86.5 : Triangle type {2,6,20} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z^-3 * y * z^-1 * y^2 * z^-1 * y * z^-3 ] T86.6 : Triangle type {2,6,88} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-63 * x * z^5 * y * z^-1 * x * y^-1 * z^-17 ] T86.7 : Triangle type {2,6,258} Group order 516 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-47 * x * z * y * x * z^22 * y^-1 * x * y^-1 * z^-13 ] T86.8 : Triangle type {2,8,116} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-24 * x * z^11 * y * x * z * y * x * y * z^-19 ] T86.9 : Triangle type {2,10,45} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-7 * x * z^22 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T86.10 : Triangle type {2,10,215} Group order 430 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * z^-3 * x * z^21 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-3 * x * z ] T86.11 : Triangle type {2,20,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-2 * z * y^10 * x * y^-1 * z^-1 * y * x * y^-4, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-9 * x * y^-1 * z^-3 ] T86.12 : Triangle type {2,20,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, x * z * y * z^-2 * y^8 ] T86.13 : Triangle type {2,20,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-8 * z^4 * y^-3 * z^4 * y^-1, z^9 * y * z^-4 * x * z^6 ] T86.14 : Triangle type {2,24,24} Group order 408 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^2 * x * y^-1 * z^-1, x * y^-5 * z^-2 * y^2 * z^-1, z^-1 * y^6 * z^-1 * y * z^-3 ] T86.15 : Triangle type {2,173,346} Group order 346 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^119 * y^-52 * z ] T86.16 : Triangle type {2,174,174} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^54 * z^-120 ] T86.17 : Triangle type {2,344,344} Group order 344 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^53 * z^-119 ] T86.18 : Triangle type {3,3,20} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^4 * y * x * y^-1 * x^-1 * z^3 * y^-1 * z^-1 * x^-1 ] T86.19 : Triangle type {3,20,20} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^6 * y^-1 * z^-1 * y^2 * x ] T86.20 : Triangle type {3,20,20} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^3 * x^-1 * y^-1 * x * z * y^3 ] T86.21 : Triangle type {3,20,20} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, y^2 * z^-1 * y^2 * z^-3, y^3 * z^-1 * x^-1 * z^2 * y * z^-1 ] T86.22 : Triangle type {3,88,88} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^72 * y^-15 ] T86.23 : Triangle type {3,258,258} Group order 258 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-73 * z * y^-12 ] T86.24 : Triangle type {4,4,87} Group order 348 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, (x * z^2 * y^-1)^2, z^-1 * x * z^-2 * y * z^-3 ] T86.25 : Triangle type {4,4,87} Group order 348 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^87 ] T86.26 : Triangle type {4,4,172} Group order 344 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^69 * y * x * y^-1 * z^-4 * x * z^11 ] T86.27 : Triangle type {4,6,26} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^4 * y^-1 * z^-5 * x^-1 * z^6 * y * x * z * y^-1 * z^-4 * x^-1 * z^3 ] T86.28 : Triangle type {4,12,44} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-5 * x^-1 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z^2 * y^-1 * z^-7 ] T86.29 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * y * x^-1 * z^3 ] T86.30 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-2 ] T86.31 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y * z^-1 ] T86.32 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-1 * z^-2 ] T86.33 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, x * z^-1 * x^-2 * z * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * y * x * z^-1 ] T86.34 : Triangle type {4,16,16} Group order 272 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, z^-1 * x * z^-1 * x * z^-1 * y ] T86.35 : Triangle type {4,30,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-4 * y^6 * z^-1 * y * z^-2 * y * z^-1 * y^8 ] T86.36 : Triangle type {4,40,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^4 * y^-1 * z^-6 * x^-1 * z, z^-2 * y^4 * z^-4 ] T86.37 : Triangle type {4,116,116} Group order 232 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^24 * z^-2 * y * z^-1 * y^10 * z^-1 * y^6 * z^-1 * y^11 ] T86.38 : Triangle type {5,44,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-6 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T86.39 : Triangle type {5,45,45} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^16 * z^-6 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T86.40 : Triangle type {5,215,215} Group order 215 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z * y^-10 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T86.41 : Triangle type {5,215,215} Group order 215 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-13 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T86.42 : Triangle type {6,6,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, z * y^2 * x^2 * z^3 ] T86.43 : Triangle type {6,6,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-2 * y * x^2 * z^-1 * y * z^-1 ] T86.44 : Triangle type {6,6,44} Group order 264 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-44 ] T86.45 : Triangle type {6,6,129} Group order 258 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^21 * y * z^-2 * x * z^3 * y^-1 * z^-8 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T86.46 : Triangle type {6,10,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x * z^-1 * x^-1, (y^-1 * z^2 * y^-1 * z)^2 ] T86.47 : Triangle type {6,10,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, y^10 ] T86.48 : Triangle type {6,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T86.49 : Triangle type {8,8,58} Group order 232 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^-2 * y * x^-2 * z * y * z^-2 ] T86.50 : Triangle type {8,8,58} Group order 232 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-13 * x * y^-1 * x * y^-1 * z^-14 ] T86.51 : Triangle type {8,10,15} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^8, z^-1 * x^-1 * y^-1 * x^2 * z * y * x ] T86.52 : Triangle type {8,26,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^17 * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 ] T86.53 : Triangle type {8,50,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^3 ] T86.54 : Triangle type {10,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, z * x^-2 * y * x, y^-6 * z * y^-1 * z * y^-2 * z * y^-6 * z^2 ] T86.55 : Triangle type {10,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, x^-1 * z * y^-1 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y * x^-1 * y, x^-1 * z * x^-2 * z^3 ] T86.56 : Triangle type {10,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^2, z * x^-1 * y^-1 * x * y^-2, x^-10 ] T86.57 : Triangle type {10,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z * x^-2 * y^-1 * z * y^-1, x^10 ] T86.58 : Triangle type {10,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^6 * x^-3 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T86.59 : Triangle type {10,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^4 * y^-2 * z, y * x^4 * z^-3 ] T86.60 : Triangle type {10,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-3 ] T86.61 : Triangle type {12,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, z^-1 * y^2 * z^-1 * y * z^-1 * y * x * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y ] T86.62 : Triangle type {18,18,33} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^-1 * x * z^2 * y^-1 * z^-2 * x^-1 * z * y * z^-3 ] T86.63 : Triangle type {20,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, y^-4 * z * y^-5 * x, y^-4 * z * y^2 * x^-1 * y^-3 ] T86.64 : Triangle type {20,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^6 * z^-2, y^-1 * z^-1 * y^8 * x ] T86.65 : Triangle type {20,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y, y * x^-1 * y^-1 * z * y * x^-1 * z * x^-1 * z * y * x^-1 * y^-1 * z * x^-1 * z ] T86.66 : Triangle type {20,20,20} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-3 * y * x^-5 * z * x^-1, z^3 * y^-1 * z * x^-1 * z^5 ] T86.67 : Triangle type {30,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, (y^-5 * x * y^-1)^2 ] T86.68 : Triangle type {30,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, (x^-9 * y * x^-1 * y * x^-1 * y * x^-2)^2 ] T86.69 : Triangle type {30,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-2 ] T86.70 : Triangle type {36,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, z^-3 * y * z^-5 * y^2 * z^-4 ] T86.71 : Triangle type {36,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^11 * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-10 * y * x^-1 * y * x^-1 * y * x^-2 ] T86.72 : Triangle type {36,45,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^4 * y^-7, z^-3 * y * z^-5 * y^2 * z^-4 ] T86.73 : Triangle type {36,60,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-19 * y^2 * x^-7 * z^2 * x^-8 ] T86.74 : Triangle type {36,60,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^3 * z^-3, x^3 * z^-1 * x * z^-4 * x^6 ] T86.75 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-1 * y^6 * x^-5 * y^2 ] T86.76 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^5 ] T86.77 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T86.78 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^9 * x^-6 * y * x^-1 * y^2 ] T86.79 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * x^-1 * y^13 * x^-1 * y^9 ] T86.80 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T86.81 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-22 * y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-2 ] T86.82 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^12 * x^-1 * z * x^-1 * z^5 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T86.83 : Triangle type {44,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T86.84 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^34 * x^-3 * y^8 ] T86.85 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T86.86 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T86.87 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^9 * x^-1 * y^5 * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^3 ] T86.88 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T86.89 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x^6 * z^-4 * x^7 ] T86.90 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-1 * y * z^-7 * y * z^-1 * y * z^-5 * y * x^2 * z^-4 * y * z^-1 * y * z^-1 ] T86.91 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T86.92 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T86.93 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-9 * y * z^-4 ] T86.94 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, x * y^-1 * x^6 * y^-5 * x^2 ] T86.95 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T86.96 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^6 * z^-3 * y^9 ] T86.97 : Triangle type {87,174,174} Group order 174 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^87, y * z^-1 ] T86.98 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x^-2 * y^-1, y^-66 * x * y^-20, x * z^-1 ] T86.99 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-46 * x * y^-11 ] T86.100 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^26 * y^-2 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T86.101 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^9 * y^-3 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T86.102 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x^7 * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T86.103 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-6 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T86.104 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T86.105 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^3 * x^-1 * y^6 * x^-6 * y^4 ] T86.106 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^2 * x^-1 * y^6 * x^-6 * y^3 ] T86.107 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^5 * z^-3 * y^2 * x^-6 * y^3 ] T86.108 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x * y^-1 * x^6 * y^-7 ] T86.109 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-2 * y^5 * x^-7 ] T86.110 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-4 * x * z^-4 * x * y * z^-4 ] T86.111 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-6, z^-5 * x * z^-4 * x * y * z^-4 ] T86.112 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 ] T86.113 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x^4 * z^-3 * x^7 ] T86.114 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T86.115 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T86.116 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^3 * y^-6 * z^5 * y^-1 * z * y^-1 * z^4 ] T86.117 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T86.118 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-6 ] T86.119 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-7 ] T86.120 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T86.121 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^4 * z^-2, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T86.122 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-15 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-6 ] T86.123 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * x^-5 * z^12 ] T86.124 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^12 * z^-3 * y^11 ] T86.125 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^3 * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T86.126 : Triangle type {173,173,173} Group order 173 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^3 * z^-2 * y^8 ] Genus 87 T87.1 : Triangle type {2,3,12} Group order 2064 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^2 * y * z^-1 * x * z * y * x * z^2 * y * z^-2 * x * z^2 * y * z^-1 * x * z^2 * y * z^-1 * x * z^3 * y * x * z * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 * x ] T87.2 : Triangle type {2,4,90} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-71 * x * z^11 * y^-1 * z^-7 ] T87.3 : Triangle type {2,4,176} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-176 ] T87.4 : Triangle type {2,4,176} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-70 * x * z^8 * y * x * z * y^-1 * z^-7 ] T87.5 : Triangle type {2,4,348} Group order 696 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y^-1 * z^-134 ] T87.6 : Triangle type {2,7,14} Group order 602 Chiral action Defining relators: [ x^2, x * y * z, y^-7, x * y^-1 * z * y^2 * x * y^-1 * z^-1 ] T87.7 : Triangle type {2,7,14} Group order 602 Chiral action Defining relators: [ x^2, x * y * z, y^-7, z^-3 * y^3 * z^-1 * x * y^-1 * z^-1 ] T87.8 : Triangle type {2,7,14} Group order 602 Chiral action Defining relators: [ x^2, x * y * z, y^-7, x * z * y^-3 * z^-1 * y^2 * z^-1 ] T87.9 : Triangle type {2,8,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-9 * x * z^2 * y * x * z^6 * y * z^-2 * x * z * y^-1 * z^-7 ] T87.10 : Triangle type {2,8,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-20 * x * z^3 * y^-1 * x * z^4 * y^-1 * z^-1 ] T87.11 : Triangle type {2,8,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-46 * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-5 ] T87.12 : Triangle type {2,8,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-24 * x * z^21 * y * z^-8 * x * z^2 * y^-1 * z^-3 ] T87.13 : Triangle type {2,8,232} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-23 * x * z^20 * y * z^-1 * x * y^-1 * z^-12 ] T87.14 : Triangle type {2,8,232} Group order 464 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-23 * x * z^20 * y * z^-8 * x * z^2 * y^-1 * z^-3 ] T87.15 : Triangle type {2,14,203} Group order 406 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-2 * z^4 * y^-1)^2, z^15 * y * z^-3 * x * z^10 ] T87.16 : Triangle type {2,24,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^9 * y * x * z^4 * y^-1 * z^-1 * x ] T87.17 : Triangle type {2,24,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^9 * z^-1 * y * z^-1, z^-3 * x * z^4 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 ] T87.18 : Triangle type {2,90,90} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-86 * z * y^-1 ] T87.19 : Triangle type {2,118,177} Group order 354 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-23 * y^13 * z^-2 * y^20 ] T87.20 : Triangle type {2,175,350} Group order 350 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^120 * y^-54 ] T87.21 : Triangle type {2,176,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-54 * y^34 ] T87.22 : Triangle type {2,176,176} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^55 * z^-120 * y ] T87.23 : Triangle type {2,348,348} Group order 348 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^54 * z^-119 * y ] T87.24 : Triangle type {3,3,6} Group order 1032 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z * y * z^-1 * x^-1 * z * y * x * z * y * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z^-1 * x * z^-1 * x * y^-1 * x * y^-1 * z^-1 * x^-1 ] T87.25 : Triangle type {3,4,12} Group order 516 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-2 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T87.26 : Triangle type {3,12,14} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^-2 * x^-1 * z^3 ] T87.27 : Triangle type {3,39,91} Group order 273 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * z^3, y^-1 * z * y^-3 * z * y^-3 * z * y^-2 * z ] T87.28 : Triangle type {3,88,264} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-74 * z * y^-10 * z * y^-1 * z ] T87.29 : Triangle type {3,261,261} Group order 261 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^10 * z^-1 * y^73 ] T87.30 : Triangle type {4,4,45} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^29 * y * z^-5 * x^-1 * y * x^-1 * z * y * z^-7 * x ] T87.31 : Triangle type {4,4,88} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^30 * y * z^-4 * x * z^2 * y^-1 * z^-6 * x ] T87.32 : Triangle type {4,4,88} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-32 * x^-1 * z^4 * y * z^-1 * x * z * y * z^-4 ] T87.33 : Triangle type {4,4,88} Group order 352 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^88 ] T87.34 : Triangle type {4,4,88} Group order 352 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-32 * x^-1 * z^4 * y * z^-1 * x * y^-1 * z^-5 ] T87.35 : Triangle type {4,4,174} Group order 348 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^74 * y * x^-1 * z^12 ] T87.36 : Triangle type {4,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z * y^-1 * z^-3 * x * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^4 ] T87.37 : Triangle type {4,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x^-1 * z^4 ] T87.38 : Triangle type {4,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, y^6, (x * z^-2)^2 ] T87.39 : Triangle type {4,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^3 * y^-1 * x * z^3, y * x * z * y * x * z * y * z^-2 * y^-1 * z^-2 * x * z ] T87.40 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^5 * y * x^-1 * z * y^-1 * z^-3 * x^-1 * y * z^-6 * x ] T87.41 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^5 * y * x^-1 * z^2 * y * z^-2 * x^-1 * z^2 * y^-1 * z^-4 * x^-1 ] T87.42 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-2 * z^2 * x^-1, z^-5 * x * z^3 * y^-1 ] T87.43 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-2 * z^2 * x^-1, z^2 * y^-1 * z^-2 * x * z^4 ] T87.44 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^6 * y * x^-1 * z^2 * y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-1 * x * z ] T87.45 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^7 * y * z^-4 * x^-1 * z * y * x^-1 * z^4 ] T87.46 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^22 * y^-1 * x * y^-1 * z^-4 * x * z^8 ] T87.47 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^21 * y * z^-1 * x^-1 * y * z^-1 * x^-1 * z^11 ] T87.48 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^2 * y * x * z * y * z^-7 * x * y^-1 * z^-1 * x * z * y * z^-1 * x * z ] T87.49 : Triangle type {4,8,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^6 * y * x^-1 * z^2 * y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-1 * x^-1 * z ] T87.50 : Triangle type {4,10,28} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^2 * z^-1, z^4 * y * x * z^2 * y * z^-1 * x * z^5 ] T87.51 : Triangle type {4,10,28} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, z^-3 * x * z^2 * y * x^-1 * z * y * x^-1 * y * x * y^-1 * z^-4 ] T87.52 : Triangle type {4,12,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^-1 * z^8 * y * x * z^8 * y^-1 * z^-4 ] T87.53 : Triangle type {4,40,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-8 * z * y^-1 * z * y^-1 * z^2 * y^-3 * z^2 * y^-1 ] T87.54 : Triangle type {4,40,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^-8 * z * y^-2 * z * y^-3 * z^3 * y^-1 * z ] T87.55 : Triangle type {4,59,236} Group order 236 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^32 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^8 * z^-3 * y^2 * z^-1 * y * z^-1 * y * z^-2 ] T87.56 : Triangle type {4,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^15 * y^-5 * z^2 * y^-4 * z^2 * y^-1 ] T87.57 : Triangle type {4,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-3 * z * y^-1 * z * y^-2 * z * y^-1 * z ] T87.58 : Triangle type {4,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-5 * y^2 * z^-2 * y^6 * z^-1 * y * z^-2 * y * z^-1 * y^7 * z^-1 ] T87.59 : Triangle type {4,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-29 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T87.60 : Triangle type {4,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^27 * z^-2 * y * z^-1 * y^12 * z^-1 * y^6 * z^-1 * y^2 * z^-1 * y^6 ] T87.61 : Triangle type {4,232,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-26 * z * y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 * z ] T87.62 : Triangle type {4,232,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-25 * z * y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-11 * z * y^-1 * z^3 ] T87.63 : Triangle type {6,10,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, (y * z^-1 * y * z^-2)^2 ] T87.64 : Triangle type {6,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * x^-1 * y * x * z^-1 ] T87.65 : Triangle type {6,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y * z^-7 * y^5 * z^-1 * y * z^-3 ] T87.66 : Triangle type {6,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T87.67 : Triangle type {7,7,7} Group order 301 Chiral action Defining relators: [ x * y * z, x^-7, z^-1 * x^-3 * y^2 * x, y * z^-1 * x^-2 * z * y * x^-1 ] T87.68 : Triangle type {7,7,7} Group order 301 Chiral action Defining relators: [ x * y * z, x * z^-1 * x^2 * z^-2, y^-3 * x * z^-1 * x, x^-7 ] T87.69 : Triangle type {7,7,7} Group order 301 Chiral action Defining relators: [ x * y * z, x^-7, x * z^-1 * x^-2 * y * x^-1 * y, z^2 * x^-2 * y * x * z ] T87.70 : Triangle type {7,7,7} Group order 301 Chiral action Defining relators: [ x * y * z, y * x * y^-1 * x * z^-1 * y, x^-7, z^-1 * x^-3 * y^-1 * z * y^-1, x * z^-2 * x^-1 * z * y^2 ] T87.71 : Triangle type {7,30,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T87.72 : Triangle type {7,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-6 * y^5 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T87.73 : Triangle type {7,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^3 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T87.74 : Triangle type {7,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-8 * y^5 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T87.75 : Triangle type {8,8,30} Group order 240 Chiral action Defining relators: [ x * y * z, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^-3 * x^-1 * z * y^-1 * z^-1, x^8 ] T87.76 : Triangle type {8,8,30} Group order 240 Chiral action Defining relators: [ x * y * z, y^-1 * z * y^-1 * x * z^-1 * x, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^-3 * x^-1 * z * y^-1 * z^-1 ] T87.77 : Triangle type {8,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^-10 * x * z * y^-1 * z^-3 ] T87.78 : Triangle type {8,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-5 * x^-1 * y * x * y^-1 * z^-8 ] T87.79 : Triangle type {8,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-16 * x * z^5 * y * z^-2 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T87.80 : Triangle type {8,8,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^17 * y^-1 * x * y * x^-1 * z^11 ] T87.81 : Triangle type {8,8,116} Group order 232 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^11 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x * z * y^-1 * z^-5 * x^-1 ] T87.82 : Triangle type {8,8,116} Group order 232 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^9 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^6 * y^-1 * z^-5 * x^-1 ] T87.83 : Triangle type {8,14,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-2 * y * z^-1 * y * z^-1 * y^2 * z^-3 * y * z^-1 ] T87.84 : Triangle type {8,14,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z^3 * y^-3 * z^3 * y^-1 * z ] T87.85 : Triangle type {8,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^5 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^4 ] T87.86 : Triangle type {8,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^17 * y^-1 * z * y^-4 * z^2 ] T87.87 : Triangle type {8,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-2 ] T87.88 : Triangle type {8,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-4 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T87.89 : Triangle type {9,66,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^3 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T87.90 : Triangle type {9,66,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-3 * z * y^-6 * z^5 * y^-7 ] T87.91 : Triangle type {10,14,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3, x^10 ] T87.92 : Triangle type {10,21,30} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y^4 * x * y^-1 * z * y, x^10 ] T87.93 : Triangle type {12,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^5 * z^-3 * y^8 ] T87.94 : Triangle type {12,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T87.95 : Triangle type {12,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y^-6 * x * y^-2 * z^3 * y^-5 ] T87.96 : Triangle type {12,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-3 * y^4 * z^-3 * y * z^-1 * y * z^-1 * y ] T87.97 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-3 * x^4 * y^-5 ] T87.98 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^2 * y * x^-1 * z^3 ] T87.99 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-4 * x * z^-1 * x^3 * z^-3 ] T87.100 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, x^-1 * y * x^-1 * y * x^-1 * z * y * z^-2 ] T87.101 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x * y^-1 * x^9 * y^-2 * x * y^-1 * x^3 ] T87.102 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^6 * y^-4 ] T87.103 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y^3 * z^-2 * y, x^6 * y^-4 ] T87.104 : Triangle type {16,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * z^-5 * x^3 * y^-1 * x ] T87.105 : Triangle type {21,27,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-4 ] T87.106 : Triangle type {21,27,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y * x^-1 * y^6 * x^-6 * y^2 ] T87.107 : Triangle type {24,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T87.108 : Triangle type {24,24,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, z^2 * y^-1 * x * y^-1 * x * z^4 ] T87.109 : Triangle type {24,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^6 * z^-2 ] T87.110 : Triangle type {24,32,32} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-3 * y^2 * z^-3, x^-7 * z * y ] T87.111 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^-5 * x * y^-2 * z^3 * y^-4 ] T87.112 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-3 * z * x^-7 * z^2 * x^-5 * y^3 * x^-8 ] T87.113 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x * y^-1 * x^6 * y^-6 * x ] T87.114 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^-6 * x * y^-6 * x * y^-2 ] T87.115 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-4 ] T87.116 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y * x^-4 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T87.117 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-4 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T87.118 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T87.119 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-9 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T87.120 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 ] T87.121 : Triangle type {26,91,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^-5 * x^5 * y^-6 * x * y^-3 ] T87.122 : Triangle type {27,27,63} Group order 189 Chiral action Defining relators: [ x * y * z, z^2 * y^-1 * x * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * y * x^-1 * z ] T87.123 : Triangle type {27,27,63} Group order 189 Chiral action Defining relators: [ x * y * z, y * x^-2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, y^-4 * x * z^2 * y^-1 ] T87.124 : Triangle type {27,27,63} Group order 189 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, z^-1 * x^-1 * y^-1 * x * y^-2, x^2 * z^-2 * x^4 * z^-3 ] T87.125 : Triangle type {30,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T87.126 : Triangle type {30,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z * x^-4 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T87.127 : Triangle type {30,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T87.128 : Triangle type {36,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-9 * z^4 * y^-7 ] T87.129 : Triangle type {36,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^-4 * y^6 * x^-4 * z * x^-5 ] T87.130 : Triangle type {36,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z * x^-1 * z^9 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T87.131 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-9 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^11 * x^-1 * y * x^-1 * y^3 ] T87.132 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T87.133 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^10 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T87.134 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y^5 * z^-3 * y^8 ] T87.135 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^4 * z^-1 * x^4 * y^-5 * x^3 ] T87.136 : Triangle type {45,60,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-23 * y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-2 ] T87.137 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^19 * x^-5 * y^8 ] T87.138 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^6 * z^-1 * y^4 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T87.139 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^20 * x^-1 * y^4 * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^3 ] T87.140 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x^2 * z^-4, x^-2 * y^6 * x^-2 * z^3 * x^-4 ] T87.141 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T87.142 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T87.143 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y * x^3 * z^-3 * y * z^-1 * y * z^-1 ] T87.144 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-12 * x * z^-1 * x * z^-4 * x^2 * z^-5 * y * z^-1 ] T87.145 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-5 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T87.146 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^7 * x^-5 * y^2 ] T87.147 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^-13 * x * y^-1 * x * y^-1 ] T87.148 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^-2 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T87.149 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T87.150 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^2 * z^-1 * y * z^-5 * y^6 ] T87.151 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-3 * x^7, y^5 * z^-3 * y^2 * x^-2 * y^5 ] T87.152 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, z^3 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T87.153 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^14 * y^-1 * z^7 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T87.154 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^6 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T87.155 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T87.156 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-59 ] T87.157 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^-3 * z * y^-7 * z^3 * y^-7 ] T87.158 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^-3 * y^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T87.159 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y, x * y^-1 * x^6 * y^-5 * x^2 ] T87.160 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T87.161 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T87.162 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^5 * z^-4 * y * x^-1 * y^5 ] T87.163 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^11 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T87.164 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T87.165 : Triangle type {59,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-8 * y * x^-6 * y^3 * x^-6 * z * x^-7 ] T87.166 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T87.167 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^5 * z^-3 * y^2 * x^-4 * y^4 ] T87.168 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T87.169 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, y^3 * z^-2 * y^3 * x^-5 * y^2 ] T87.170 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^10 * y^-1 * x^12 * y^-1 * x^65, y * z^-1 ] T87.171 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^6 * z^-3 * x^2 * y^-6 * x * y^-1 * x^2 ] T87.172 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^-1 * x * y^-1 * x^6 * y^-8 ] T87.173 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-28 * y * z^-5 * y * z^-1 ] T87.174 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T87.175 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-28 * z * x^-8 * z * x^-7 ] T87.176 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^5 * z^-3 * x^6 * y^-1 * x ] T87.177 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-9 * y^18 * x^-1 * y * x^-1 * y^3 ] T87.178 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-54 * x * z^-4 ] T87.179 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^5 * z^-4 * y * x^-3 * y^4 ] T87.180 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-12 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T87.181 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^3 * z^-1 * x^4 * y^-5 * x^2 ] T87.182 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y * z^-1 * y^8 * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T87.183 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T87.184 : Triangle type {88,176,176} Group order 176 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-6 * y * x^-6 * z^3 * x^-8 ] T87.185 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * z^-4 * y * x^-1 * y^7 ] T87.186 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^9, y^4 * z^-5 * y^6 ] T87.187 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-6 * x * y^-1 * z^5 * y^-5 ] T87.188 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-53 * x^2 * z^-4 ] T87.189 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, y^10 * x^-6 * y * x^-1 * y^3 ] T87.190 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x^-2 * y^-1, y^70 * x^-1 * y^17, x * z^-1 ] T87.191 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-5 * y^6 ] T87.192 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-3 * y^2 * x^-2 * y^4 ] T87.193 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * z^-4 * y * x^-3 * y^6 ] T87.194 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y^4 * z^-5 * y^6 ] T87.195 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-20 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-2 ] T87.196 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, y^3 * z^-1 * y^4 * x^-6 * y^2 ] T87.197 : Triangle type {175,175,175} Group order 175 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] Genus 88 T88.1 : Triangle type {2,4,178} Group order 712 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-178 ] T88.2 : Triangle type {2,4,352} Group order 704 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-40 * x * y^-1 * z^-135 ] T88.3 : Triangle type {2,6,32} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-17 * x * z^8 * y * z^-6 ] T88.4 : Triangle type {2,6,90} Group order 540 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-6 * x * z * y * x * z^2 * y * x * z^6 * y^-1 * x * z * y^-1 * z^-10 ] T88.5 : Triangle type {2,6,90} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-50 * x * z * y * x * z^20 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-5 ] T88.6 : Triangle type {2,6,90} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^68 * y * x * y^-1 * x * y^-1 * z^-5 * x * z^14 ] T88.7 : Triangle type {2,6,264} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-50 * x * z^20 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-5 ] T88.8 : Triangle type {2,10,46} Group order 460 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-12 * x * z^11 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-16 ] T88.9 : Triangle type {2,10,220} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-11 * x * z^19 * y * z^-7 * x * z^2 * y^-1 * z^-3 ] T88.10 : Triangle type {2,12,72} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12, z^2 * y * z^-1 * x * z^6 * y^-1 * z^-1 * x ] T88.11 : Triangle type {2,12,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^2 * y * x * z^15 * y * z^-4 * x * y^-1 * z^-9 * x * z^3 ] T88.12 : Triangle type {2,12,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^8 * y * x * z * y * x * z^2 * y * x * z * y * x * y^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-3 * x * y^-1 * z^-3 * x * z^3 ] T88.13 : Triangle type {2,16,52} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y * x * y^-1 * z * y * x * y^-10 * z^-1 * y, z^-5 * x * z * y * x * z * y * x * y^-1 * z^-9 * x * y^-1 * z^-6 ] T88.14 : Triangle type {2,18,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, z * y^-4 * z^-1 * x * y^-1 * z, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T88.15 : Triangle type {2,18,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y * z^-2 * y * x * y^-1 * z^-2 * x * z^2, y * x * z * y^4 * x * y^-1 * z^-1 * x * z ] T88.16 : Triangle type {2,18,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, (y * z^-1 * y^4)^2, y^-5 * z * y^5 * x * y^-6 * z^-1 * x ] T88.17 : Triangle type {2,18,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * y^-3 * z * y * x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y^4, z^-4 * x * z^3 * y * x * z^7 * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T88.18 : Triangle type {2,18,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z^3 * y^-1 * z^-4, y * x * z * y^4 * x * y^-1 * z^-1 * x * z ] T88.19 : Triangle type {2,18,198} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^9 * y * z^-4 * x * z * y^-1 * z^-5 ] T88.20 : Triangle type {2,34,187} Group order 374 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-2 * z^4 * y^-4 * z^4 ] T88.21 : Triangle type {2,42,63} Group order 378 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-2 * y * z^-1, y^-1 * z * y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-7 * z * y^-1 * z * y^-1 ] T88.22 : Triangle type {2,42,63} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-8 * z^4 * y^-4 * z^5 ] T88.23 : Triangle type {2,46,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-10 * y^12 * z^-4 * y^18 * z^-2 ] T88.24 : Triangle type {2,90,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-56 * y^34 ] T88.25 : Triangle type {2,177,354} Group order 354 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^121 * y^-54 * z ] T88.26 : Triangle type {2,178,178} Group order 356 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^56 * z^-122 ] T88.27 : Triangle type {2,352,352} Group order 352 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^55 * z^-121 ] T88.28 : Triangle type {3,10,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^2 * x^-1 * y^-1 * x * y^-1 * x * z ] T88.29 : Triangle type {3,32,32} Group order 288 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-2 * y * z^-5 * y^10 * z^-1 * y^2 * z^-2 * y^2 * z^-1 * y * z^-1 * y ] T88.30 : Triangle type {3,32,32} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-14 * y^11 * z^-2 * y^2 * z^-1 * y ] T88.31 : Triangle type {3,46,69} Group order 276 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-1 * y * z^-1 * y^9 * z^-1 * y * z^-3 * y^5 ] T88.32 : Triangle type {3,89,267} Group order 267 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^10 * z^-1 * y^73 * z^-1 ] T88.33 : Triangle type {3,90,90} Group order 270 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-9 * y * z^-2 * y^2 * z^-1 * y^6 * z^-2 * y^3 * z^-1 * y^2 ] T88.34 : Triangle type {3,90,90} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^73 * y^-14 * z * y^-1 ] T88.35 : Triangle type {3,90,90} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-11 * y * z^-2 * y^7 * z^-3 * y^5 ] T88.36 : Triangle type {3,90,90} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-75 * z * y^-10 * z * y^-2 * z ] T88.37 : Triangle type {3,264,264} Group order 264 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-74 * z * y^-10 * z * y^-2 ] T88.38 : Triangle type {4,4,89} Group order 356 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z * y^-1 * z^4 * y^-1 * z^-1 * x^2 * z^5 ] T88.39 : Triangle type {4,4,89} Group order 356 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^75 * y^-1 * x^-1 * z^13 ] T88.40 : Triangle type {4,4,176} Group order 352 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^75 * y * x^-1 * z^12 ] T88.41 : Triangle type {4,6,10} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y)^2, z^10 ] T88.42 : Triangle type {4,6,12} Group order 348 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x^-2 * z * x^-1 * z * x^-1 * z * y * x * z * y^-1 ] T88.43 : Triangle type {4,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^-2 * z * x^-1 * y^-3, y * z^-3 * x^-1 * z^4 ] T88.44 : Triangle type {4,12,132} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^-1 * z^8 * y * x * z^9 * y * z^-3 ] T88.45 : Triangle type {4,21,84} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^2 * z^-1 * y^3 * x^-1 * y^4 * z^-6 * y^2 * z^-1 ] T88.46 : Triangle type {4,60,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-4 * y^9 * z^-1 * y * z^-1 * y^8 ] T88.47 : Triangle type {4,118,236} Group order 236 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^33 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^8 * z^-3 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y ] T88.48 : Triangle type {5,46,46} Group order 230 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y * z^-1 * y * z^-10 * y^3 * z^-1 * y^10 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^11 ] T88.49 : Triangle type {5,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-6 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T88.50 : Triangle type {5,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-6 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T88.51 : Triangle type {6,6,16} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^-1 * x * z^4 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^5 * y * z^-1 ] T88.52 : Triangle type {6,6,16} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^4 * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-3 * x^-1 * z^4 ] T88.53 : Triangle type {6,6,16} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, z * y * z^-3 * x^-1 * z^3 * y * x^-1 * y^-1 * x * z^6 ] T88.54 : Triangle type {6,6,45} Group order 270 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^5 * y * x * z^7 * y * z^-1 * x ] T88.55 : Triangle type {6,6,45} Group order 270 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^4 * y^-1 * z^-1 * x^-1 * z^9 ] T88.56 : Triangle type {6,6,45} Group order 270 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-26 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x^-1 * y^-1 * z^-3 * x * z^2 * y * z^-3 * x^-1 * z * y ] T88.57 : Triangle type {6,6,45} Group order 270 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^45 ] T88.58 : Triangle type {6,6,132} Group order 264 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^23 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z^6 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 ] T88.59 : Triangle type {6,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, y^10 ] T88.60 : Triangle type {6,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z * y^-1 * x * y^-1 * x * z^5 * y^-1 * z^-1 * x * z^10 ] T88.61 : Triangle type {6,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 * x^-1 * y^2 * z^-1 * y * z^-4 * y^4 ] T88.62 : Triangle type {6,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-1 * y^4 * x^-1 * z^-1 * y * z^-5 * y * z^-1 * y^2 * z^-1 ] T88.63 : Triangle type {6,72,72} Group order 216 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z * y^-1 * z^2 * y^-3 * x * y^-4 * z ] T88.64 : Triangle type {6,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T88.65 : Triangle type {6,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 ] T88.66 : Triangle type {6,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^5 * z^-2 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^12 ] T88.67 : Triangle type {8,18,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-1 * z * y^-4 * z^3 ] T88.68 : Triangle type {8,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^3 * z^-1 * x, x^8 ] T88.69 : Triangle type {8,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^3 * x^-1 * z * y * x^-1, z^-2 * y * x^-1 * y * z^-1 * y ] T88.70 : Triangle type {8,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z^4 * y^-1 * x * z^4 ] T88.71 : Triangle type {8,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z * y^-1 * z^-3 * x * z^4 ] T88.72 : Triangle type {8,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z * y^-1 * z * y^-8 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-3 * z * y^-1 ] T88.73 : Triangle type {9,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, (y^-1 * x)^3, x * z * y^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2 ] T88.74 : Triangle type {9,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^2 * z^2, (z^-1 * y)^3, x^-9 ] T88.75 : Triangle type {9,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (z^-1 * y)^3, z^-2 * x^-2 * z * x^-1 * y, z^-1 * x^4 * y^-1 * z^-2 ] T88.76 : Triangle type {9,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, (z^-1 * y)^3, (x * z^-1)^4 ] T88.77 : Triangle type {9,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, (y^-1 * x)^3, (z^-1 * x)^3 ] T88.78 : Triangle type {9,23,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-9 ] T88.79 : Triangle type {9,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^4 * y^-1 * z^-1, y^10 * z^-1 * y^4 * z^-1 * y^4 * z^-2 * y^2 ] T88.80 : Triangle type {9,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, z^-2 * x^2 * z * y^-1, x * y^-2 * x * z^-1 * y, z^-2 * y^3 * z^-2 * y ] T88.81 : Triangle type {9,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^4 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^9 * z^-1 ] T88.82 : Triangle type {9,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, z^-1 * y^4 * z^-3, x^-9 ] T88.83 : Triangle type {9,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T88.84 : Triangle type {9,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^3 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T88.85 : Triangle type {10,10,23} Group order 230 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-7 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-6 ] T88.86 : Triangle type {10,10,110} Group order 220 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^-3 * x * z^6 * y^-1 * z^-2 * x^-1 * z^2 * y^-1 * z^-7 ] T88.87 : Triangle type {10,10,110} Group order 220 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-2 * x^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x^-1 * z^4 * y * z^-4 * x * z^3 * y * z^-1 ] T88.88 : Triangle type {10,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * y^2 * z^-4, x^10 ] T88.89 : Triangle type {10,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^7 * z^-1 * y * z^-1, x^10 ] T88.90 : Triangle type {10,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-4, x^10 ] T88.91 : Triangle type {10,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y^3 * z^-4, x^10 ] T88.92 : Triangle type {12,12,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^3 * x^-1 * z^2 * y^-1, z * y * x * y^-1 * x * z^3 ] T88.93 : Triangle type {12,12,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^2 * z * y, x^-1 * y * x^-1 * y * x^-1 * z * y * z^-2 ] T88.94 : Triangle type {12,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^-4 * x * y^-1 * x * y^-1 * x * z^5 * y^-1 * z^-6 ] T88.95 : Triangle type {12,12,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-5 * x * z * y^-1 * x * z^6 * y * z^-4 ] T88.96 : Triangle type {12,17,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T88.97 : Triangle type {12,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, y^3 * x^-1 * y^2 * z^-1 ] T88.98 : Triangle type {12,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * x^-3 * y * z^-1 * x^-1 ] T88.99 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-1 * y^4 * x^-1 * z^-1 * y * z^-5 * y^5 ] T88.100 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y^-1 * x * y^-1 * x * z^3, (x * z^-3)^2 ] T88.101 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y ] T88.102 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, y * x^-3 * z * x^-2, x^2 * z^-1 * x^-9 * y^-1 ] T88.103 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-12, y^-7 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^2 ] T88.104 : Triangle type {12,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, y^-1 * z * y^-4 * z * y^-1 * z ] T88.105 : Triangle type {12,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^12, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T88.106 : Triangle type {14,15,30} Group order 210 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * y * x^2 * z * y^-1, z^2 * y^-2 * z * y^-1 * z^2 * y^-4 * z^3 ] T88.107 : Triangle type {15,39,65} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-5 * y^2 * z^-4, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T88.108 : Triangle type {16,16,26} Group order 208 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^-3 * x^-1 * y^-1 * z^-2, x^-1 * y^2 * x^-2 * y^2 * x^-1 * z ] T88.109 : Triangle type {16,16,26} Group order 208 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y^2 * x^-1, z * y^-1 * x * y^-1 * x * y^-1 * x * z^5 * y^-1 * z^-1 * x * z^2 ] T88.110 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^7 * z^-4 * x^2 * y^-4 * x^4 ] T88.111 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^2 * z^-4, y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^2 ] T88.112 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^2 * z^-4, y^-2 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T88.113 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y^9, z^2 * x^-5 * z^4 * x^-1 * z * x^-1 * z^4 ] T88.114 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-4 * x^2 * y^-7 ] T88.115 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y * x^-5 * y^2, z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T88.116 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-3, x^7 * z^-4 * x^2 * y^-4 * x^4 ] T88.117 : Triangle type {17,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T88.118 : Triangle type {18,18,99} Group order 198 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-4 * x^2 * y^-4, z^8 * y^-1 * z^-2 * x ] T88.119 : Triangle type {18,18,99} Group order 198 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-4 * y * x^2 * z^-3, z^-2 * x^-1 * z * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 ] T88.120 : Triangle type {21,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2, z^-1 * y^8 * z^-1 * y * z^-1 ] T88.121 : Triangle type {21,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * y * x^-1 * y^2, z * x^-1 * z * x^-2 * z^4 ] T88.122 : Triangle type {21,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y * z^-1 * y^2 * z^-2, x^-1 * z * x^-7 * z^2 * x^-1 ] T88.123 : Triangle type {21,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^4 * x^-4 * y^2, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T88.124 : Triangle type {21,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T88.125 : Triangle type {21,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3, y^-2 * x^6 * y^-7 ] T88.126 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^6 * y^-7, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T88.127 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^3 ] T88.128 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-4 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-4 ] T88.129 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x^4 ] T88.130 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-5 * y^2, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T88.131 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^4 * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T88.132 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-4 * y * z^-5 * y^2 * z^-4 ] T88.133 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^4 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T88.134 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-5 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T88.135 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x^-8 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T88.136 : Triangle type {23,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^11 * y^-4 * x^2 * y^-4 * x^6 ] T88.137 : Triangle type {45,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T88.138 : Triangle type {45,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^8 * x^-4 * z^4 * x^-1 * z^8 ] T88.139 : Triangle type {45,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T88.140 : Triangle type {45,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^6 * z^-4 * x^7 ] T88.141 : Triangle type {45,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-29 * y * x^-8 * z * x^-7 ] T88.142 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-10 * x^3 * y^-11 * z ] T88.143 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y^3 * x^-1 * y^5 * z^-1 * y^3 ] T88.144 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, x * y^-3 * x * y^-1 * x * y^-2 * z * y^-3 ] T88.145 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^4 * y^-4, z^-4 * x^2 * z^-4 ] T88.146 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, z^-1 * x * z^-3 * x * z^-1 * x * y * z^-4 ] T88.147 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^7 * z^-1 * x * z^-1, y^6 * z^-4 ] T88.148 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^2 * x^-2 * z * x^-1 * z * x^-5 * z^6 ] T88.149 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^5 * z^-1 * x * z^-1, y^3 * z^-1 * y^2 * x^-1 * y^3 * z^-2 * y ] T88.150 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8 * y^-2, z^-1 * y * z^-1 * y^3 * z^-4 ] T88.151 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^-2 * z^2 * x^-1 * y^2 * x^-6 * z^2 * x^-3 ] T88.152 : Triangle type {46,46,92} Group order 184 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^-5 * x * z^-1 * x * z^-3 * y * z^-1 * y * z^-1 ] T88.153 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T88.154 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^2 * z^-4, x^-1 * y^6 * x^-7 ] T88.155 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-3 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T88.156 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^2 * z^-4, x^4 * z^-3 * x^7 ] T88.157 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^7 * z^-2 * x^3 * y^-6 * x * y^-1 * x * y^-1 * x^2 ] T88.158 : Triangle type {60,90,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-39 * y * x^-1 * y * x^-1 * y * x^-17 ] T88.159 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-26 * y * x^-1 * y^2 * x^-9 * y * x^-1 * y * x^-1 * y * x^-2 ] T88.160 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-12 * y * x^-11 * y * x^-1 * y * x^-1 * y * x^-2 ] T88.161 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * z^2 * x^-9 * y * x^-5 ] T88.162 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x^4 ] T88.163 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^6 * z^-4 * x^4 * y^-2 * x^2 ] T88.164 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-2, x^5 * z^-4 * x^6 ] T88.165 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^4 * y^-4 * x, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T88.166 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T88.167 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T88.168 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^3 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T88.169 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, z^-5 * x * z^-4 * x * y * z^-4 ] T88.170 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^8 * z^-4 * y^6 * z^-1 * y^3 ] T88.171 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T88.172 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^10 * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T88.173 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-9 * y * z^-4 ] T88.174 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T88.175 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^7 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * x^-1 * y^5 * z^-1 * y * z^-1 * y^2 ] T88.176 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T88.177 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^4 * z^-1 * y * z^-5 * y * x^-1 * y^6 ] T88.178 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, z^2 * x^-6 * z^4 * x^-1 * z^6 ] T88.179 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^22 * y^-1 * z^13 ] T88.180 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y^4 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T88.181 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^-1 * y^6 * x^-7 ] T88.182 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 ] T88.183 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, y^6 * z^-4 * y * x^-6 * y * x^-1 * y^2 ] T88.184 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T88.185 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T88.186 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^20 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T88.187 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^31 * z^-1 * y^4 * x^-2 * y^8 ] T88.188 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-4 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T88.189 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^2 * z^-4, x * y^-1 * x^6 * y^-7 ] T88.190 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 ] T88.191 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, x^8 * y^-6 * x^2 ] T88.192 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^4 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T88.193 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^12 * z^-2 * y^3 * x^-1 * y^9 ] T88.194 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * y^2 * z^-4, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T88.195 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] T88.196 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-3 * x^4 * y^-7 ] T88.197 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^-3 * x^5 * y^-6 * x * y^-1 ] T88.198 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x^5 * z^-4 * x * y^-6 * x^2 ] T88.199 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^7 * z^-4 * x^8 ] T88.200 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^10 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T88.201 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-54 * x^2 * z^-4 ] T88.202 : Triangle type {89,178,178} Group order 178 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^89, y * z^-1 ] T88.203 : Triangle type {90,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-10 * y^2 * z^-4 ] T88.204 : Triangle type {90,90,90} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^32 * x^-1 * z^4 * x^-1 * z^8 ] T88.205 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x^-2 * y^-1, y^70 * x^-1 * y^18, x * z^-1 ] T88.206 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-2 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T88.207 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^8 * x^-5 * y^3 ] T88.208 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^11 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^3 ] T88.209 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^2 * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T88.210 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x^9, z^-4 * y * z^-5 * y^6 * z^-1 ] T88.211 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^11 * x^-6 * y * x^-1 * y^4 ] T88.212 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^5 * z^-4 * y * x^-3 * y^4 ] T88.213 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T88.214 : Triangle type {177,177,177} Group order 177 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^3 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y^2 ] Genus 89 T89.1 : Triangle type {2,3,10} Group order 2640 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, x * z^2 * y * z^-1 * x * z^3 * y * x * z * x * z^2 * y^-1 * z^-3 ] T89.2 : Triangle type {2,3,10} Group order 2640 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^10, x * z * y * z^-1 * x * z^3 * y * x * z * y * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-1 ] T89.3 : Triangle type {2,4,15} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x, z^-15 ] T89.4 : Triangle type {2,4,48} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, y^-1 * z * y * z^-2 * y * x * z * y^-1 * z * y^-1 * z^2, z^2 * y * z^-2 * x * z^5 * y^-1 * z^-1 * x ] T89.5 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, z^-8 * x * z^4 * y * x * z^3 * y^-1 * z^-2 * x * z * y^-1 * z^-3 ] T89.6 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-32 * x * z^8 * y^-1 * x * z^2 * y^-1 * z^-4 ] T89.7 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-5 * x * z^2 * y * z^-1 * x * z * y * x * z * y * z^-4 * y * z^6 * y^-1 * z^-1 ] T89.8 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-3 * x * z * y * z^-2 * x * z^7 * y * x * y^-1 * z^-3 * x * y^-1 * z^-4 ] T89.9 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-29 * x * z^11 * y * x * z^2 * y^-1 * z^-4 ] T89.10 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z^4 * y * z^-2 * x * z^3 * y * z^-5 * x * z^5 * y^-1 * z^-1 * x * z ] T89.11 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * x * z * y^-1 * z * y * x * y^-1 * z^-2 * y, z * y * z^-5 * x * z^6 * y^-1 * z^-7 * x * y^-1 * z^-1 * x * z ] T89.12 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-2 * z^-4 * y, z^-3 * x * z^8 * y * z^-5 * x * z^3 * y^-1 * z^-3 ] T89.13 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z * y * x * z^3 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2, (y^-1 * z * y^-1 * z^3 * y^-1 * z)^2 ] T89.14 : Triangle type {2,4,48} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T89.15 : Triangle type {2,4,92} Group order 736 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-74 * x * z^8 * y * x * y * z^-8 ] T89.16 : Triangle type {2,4,180} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-180 ] T89.17 : Triangle type {2,4,356} Group order 712 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y^-1 * z^-136 ] T89.18 : Triangle type {2,5,6} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y * z^-1 * y * z^-1 * x * y^-2 * z^-2 * y * z^-1 * x ] T89.19 : Triangle type {2,5,6} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^6, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T89.20 : Triangle type {2,6,14} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T89.21 : Triangle type {2,6,14} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * z^-3 * x * y^-1 * z^-4 * x ] T89.22 : Triangle type {2,6,14} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y * z^-1 * y)^2, z^4 * y^2 * z^-2 * y * x, z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-1 * y ] T89.23 : Triangle type {2,6,69} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-1 * x * z * y * x * z * y * z^-1 * x * z^2 * y * x * z * y * x * z * y^-1 * z^-10 ] T89.24 : Triangle type {2,6,267} Group order 534 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-51 * x * z^20 * y * z^-1 * x * y * z^-6 * x * z * y^-1 * z^-7 ] T89.25 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, (y * z^-4)^2, z^10 ] T89.26 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-4)^2, z^10, y * z^-1 * y * x * y^-2 * z^-1 * x * z^3 ] T89.27 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T89.28 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * z^-1 * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T89.29 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^10, z^-3 * x * y^-2 * z^-4 * y ] T89.30 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^10, z^-3 * x * y^-2 * z^-4 * y ] T89.31 : Triangle type {2,8,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-4)^2, z^10 ] T89.32 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-8 * x * z^11 * y^-1 * z^-12 ] T89.33 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-5 * x * z * y * x * z * y * z^-2 * x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-4 ] T89.34 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-4 * x * z^3 * y * z^-5 * x * y^-1 * z^-2 ] T89.35 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-4 * x * z^3 * y * z^-4 * x * z^2 * y^-1 * z^-1 ] T89.36 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-4 * x * z^3 * y * z^-2 * x * z^2 * y^-1 * z^-3 ] T89.37 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, z^-3 * x * z * y * z^-6 * x * y^-1 * z^-4 ] T89.38 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-2 * x * y^-2 * z^-3 * y, z^-10 * x * z^3 * y^-1 * z^-2 ] T89.39 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * x * z^2 * y^-1 * z^-4 ] T89.40 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, x * z^2 * y * z^-1 * x * z^4 * y^-1 * z^-4 * x * y^-1 * z^-2 ] T89.41 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, z^-1 * x * z * y * x * z * y * z^-2 * x * z^3 * y^-1 * z^-5 ] T89.42 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, x * z^4 * y * z^-4 * x * y * z^-6 ] T89.43 : Triangle type {2,8,32} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z^4 * y * z^-2 * x * z^7 * y^-1 * z^-1 ] T89.44 : Triangle type {2,8,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-46 * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T89.45 : Triangle type {2,8,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-24 * x * z^21 * y * z^-1 * x * y^-1 * z^-12 ] T89.46 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-2 * x * y^-1 * z^-3 * x, y^12 ] T89.47 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, (y * z^-4)^2 ] T89.48 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, (y * z^-3)^2, x * z * y^-3 * z * y^-1 * z^-1 * y, y^12, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-5 ] T89.49 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, (y * z^-3)^2, x * z * y^-3 * z * y^-1 * z^-1 * y, y^12, x * z * y * x * z * y * x * y^-1 * z^-5 ] T89.50 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, z^9 * y * x * y * z^-5 * x * z * y^-1 * z^-1 * x * z ] T89.51 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, z^-2 * x * y^-3 * z^-3 * y^2, x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-2 * y ] T89.52 : Triangle type {2,12,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-1 * z^-1 * x, (y * z^-3 * y)^2 ] T89.53 : Triangle type {2,14,28} Group order 448 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-1 * y^2 * z^-2, y^14 ] T89.54 : Triangle type {2,15,15} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * y^-1 * z * y^-2 * z^-2 * y * z^-1, y^-1 * z^2 * y^-1 * z^2 * y^-7 * z * y^-1 ] T89.55 : Triangle type {2,20,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * z^2 * y^-2 * z^-1 * y * z^-2, y^-4 * z^4 * y^-1 * z * y^-6 * z * y^-3 ] T89.56 : Triangle type {2,20,20} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^-2 * z * y^-4 * z^2 * y^-9 * z * y^-1 ] T89.57 : Triangle type {2,32,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-19 * z^4 * y^-5 * z^4 ] T89.58 : Triangle type {2,32,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y^-4 * z^4 ] T89.59 : Triangle type {2,32,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^2 * z^-2 * y^9 * z^-2 * y ] T89.60 : Triangle type {2,32,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * z^-4 * x * z^2 * y^-1 * z^-1 * x, y^2 * z^-2 * y^9 * z^-2 * y ] T89.61 : Triangle type {2,48,48} Group order 384 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, z^-1 * y^6 * z^-1 * y^2 * z^-2 ] T89.62 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-48 ] T89.63 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^-1 * z^3 * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-6 * z^3 * y^-1 ] T89.64 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-6 * z^3 * y^-12 * z^3 ] T89.65 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z * y^-1 * z * y^-1 * z^2 * y^-1 * z^2 * y^-10 * z^4 * y^-1 ] T89.66 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^2 * z^-13 * y^11 * z^-4 * y * z^-15 * y^2 ] T89.67 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^2 * y^-2 * z^2 * y^-1 * z * y^-1 * z^2 * y^-9 * z^2 * y^-1 * z ] T89.68 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^4)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T89.69 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^9 * z^-1 * y * z^-1, z^-2 * y^2 * z^-1 * y^2 * z^-5 ] T89.70 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^3 * y^-2 * z * y^-1 * z * y^-1 * z^2 * y^-9 * z^2 * y^-1 * z ] T89.71 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-32 * z^3 * y^-12 * z ] T89.72 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^3 * z^-4 * y^3 * z^-1 * y^6 * z^-3 * y * z^-1 * y * z^-1 ] T89.73 : Triangle type {2,48,48} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z * y^-1 * z^2 * y^-2 * z * y^-12 * z * y^-1 * z^3 ] T89.74 : Triangle type {2,92,92} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-57 * y^33 * z^-1 ] T89.75 : Triangle type {2,179,358} Group order 358 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^122 * y^-56 ] T89.76 : Triangle type {2,180,180} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^57 * z^-122 * y ] T89.77 : Triangle type {2,356,356} Group order 356 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^56 * z^-121 * y ] T89.78 : Triangle type {3,3,5} Group order 1320 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-2 * x^-1 * z * y * x * z^2 * y * z^-1 * x^-1, x * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y ] T89.79 : Triangle type {3,3,5} Group order 1320 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * x^-1 * z * y * x * z * y * z^-1 * x^-1 ] T89.80 : Triangle type {3,3,14} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^3, (x * z^2 * y)^2, z^2 * y^-1 * z^-1 * x^-1 * y * z^-2 * x ] T89.81 : Triangle type {3,4,20} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y^-1 * z^-5, x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T89.82 : Triangle type {3,5,5} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y^-2 * x * y^-1 * z^2, (x^-1 * z * y^2)^2 ] T89.83 : Triangle type {3,5,5} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, y^-1 * z * y^-2 * x * z * y^-1 * x ] T89.84 : Triangle type {3,5,5} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, (z^-1 * y)^3, y * z^-2 * x^-1 * y^-1 * x * z * y^-1 * x * z ] T89.85 : Triangle type {3,8,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x^-1 * y^-1 * x * z * y^2, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T89.86 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * y^-2 * x * z * y^-2, y * x^-1 * z * y^-1 * x * z^2 * y ] T89.87 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x * y^-1 * x * y^-1 * z^-2, y^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z^-2 ] T89.88 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y, y^2 * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T89.89 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T89.90 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2, y^8 ] T89.91 : Triangle type {3,8,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-2 * z, y^2 * x * y^-1 * x * y^-1 * z^2 ] T89.92 : Triangle type {3,14,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^4 * x * y^-2 * z^-1, z^-1 * y * z^-1 * y * x^-1 * z * y^2 ] T89.93 : Triangle type {3,14,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, (y * z^-2 * y)^2, (y * z^-1 * y^3)^2 ] T89.94 : Triangle type {3,14,14} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^4, y^-1 * z^3 * y^-2 * z * y^-2 * z^3 ] T89.95 : Triangle type {3,69,69} Group order 276 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, z^-1 * y * z^-5 * y * z^-2 * y * x * z^-1 * y * z^-2 * y * z^-2 * y^3 * z^-2 ] T89.96 : Triangle type {3,267,267} Group order 267 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^85 ] T89.97 : Triangle type {4,4,24} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x * y^-1 * x * z^2 * y^-1, x^-1 * z^2 * y^-1 * x * z * y * z^-1 ] T89.98 : Triangle type {4,4,24} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z, z * y * x * z * y * z^-1 * x^-1 * z * y^-1 * z^-3 * x * z^2 ] T89.99 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^9 * y^-1 * z^-1 * x * z^4 * y * z^-1 * x^-1 * z * y^-1 * z^-5 * x^-1 ] T89.100 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^-3 * y * x^-1 * z^2 * y^2, y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-3 * x ] T89.101 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y * z^-2 * x^-1 * z^3 ] T89.102 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-3 * y * x^-1 * z^2 * y^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T89.103 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^15 * y * x^-1 * z^2 * y^-1 * z^-5 * x ] T89.104 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^4 * y^-1 * z^-6 * x^-1 * z ] T89.105 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-3 * x^-1 * z^3 * y * z^-5 ] T89.106 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^-3 * y * x^-1 * z^2 * y^2, y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-3 * x^-1 ] T89.107 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-3 * y * x^-1 * z^2 * y^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.108 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T89.109 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^-3 * y * x^-1 * z^2 * y^2, z^5 * y * z^-2 * x * z * y * z^-2 * x^-1 ] T89.110 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z, z^-3 * y * x^-1 * z^2 * y^2, z^4 * y^-1 * z^-3 * x * y^-1 * z^-3 * x ] T89.111 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z, y * z^-2 * y * x^-1 * z^2 * y^-1 * z, z^4 * y^-1 * z^-3 * x * z * y * z^-2 * x^-1 ] T89.112 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, y * z^-2 * y * x^-1 * z^2 * y^-1 * z, z^5 * y * z^-2 * x * y^-1 * z^-3 * x ] T89.113 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^15 * y * z^-2 * x^-1 * y^-1 * x * y^-1 * z^-2 * x^-1 * z^2 ] T89.114 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^9 * y * x^-1 * z * y^-1 * z^-4 * x^-1 * y^-1 * z^-3 * x * z * y^-1 * x * z^2 ] T89.115 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-5 * x^-1 * y * x * z^4 ] T89.116 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, z * y * z^-1 * y * x^-1 * z^2 * y^-1 * z, z^-2 * x^-1 * z^3 * y^-1 * z^-1 * x * y^-1 * z^-4 ] T89.117 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-1 * x^2 * z^2 * y^-1, z^3 * y * z^-2 * x^-1 * y^-1 * x * z * y * x * z^3 ] T89.118 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-3 * x * z^2 * y * x * z^4 ] T89.119 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^2 * y^-1 * z^-3 * x^-1 * z * y^-1 * x^-1 * z^4 ] T89.120 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z^2 * y * x^-1 * z * y * z^-2 * x^-1 * y^-1 * x^-1 * z^4 ] T89.121 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y * x^-1 * z * y * x * z^3 ] T89.122 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3 ] T89.123 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^10 * y * x * z^5 * y * z^-1 * x * z * y * z^-4 * x ] T89.124 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^14 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-2 * x * z^3 ] T89.125 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x * z * y^-1 * x * z^2 * y^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T89.126 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^5 * y * z^-1 * x * z^5 ] T89.127 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^-6 * x * z * y * x * z * y * z^-2 ] T89.128 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z^-2 * x^-1 * z^2 * y * x^-1 * z^2 * y * z^-4 ] T89.129 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2, z^3 * y * z^-2 * x^-1 * y^-1 * z^-3 * x * z^2 ] T89.130 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^3 * y * z^-2 * x^-1 * y^-1 * z^-3 * x * z^2 ] T89.131 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T89.132 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, (x * z^2 * y^-1)^2, z^4 * x^-1 * z^3 * y^-1 ] T89.133 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-10 * x^-1 * z * y^-1 * z^-6 * x^-1 * z * y^-1 * z^-4 ] T89.134 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^5 * y * z^-2 * x^-1 * z^4 ] T89.135 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^3 * y * z^-2 * x * z * y^-1 * x * z^4 ] T89.136 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^19 * y * z^-3 * x * z ] T89.137 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * z^3 * y^-1 * z^-4 * x^-1 * z^3 * y ] T89.138 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^2 * y * x^-2 * z^3 * x^-1, z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y^-1 * z^-2 * x^-1 * z^3 * y^-1 ] T89.139 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-12 * x * z^4 * y * z^-3 * x^-1 * z^3 * y^-1 ] T89.140 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * z^3 * y * z^-4 * x^-1 * z^3 * y^-1 ] T89.141 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, x^-1 * y^-1 * z^-3 * x^-1 * z * y^-1 * x * z * y * z^-4 ] T89.142 : Triangle type {4,4,24} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, x^-1 * y^-1 * z^-3 * x^-1 * z * y^-1 * x * z * y^-1 * z^-4 ] T89.143 : Triangle type {4,4,46} Group order 368 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^30 * y^-1 * z^-4 * x * z^2 * y^-1 * z^-8 * x ] T89.144 : Triangle type {4,4,90} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^6 * y * z^-4 * x * z * y * z^-4 * x^-1 * y * x^-1 ] T89.145 : Triangle type {4,4,90} Group order 360 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^76 * y^-1 * x^-1 * z^13 ] T89.146 : Triangle type {4,4,178} Group order 356 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^75 * y^-1 * x * z^13 ] T89.147 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, x^-1 * z * y * x^2 * z * y * x^-1 ] T89.148 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, y * z^-2 * x^-1 * z * x^-1 * z, y^-2 * z^-1 * x^2 * z^2 * x^-1 ] T89.149 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, x^-1 * z * y * x^2 * z * y * x^-1, (x * y^-1)^4 ] T89.150 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x * z^-2)^2, y^2 * z^-1 * x^-1 * z * y * z^-1, x^-1 * z * y * x^2 * z * y * x^-1 ] T89.151 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, x^-1 * z * y * x^2 * z * y * x^-1, (x * y^-1)^4 ] T89.152 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z * y * z^-1 * y * x * z^-2 * x, (y * z^-1)^4 ] T89.153 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y * x^-2 * z^3, z^-1 * y^2 * x^2 * y^-1 * z * y, (x * z^2 * y)^2 ] T89.154 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, x^-1 * z * y * x^2 * z * y^-1 * z^-1 ] T89.155 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T89.156 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, (y * z^-1 * y)^2, z^-2 * y * x^2 * z * y * z^-1 ] T89.157 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T89.158 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, y^-1 * z^-2 * x^-1 * y^-1 * z * y^-1 ] T89.159 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z * y^2 * x * z * y^2 ] T89.160 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, y^-1 * z^-1 * x^-2 * z * y^-2, y * x^-1 * y * x^2 * y^-1 * z^-1 * y, x^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T89.161 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^-1 * x * z^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * z^2 * y * x^-1 * z * y^-1 * z^-1 ] T89.162 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, z^-1 * x * z^-1 * x^-1 * z^2 * y^-1 ] T89.163 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T89.164 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x * z^2, y^-1 * z^2 * x^-1 * y^-1 * z * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T89.165 : Triangle type {4,6,8} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y, z * y^2 * x^-1 * z * y^-1 * x ] T89.166 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * z * y * x^-1 ] T89.167 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, y * z^-2 * x^-1 * z * x^-1 * z ] T89.168 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, x^-1 * z * y * x^2 * z * y^-1 * z ] T89.169 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z * x^-1 * z ] T89.170 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z ] T89.171 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3 ] T89.172 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, (z^-1 * x)^3, x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T89.173 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T89.174 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y^-2 * z^-1 * x^2 * z^2 * x^-1, x * z^-1 * x * y^-1 * x * z^2 * y ] T89.175 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * z * y * x^-1, (x * z^2 * y)^2 ] T89.176 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z * y * x^2 * z * y^-1 * z, x * z^2 * y * x^-1 * z * y^-1 * z^-1 ] T89.177 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.178 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, y^-1 * z^-1 * y * x^-1 * y^-1 * x * z ] T89.179 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z * x^-1 * z, y^-2 * z^-1 * x^2 * z^2 * x^-1 ] T89.180 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.181 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, y * z^-2 * x^-1 * z * x^-1 * z, x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T89.182 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, x^-1 * z * y * x^2 * z * y^-1 * z, x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T89.183 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z, (x * z^2 * y)^2 ] T89.184 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T89.185 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y^2 * x^2 * z * x^-1 * z, z^-1 * y * x * y^-1 * x * y^-1 * z^-1 * y ] T89.186 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * x^-1 * y^-1 * x * z * y^2, z^-1 * y * x * y^-1 * x * y^-1 * z^-1 * y, z^-1 * x^-1 * y^-2 * x * y^-1 * z * y, (x * z^-2 * y)^2 ] T89.187 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * y * x * z^2 * y ] T89.188 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * z * y * x^2 * z * y * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x^-1 * z, z^-1 * y * x * y^-1 * x * y^-1 * z^-1 * y ] T89.189 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, y * z^-1 * x^-2 * z^2 * x^-1, x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y ] T89.190 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, z^2 * y^-1 * z^-1 * x * z^2 * y^-1 ] T89.191 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z * x^-1 * z ] T89.192 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, (x * y^-1)^4 ] T89.193 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, y * z^-1 * x^-2 * z^2 * x^-1, (x * y^-1)^4 ] T89.194 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (x * z^-1 * y^2)^2, (x^-1 * z * y^2)^2, x * z^-2 * y * x * z * y^-1 * z^-1 ] T89.195 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^2 * y^-1 * z^-2 ] T89.196 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, (x * z^2 * y)^2 ] T89.197 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, x^-1 * y^2 * x^2 * z * x^-1 * z, (x^-1 * z * y^2)^2 ] T89.198 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^2 * y^-1 * z^-2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T89.199 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T89.200 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (y * z^-1 * y)^2 ] T89.201 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z * y^-1 * z^-1, z^8 ] T89.202 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z^2 * y, z^8 ] T89.203 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1, z^8 ] T89.204 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, x^-1 * z^2 * y * x * z^2 * y, z^8 ] T89.205 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T89.206 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, (y * z^-1)^4, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.207 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.208 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, (y * z^-1)^4, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T89.209 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T89.210 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z^-1, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.211 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^2 * y^-1 * z^-2 ] T89.212 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y^-1 * z^-1, z^-2 * y * x^2 * y^-1 * z^-2 ] T89.213 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3 ] T89.214 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T89.215 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (x * z^-1 * y^2)^2, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (x * z^-2 * y)^2 ] T89.216 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.217 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T89.218 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.219 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T89.220 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z^2 * y, x^-1 * y^2 * x^-2 * z * y * z^-2 ] T89.221 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T89.222 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x^2 * z * y * x^-1 ] T89.223 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, y * z^-1 * y * x^-1 * z^2 * y, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.224 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, y * z^-1 * y * x^-1 * z^2 * y, x^-1 * z * y * x^2 * z * y * x^-1 ] T89.225 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z^2 * y, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.226 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, (y * z^-1 * y)^2, x^-1 * y^2 * x^2 * z * x^-1 * z ] T89.227 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z^2 * y * x * z * y^-1 * z^-1, x^-1 * y^2 * x^-2 * z * y * z^-2 ] T89.228 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, y^2 * x^-2 * y^-1 * z * x^-1, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T89.229 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, y^2 * x^-2 * y^-1 * z * x^-1, (x^-1 * z * y^2)^2 ] T89.230 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (y * z^-1)^4, z^8 ] T89.231 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^8, z^-2 * y^2 * x^-1 * z * y^3, z^-3 * y * x^-1 * y * z^-2 * y ] T89.232 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, z^8, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T89.233 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, y * z^-1 * x^-1 * z * y * x^-1 * z * y^-2 * z^-1, z^2 * y * x^-1 * z * y * z^-1 * y * x * y^-1 ] T89.234 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^8, y * z^-1 * y^2 * x^-1 * z * y^-2 * z, z^-3 * y * x^-1 * y * z^-2 * y ] T89.235 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, z^3 * y * x^-1 * z^2 * y^-1 ] T89.236 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x * z^2, y * z^-1 * x^-2 * z^2 * x^-1 ] T89.237 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, y * x * z^-1 * x^-1 * z^3 ] T89.238 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^8, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-2 * y ] T89.239 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^8, y * x^-1 * z * y * x^-1 * z * y^-1 * z^2 ] T89.240 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^8, z^-1 * x * z^2 * y * z^-2 * x^-1 * z^2 * y * z^-1 ] T89.241 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, (x * y^-1)^4, (x * z^-1 * y^2)^2 ] T89.242 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^-1 * z^-1 * y^2 * x * z * y * x^-1 ] T89.243 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y^2)^2, z^8 ] T89.244 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * y^-1)^4, y^-1 * z^-1 * y^2 * x * z * y * x^-1 ] T89.245 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, (y * z^-1)^4, z^8, z^-4 * x^-1 * z^3 * y^-1, z * y * z^-1 * y^2 * x * z^-2 * y * x ] T89.246 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, (y * z^-1)^4, z^8, x^-1 * z * y^2 * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.247 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, (y * z^-1)^4, x^-1 * z * y^2 * x^-1 * z * x^-1 * y^-1 * z ] T89.248 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, (y * z^-1)^4, x^-1 * z * y^2 * x^-1 * y^-1 * z^-1 * x^-1 * z ] T89.249 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, (x * y^-1)^4, z^-1 * x * z^-1 * y * x^-1 * z * x^-1 * y^-2 ] T89.250 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, (x * y^-1)^4, z^-1 * x * z^-1 * y * x^-1 * z * y^2 * x ] T89.251 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, (x * y^-1)^4, z^-1 * x * z^-1 * y * x^-1 * z * x^-1 * y^-2 ] T89.252 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, (x * y^-1)^4, x^-1 * y^-1 * z^-1 * y * x^-1 * z * x^-1 * y^-1 * z^-1 ] T89.253 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^8 ] T89.254 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T89.255 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, y^2 * z^-1 * x^-1 * z * y * z^-1, (x * y^-1)^4, (x * z^-1 * y^2)^2 ] T89.256 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T89.257 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^8, z^2 * y * x^-2 * z^3 * x^-1, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T89.258 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^8 ] T89.259 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^8, z^-1 * x * z^-1 * x^-2 * z^2 * y^-1 * z^-1 ] T89.260 : Triangle type {4,6,8} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^8, z^2 * y * x^-2 * z^3 * x^-1, z^-1 * x * z^-2 * x^-1 * z * y * z^-1 * x ] T89.261 : Triangle type {4,6,52} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^4 * y^-1 * z^-5 * x^-1 * z^6 * y * x * z * y^-1 * z^-4 * x * z^3 ] T89.262 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^3 * y * z^-3 * x * z^2 * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-3 * x^-1 * z ] T89.263 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^5 * y * z^-1 * x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-3 * x * z ] T89.264 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^3 * y * z^-3 * x * z^2 * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-3 * x * z ] T89.265 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^5 * y * z^-1 * x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-3 * x^-1 * z ] T89.266 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^21 * y * z^-1 * x^-1 * z^13 ] T89.267 : Triangle type {4,8,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^22 * y^-1 * x * z^13 ] T89.268 : Triangle type {4,9,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1, y^-9 ] T89.269 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, z^-3 * y * x * z * y^2 ] T89.270 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y^3 * z^-1 * x^-1 * z, z^-3 * y * x * z * y^2 ] T89.271 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^3 * x^-1 * z^3 * y^-1, y^10 ] T89.272 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * z * y, y * x^-1 * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T89.273 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, y^2 * z^-1 * y * x^-1 * z * y^-1 * z^2 ] T89.274 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y^3 * z^-1 * x * z, z^-3 * y * x * z * y^2 ] T89.275 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y^3 * z^-1 * x^-1 * z, z^-3 * y * x * y^-1 * z^-1 * y ] T89.276 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y^-1 * z * y^2 * x * y^-1 * z * y ] T89.277 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^4 * x^-1 * z^4, y^10 ] T89.278 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y * z^-1 * y^3 * z^-1 * x^-1 * z ] T89.279 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^3 * x^-1 * z^3 * y^-1, y^10 ] T89.280 : Triangle type {4,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^4 * x^-1 * z^4, y^10 ] T89.281 : Triangle type {4,14,20} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x^-1 * z * y * x^-1 * y * x * z^3, y^-1 * z^-1 * x^-1 * z * y^2 * x * y^-3 * z^-1 * y^4 * x^-1 * y^-1 ] T89.282 : Triangle type {4,28,63} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, z^4 * y * x * z^4 ] T89.283 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * z^-2 * y * z^-3 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y ] T89.284 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y^2 * z^-2 * y^6 * z^-1 * y * z^-2 * y^6 * z^-2 ] T89.285 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y * z^-1 * y^4 * z^-1 * y^6 * z^-2 * y ] T89.286 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * x^-1 * y^-4, y * z^-1 * y^3 * z^-1 * x * z^-1 * y^3 * z^-4 * y^2 ] T89.287 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-3 * y * z^-1 * y * z^-1 * x^-1 * y^2 * z^-1 * y * z^-2 * y * z^-1 ] T89.288 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-1 * z * y^-2 * z^3 * y^-1 * z^3 * y^-4 * z ] T89.289 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, z^2 * y^-3 * z^2 * y^-1 * z * y^-3 * z^2 * y^-1 * z ] T89.290 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 * z^-2 * y * z^-1 * y^9 * z^-1 * y^8 * z^-2 ] T89.291 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * x^-1 * y^-4, z^6 * y^-5 * z * y^-2 * z * y^-1 ] T89.292 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-1 * z * y^-2 * z^3 * y^-1 * z^3 * y^-1 * z^3 * y^-1 ] T89.293 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, z^-1 * y * z^-3 * y * z^-3 * y * z^-2 * y^3 * z^-1 ] T89.294 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, z^-1 * y^4 * z^-2 * y * x^-1 * y * z^-1 * y^4 * z^-1 * y ] T89.295 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^4 * z^-3 * y^3 * z^-1 * y^3 * z^-2 ] T89.296 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, z^2 * y^-2 * z^3 * y^-1 * z^3 * y^-3 * z^2 ] T89.297 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-2 * z * y^-2 * z * y^-6 * z * y^-2 * z ] T89.298 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^-1 * z * y^-1 * z^8 * y^-2 * z * y^-2 ] T89.299 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, z * y^-1 * z * y^-2 * z * y^-7 * z * y^-2 ] T89.300 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-4 * y^9 * z^-1 * y^7 * z^-1 ] T89.301 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * x^-1 * y^-4, z^6 * y^-4 * z * y^-2 * z * y^-2 ] T89.302 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^3 * y^-1, y^-5 * z * y^-5 * z^5 ] T89.303 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^3 * y^-1, z * y^-4 * z * y^-5 * z^3 * y^-1 * z ] T89.304 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-3 * x^-1 * z^4, z * y^-6 * z * y^-2 * x * z * y^-2 * z * y^-1 * z ] T89.305 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-4 * x^-1 * z^3 * y^-1, z * y^-4 * z * y^-5 * z^3 * y^-1 * z ] T89.306 : Triangle type {4,32,32} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * x^-1 * z^4, z * y^-4 * z^2 * y^-1 * z * y^-1 * x * y^-2 * z^2 * y^-1 * z ] T89.307 : Triangle type {4,120,120} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y * z^-1 * y^24 * z^-2 * y * z^-1 * y^12 * z^-1 * y^6 * z^-1 * y^2 * z^-1 * y^6 ] T89.308 : Triangle type {4,120,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-32 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T89.309 : Triangle type {5,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * y^-2, x^-1 * z * y^-1 * x * y^-1 * z ] T89.310 : Triangle type {5,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y * x)^2 ] T89.311 : Triangle type {5,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, (x * z * y^-1)^2, z^-1 * x * z^-1 * x^-1 * z * y^-1 ] T89.312 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, (y * z^-1 * y)^2, y^3 * x^-1 * z^3 ] T89.313 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-2, x^-1 * y * x^-2 * z^3 ] T89.314 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T89.315 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T89.316 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y * x^-2 * y^-2 * z, z^-2 * x^-2 * z * x^-1 * y, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T89.317 : Triangle type {5,8,8} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, (x^-1 * z * y)^2, y^3 * x^-1 * z^3 ] T89.318 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y * x^-1 * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3, z^3 * y^-1 * x^-1 * z^3 ] T89.319 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y * x^2 * z^2, y^6, y * z^-1 * y * x * y^-1 * z^-1 ] T89.320 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^6, x * z^-1 * y * x^-1 * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * y^-2 * x, x^-1 * y^2 * x^-1 * y^2 * z^-1 ] T89.321 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, z * y^2 * x * y^-1 * z, x * z^-1 * x^-2 * y * x * y^-1 ] T89.322 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^6, z * y * z^-1 * x^-1 * y^-2 * z ] T89.323 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 ] T89.324 : Triangle type {6,6,7} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-1 * y, z^3 * y^-1 * x^-1 * z^3 ] T89.325 : Triangle type {6,6,7} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z^2 * y^-1)^2 ] T89.326 : Triangle type {6,6,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^6, (x * z^-1 * x)^2, y^6, (y * z^-1 * y)^2, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1 * x ] T89.327 : Triangle type {6,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^4 * y^-1 * z^-5 * x * y^-1 * z^-1 * x * z^8 ] T89.328 : Triangle type {6,15,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z^-2 * y * x * z^-1 * y, y * x^-3 * z * x^-2 ] T89.329 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, y^6 * z^-1 * y^2 * z^-1 ] T89.330 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T89.331 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T89.332 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T89.333 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x^-1 * z * y)^2, y * x^-3 * z * x^-2, y^2 * x * y^-1 * x * y^-2 * z ] T89.334 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^4 * x^-1 * z^4 ] T89.335 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (y * z^-1 * y^2)^2 ] T89.336 : Triangle type {6,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y^-3 * z^3 * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z^7 ] T89.337 : Triangle type {6,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T89.338 : Triangle type {7,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y * z^-1, (x * z * y)^2, x^-7 ] T89.339 : Triangle type {7,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * y^-1 * z, (x * z * y)^2, (x * z^-2)^2 ] T89.340 : Triangle type {7,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, (x * z * y)^2, x^-7, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T89.341 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^2 * x * z * x^-1, z * x^-2 * y^-1 * x^-2 * z * y^-1, z^-2 * x * z^2 * y * z^-2 * x^-1 * y ] T89.342 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * z * y, y * x^-3 * y^-2 * z^-1, z * x^-3 * z * y^-1 * z ] T89.343 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, (x * z^-2)^2, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T89.344 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, z^-2 * x^-2 * y * z^-1 * x, x^-1 * z * x^-2 * y^-1 * z^-2 ] T89.345 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-2)^2, x^-1 * z * x^-2 * y^-1 * z^-2, y^-1 * z^-1 * x^3 * y^-1 * z^-1 * x^-1 ] T89.346 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * z * y^-2, z^-3 * x^-1 * y^-3 ] T89.347 : Triangle type {8,8,16} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, y^2 * z^-1 * x^-1 * y^-1 * z^-2 ] T89.348 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * y^-1 * x)^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, x^8, z^-4 * x^-1 * z * y * z^-2 ] T89.349 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, x^8, z * y * z^-2 * x^-1 * z^4 ] T89.350 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^8, z * y * z^-2 * x^-1 * z^4 ] T89.351 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, (x * y^-1 * x)^2, (y * z^-2)^2, x^8, z^-4 * x^-1 * z * y * z^-2 ] T89.352 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T89.353 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y * x^-2 * y * x^-1 * y^-1, x^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.354 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^2 * y^-1 * x^2 * y^-3, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.355 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.356 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, x^2 * z^-1 * x^2 * z^-3 ] T89.357 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^8, y^8, (x * z^-1)^4 ] T89.358 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^8, x^2 * z^-1 * x^2 * z^-3 ] T89.359 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * z^2, x^8, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T89.360 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-2 * x^-2 * z * y^-1 * x, x^8 ] T89.361 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, z^-2 * x^-2 * z * y^-1 * x, y * x^-1 * y * x^-1 * y * x^-1 * z, x^8 ] T89.362 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^-1 * z * x^-2 * z * y^-1 * z^-1, x^8 ] T89.363 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^8, y^-1 * z^-1 * x^3 * y^-1 * x * z ] T89.364 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-1 * y * x^2 * z^-1 * y, x^8, (x * z^-1)^4 ] T89.365 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * y^2 * z^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, (x * z^-1)^4 ] T89.366 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * y^2 * z^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, z^-1 * x * z^-1 * x^-2 * y * x * z^-1 * x ] T89.367 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-1 * y * x^2 * z^-1 * y, x^8, z^-1 * x * z^-1 * x^-2 * y * x * z^-1 * x ] T89.368 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1 ] T89.369 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^-2 * x^-2 * z * y^-1 * x, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.370 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.371 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x^8, y^-1 * z^-2 * x * y^-1 * x * z^4 ] T89.372 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * z * y^-1 * x, z^-2 * y * x^-1 * z * y^2, y^2 * z^-1 * x^-1 * z * y * z^-1 ] T89.373 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y ] T89.374 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * x^-3 * z^2 * y, z^-2 * y * x^-1 * z * y^2 ] T89.375 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T89.376 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z * x^-3 * y^-3, z * y^2 * x^-1 * z * y^-1 * z, z * y * z^-2 * x^-1 * z^4 ] T89.377 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z * x^-3 * y^-3, z * y^2 * x^-1 * z * y^-1 * z, z * y * z^-2 * x^-1 * z^4 ] T89.378 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, (y * z^-2)^2, z * x^-3 * y^-3, z^-4 * x^-1 * z * y * z^-2 ] T89.379 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (y * z^-2)^2, z * x^-3 * y^-3, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.380 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-2)^2, y * x^-3 * y^-1 * z * y, x^-1 * y * x^-2 * y^-2 * z, z * y^-1 * x * z * y^-1 * x * z^4 ] T89.381 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, y^-1 * z^-1 * x^-2 * y^-1 * x * y^-1, z * y * z^-2 * x^-1 * z^4 ] T89.382 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-1 * x)^2, z * y * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x^-1, z * y * z^-2 * x^-1 * z^4 ] T89.383 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^2 * z^-1 * y, x^8, x^-1 * z^3 * y * x^-1 * z * y^-1 * z^-2 ] T89.384 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, y^8, z * y * x * z * y * x * z^4 ] T89.385 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y * x^-2 * y * x^-1 * y^-1, x^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.386 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^2 * y^-1 * x^2 * y^-3, y * z^-1 * x^-1 * y * z^-1 * x^-1 * z^4 ] T89.387 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.388 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y * x^-2 * y * x^-1 * y^-1, x^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T89.389 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^2 * y^-1 * x^2 * y^-3, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.390 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T89.391 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z * y^2 * x^-1 * z * x^-1, y^2 * x^-2 * y * x * z^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.392 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, x^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.393 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * y * x * z * x^-1, x^8, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T89.394 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * y * x * z * x^-1, x^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.395 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, x^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.396 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z * y^2 * x^-1 * z * x^-1, y^2 * x^-2 * y * x * z^-1, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.397 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.398 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^-2 * x^-2 * z * y^-1 * x, z^-3 * x^-1 * y^-1 * x * z^3 * y ] T89.399 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^-2 * x^-2 * z * y^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.400 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.401 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^3 * y^-1 * z^-4 * x^-1 * y^-1 * x^-1 * y^-1 * z^-6 * x^-1 ] T89.402 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^2 * y * x^-1 * y^-1 * z^-3 * x^-1 * z * y^-1 * z^-1 * x^-1 * z^5 * y * x^-1 ] T89.403 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, y^-1 * z^-1 * x * z^3 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x^-1 * z^2 * y * x ] T89.404 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.405 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z^-1 * y^2 * x * z^-1 * x, y * x^-3 * y^-1 * z * y, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.406 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.407 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.408 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, x^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.409 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z^-3 * x^-1 * z * y * x * z^2 * y^-1 ] T89.410 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T89.411 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.412 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.413 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z * y^-1 * x * z * y^-1 * x * z^4 ] T89.414 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, z * y^-1 * x * z * y^-1 * x * z^4 ] T89.415 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T89.416 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, y^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.417 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, y^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.418 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.419 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * x^-3 * y^-3, x^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T89.420 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * z^-1 * y)^2, z * x^-3 * y^-3 ] T89.421 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1 * y)^2, z^-1 * x^-3 * z^2 * y^-1, z * x^-3 * y^-3 ] T89.422 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, (x * z * y)^2, x^-1 * y * x^-2 * y^-2 * z ] T89.423 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2, (x * z * y)^2, (y * z^-2)^2 ] T89.424 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-2)^2, y^2 * x^-2 * y^-1 * x * z^-1, z^-1 * y * x^-2 * y^2 * x, x * z * x^-2 * y^-1 * z^-2 ] T89.425 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * y * x^-2 * y^-2 * z, y^2 * x^-2 * z * x^-1 * y, x * z * x^-2 * y^-1 * z^-2, z^2 * x^-2 * z * y^-1 * x ] T89.426 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y * x * y^-1 * x * z^2, x^8, y^8, y^2 * z^-1 * y^2 * z^-3 ] T89.427 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^8, z * y^3 * x^-1 * y^-1 * z^2 * y^-1 ] T89.428 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (x * z * y^-1)^2, (x * z * y)^2, y^8, y^2 * z^-1 * y^2 * z^-3 ] T89.429 : Triangle type {8,8,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, y * x * y^-1 * x * z^2, x^8, y^8, y * z^-1 * y^2 * x^-1 * y^-1 * z * y^-1 * z^-1 ] T89.430 : Triangle type {8,8,60} Group order 240 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z * y * x^-1 * y^-1 * x * z^3 ] T89.431 : Triangle type {8,8,60} Group order 240 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1 ] T89.432 : Triangle type {8,8,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-9 * x * z^6 * y^-1 * x^-1 * z^7 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T89.433 : Triangle type {8,8,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^17 * y^-1 * x * y^-1 * x * z^11 ] T89.434 : Triangle type {8,10,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^3 * x^-1 * y^2 * z^-1, x^8, y * z^-1 * x * y^-1 * x * z^3 ] T89.435 : Triangle type {8,10,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^3 * x^-1 * y^-2 * z^-1, x^8, z^-1 * x * z * y^-1 * x * y^-1 * z^-2 ] T89.436 : Triangle type {8,10,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, x^8, y^10 ] T89.437 : Triangle type {8,10,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^10 ] T89.438 : Triangle type {8,14,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^2 * y^-1 * z^3 * y^-2 * z * y^-1 * z^2 * y^-1 ] T89.439 : Triangle type {8,14,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-1 * z^3 ] T89.440 : Triangle type {8,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^17 * y^-1 * z * y^-3 * z * y^-1 * z ] T89.441 : Triangle type {8,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T89.442 : Triangle type {10,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-2, y * x^-1 * y^-1 * x * y^-1 * z^-1, x^-4 * y^-1 * x * z^-1, y^-4 * z * y^-1 * z * y^-1 * z^4 ] T89.443 : Triangle type {10,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^-4 * y^-1 * x * z^-1, y^-2 * z * y^-3 * z * x * y^-1 * z * y^-3 ] T89.444 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * z * y, x * y^-2 * z * y^-2 * x * z^-1 * y^4, (z^-2 * y^4)^2 ] T89.445 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^-1 * z * y^-1 * x^2 * z * y^-1 * z ] T89.446 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x^2 * z * x^-1, (x * z * y^-1)^2, z * y^2 * x^-2 * z^2 * y * x^-1 ] T89.447 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, (x * y^-1 * x)^2, (x * z^-1 * x)^2 ] T89.448 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^10, y * z^-3 * y * z^-2 * y * z^-3 * y ] T89.449 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * y^-1 * x^2 * z * x^-1, (x^-1 * z * y)^2, (x * y^-1)^4 ] T89.450 : Triangle type {10,12,12} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x^2 * z * x^-1, y^2 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T89.451 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, y^-3 * x * z^-1 * x^-1, z^-2 * x^3 * z^-1 * x * z^-1 ] T89.452 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-1 * y^-2 * x * y^-1 * z^-1, z^2 * y^-1 * x * z^-1 * x, x * z^-2 * y * x * z^-3 ] T89.453 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, z * y^-2 * x * z * x^-1, x * z^-1 * x^2 * y^-1 * x^3 * z^-2 * x^2 ] T89.454 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z * y, y * x^-1 * y^-1 * x * y^-1 * z, x^-10 ] T89.455 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, y * x^3 * z^-1 * x^-1, x^-1 * z * y * x * z^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T89.456 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, y * x^3 * z^-1 * x^-1, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1 ] T89.457 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1, x * z^-1 * x * y^-1 * x^4 * z^-1 * x * z^-1 * x ] T89.458 : Triangle type {10,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * z, x^-1 * y^-1 * x^2 * z * x^-1, x^-10 ] T89.459 : Triangle type {10,21,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * y^-1 * z * y^-1, x^10 ] T89.460 : Triangle type {10,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^12 * y^-6 * z^2 ] T89.461 : Triangle type {10,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^4 * y^-1 * z * y^-1 * z^5 * y^-6 * z^2 ] T89.462 : Triangle type {14,14,14} Group order 224 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (x * z * y)^2, y * x^-3 * y^-2 * z, (x * y^-3)^2 ] T89.463 : Triangle type {14,14,14} Group order 224 Chiral action Defining relators: [ x * y * z, (x * y^-1 * x)^2, y^2 * x^2 * z^2, (y * z^-1 * y)^2 ] T89.464 : Triangle type {14,15,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * z * y, x^-1 * z * x^-2 * z * x^-5 * z^4 ] T89.465 : Triangle type {15,39,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T89.466 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^-2 * z^3 * y^-2 * x * y^-5 ] T89.467 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T89.468 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T89.469 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^-2 * z^3 * y^-3 * z * y^-1 * z^2 ] T89.470 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, (y^-5 * x * y^-1)^2 ] T89.471 : Triangle type {16,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^-2 * z^3 * y^-4 * z^3 ] T89.472 : Triangle type {18,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y^2 * z^-4, y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^2 ] T89.473 : Triangle type {24,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, y^-2 * z^-2 * x * z^-2 * x^6 * y^-1 * x * y^-1 ] T89.474 : Triangle type {24,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^13 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T89.475 : Triangle type {24,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y^2 * z^-3, x * y^-1 * z^-1 * x * z^-2 * x^6 * y^-1 * x * y^-1 ] T89.476 : Triangle type {24,32,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-5 * y^2, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T89.477 : Triangle type {24,48,48} Group order 192 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x * y^-1 * x^3 * y^-3, x * z^-1 * x^3 * z^-3 ] T89.478 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-11 * y^2 * x^-8 * y * x^-2 * z * x^-1 ] T89.479 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^-1 * y^5 * x^-2 * z * x^-6 ] T89.480 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, x * z^-1 * x * z^-1 * x^9 ] T89.481 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2, x^3 * z^-2 * x * y^-2 * x^6 ] T89.482 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-4 * y * x^-1 * y ] T89.483 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, x^-4 * z * x^-1 * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T89.484 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-8 * y^2 * x^-6 * z^2 * x^-8 ] T89.485 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^9 * y^-1 * z^-1 * x^2 ] T89.486 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^-3 * y * x^-7 * z^2 * y ] T89.487 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-5 * z * x^-13 * y * x^-5 ] T89.488 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-2 * y^4 * x^-8 ] T89.489 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x * z^-2 * x * z^-2 * x^8 ] T89.490 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, x * z^-2 * x * z^-2 * x^8 ] T89.491 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-4 * z^2 * x^-2 * z^2 * x^-1 ] T89.492 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, (y * z^-1)^4 ] T89.493 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, (y * z^-1)^4 ] T89.494 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-3 * z * x^-2 * y * x^-2 * y * x^-1 * y * x^-6 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T89.495 : Triangle type {24,48,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x^-1 * z * y * x^-6 * z^2 * x^-1 * z^2 * x^-1 ] T89.496 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^3 * z^-2 * x^5 * z^-2 ] T89.497 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z * y^-1 * x * y^-1 * x * z^3 ] T89.498 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, z^-2 * x^4 * z^-4 ] T89.499 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-4 * x * z^-1 ] T89.500 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * y^-1 * z^3 ] T89.501 : Triangle type {32,32,48} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x * y^-1 * x * z^2 * y^-1, z^2 * y^-1 * z * x^-1 * z^4 ] T89.502 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-8 * z * y^-7 * z * y^-7 ] T89.503 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^7 * y^-18 * x * y^-1 * x * y^-1 * x * y^-2 ] T89.504 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-1 * x^4 * y^-5 * x^2, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T89.505 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-4 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T89.506 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^-1 * y^6 * x^-5 * y^2 ] T89.507 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T89.508 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T89.509 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y^-6 * x * y^-2 * z^3 * y^-5 ] T89.510 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T89.511 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-9 * z^4 * y^-7 ] T89.512 : Triangle type {46,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^46 ] T89.513 : Triangle type {90,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-8 * y^2 * x^-6 * y^3 * x^-6 * z * x^-7 ] T89.514 : Triangle type {90,180,180} Group order 180 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^11 * y^-1 * x^12 * y^-1 * x^66, y * z^-1 ] T89.515 : Triangle type {90,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y^5 * z^-4 * y * x^-3 * y^4 ] T89.516 : Triangle type {90,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^8 * x^-3 * y^-1 * z^5 * y^-1 * z^7 ] T89.517 : Triangle type {90,180,180} Group order 180 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^7 * z^-3 * x^2 * y^-5 * x^5 ] T89.518 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x^-2 * y^-1, y^71 * x^-1 * y^18, x * z^-1 ] T89.519 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^48 * x^-4 * y^9 ] T89.520 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^21 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^3 ] T89.521 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^10 * x^-1 * y^5 * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^3 ] T89.522 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-3 * y^5 * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y^3 ] T89.523 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T89.524 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-1 ] T89.525 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T89.526 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^3 ] T89.527 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T89.528 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^5 * z^-3 * y^2 * x^-4 * y^4 ] T89.529 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T89.530 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, z^-4 * x * z^-4 * x * y * z^-4 ] T89.531 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T89.532 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-15 * x^3 * z^-3 * y * z^-1 * y * z^-1 ] T89.533 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^6, y^-5 * x^2 * y^-8 ] T89.534 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, x^6 * z^-3 * x^6 * y^-1 * x^2 ] T89.535 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^11 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T89.536 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^3 * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T89.537 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * z * y^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T89.538 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T89.539 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, y * x^-1 * y^6 * x^-6 * y^2 ] T89.540 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-4 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T89.541 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T89.542 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^8, y^-6 * x * y^-1 * z^5 * y^-5 ] T89.543 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T89.544 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y^2 * z^-1 * y * z^-5 * y^4 * z^-2 ] T89.545 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-19 * y * x^-8 * y * x^-8 ] T89.546 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T89.547 : Triangle type {179,179,179} Group order 179 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^4 * z^-1 * y^4 * x^-6 * y^3 ] Genus 90 T90.1 : Triangle type {2,4,93} Group order 744 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-74 * x * z^11 * y^-1 * z^-7 ] T90.2 : Triangle type {2,4,182} Group order 728 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-182 ] T90.3 : Triangle type {2,4,360} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-42 * x * y^-1 * z^-137 ] T90.4 : Triangle type {2,6,92} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^55 * y * x * z^20 * y * x * z * y * z^-7 * x * z^6 ] T90.5 : Triangle type {2,8,8} Group order 712 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y * z^-1 * y * x * y^-1 * z^3 * y^-1 * z ] T90.6 : Triangle type {2,8,62} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-38 * x * z^3 * y * x * z^8 * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-8 ] T90.7 : Triangle type {2,12,38} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-4 * x * z^11 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-16 ] T90.8 : Triangle type {2,14,32} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^7 * y * x * z * y * x * z * y * x * y^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-3 * x * y^-1 * z^-3 * x * z^3 ] T90.9 : Triangle type {2,14,210} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-2 * z^4 * y^-1)^2, z^2 * y * z^-8 * x * z^4 * y^-1 * z^-13 * x * z ] T90.10 : Triangle type {2,20,22} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^3 * x * y^-3 * z * y * x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y^5, z^-15 * x * y * z^-6 ] T90.11 : Triangle type {2,21,35} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-1 * y * x * z * y^2 * z^-1 * y * z^-1 * y, y * z^-3 * x * y^-1 * z^-4 ] T90.12 : Triangle type {2,22,198} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-9 * z^4 * y^-5 * z^4 ] T90.13 : Triangle type {2,26,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^13 * y^-1 * z^-1 * x ] T90.14 : Triangle type {2,38,190} Group order 380 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, z^-3 * y^9 * z^-4 * y^21 * z^-1 ] T90.15 : Triangle type {2,62,186} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-26 * y^13 * z^-2 * y^20 ] T90.16 : Triangle type {2,74,185} Group order 370 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y * z^-1 * y^10 * z^-4 * y^21 ] T90.17 : Triangle type {2,92,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-9 * y^12 * z^-4 * y^19 * z^-1 ] T90.18 : Triangle type {2,93,93} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-89 * z * y^-1 ] T90.19 : Triangle type {2,122,183} Group order 366 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-25 * y^13 * z^-2 * y^18 * z^-2 ] T90.20 : Triangle type {2,181,362} Group order 362 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^123 * y^-56 * z ] T90.21 : Triangle type {2,182,182} Group order 364 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^58 * z^-124 ] T90.22 : Triangle type {2,360,360} Group order 360 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^57 * z^-123 ] T90.23 : Triangle type {3,3,181} Group order 543 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x^-1 * z^3 * y^-1 * z^-9 ] T90.24 : Triangle type {3,91,273} Group order 273 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^4 * z^-1 * y^10 * z^-1 * y^74 * z^-1 ] T90.25 : Triangle type {3,92,92} Group order 276 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^74 * y^-14 * z^2 * y^-1 ] T90.26 : Triangle type {3,270,270} Group order 270 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-75 * z * y^-14 ] T90.27 : Triangle type {4,4,91} Group order 364 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-2 * x^2 * z^2 * y^-1, z^-2 * x^-1 * y * x^-1 * z^2 * y * z^-1 ] T90.28 : Triangle type {4,4,91} Group order 364 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^77 * y^-1 * x^-1 * z^13 ] T90.29 : Triangle type {4,4,180} Group order 360 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^76 * y^-1 * x * z^13 ] T90.30 : Triangle type {4,6,78} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^9 * y * z^-1 * x^-1 * z^2 * y * z^-4 * x * z^8 ] T90.31 : Triangle type {4,10,70} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1, y^10 ] T90.32 : Triangle type {4,20,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z^-1 * y * z^-1 * x * z^-2 ] T90.33 : Triangle type {4,20,65} Group order 260 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, y * z^-3 * y^3 * z^-3, z^-1 * x^-1 * z^3 * y^-1 * z^-3 * x^-1 * z^4 * y^-1 ] T90.34 : Triangle type {4,22,33} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * x * z^-1 * x^-1 * z * x^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^-3 * z * y^-1 * x * y^-1 * z * y^-1 * z^2 * y^-1 ] T90.35 : Triangle type {4,28,126} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, z^4 * y * x^-1 * z^4 ] T90.36 : Triangle type {4,36,63} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * y^2 * x^-1 * y * z^-3 ] T90.37 : Triangle type {4,61,244} Group order 244 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-33 * z * y^-1 * z * y^-2 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T90.38 : Triangle type {4,62,62} Group order 248 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-28 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-11 * z * y^-1 ] T90.39 : Triangle type {4,240,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-30 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T90.40 : Triangle type {5,5,61} Group order 305 Chiral action Defining relators: [ x * y * z, x^-5, y^-5, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * y * z^-2 ] T90.41 : Triangle type {5,5,61} Group order 305 Chiral action Defining relators: [ x * y * z, x^-5, z^2 * x^-1 * y^-1 * z, y^-5 ] T90.42 : Triangle type {5,46,230} Group order 230 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^13 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T90.43 : Triangle type {5,225,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^17 * z^-5 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T90.44 : Triangle type {5,225,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^16 * z^-6 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T90.45 : Triangle type {6,6,46} Group order 276 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^36 * y^-1 * x * y * x^-1 * z^8 ] T90.46 : Triangle type {6,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-7 * x * y^-1 * z^-2 * x * z^2 * y * z^-1 * x^-1 * z^3 ] T90.47 : Triangle type {6,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, z^2 * y * z^-1 * x^-1 * z^4, x^-1 * y^-1 * z^-1 * x * z^-1 * y^3 * x^-1 * y^-2 * z * y ] T90.48 : Triangle type {6,37,222} Group order 222 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^9 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T90.49 : Triangle type {6,38,38} Group order 228 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y * z^-1 * y^3 * z^-2 * y * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y^10 ] T90.50 : Triangle type {6,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-1 * y^6 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T90.51 : Triangle type {7,31,217} Group order 217 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^3 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T90.52 : Triangle type {7,32,32} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^3 * z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^12 ] T90.53 : Triangle type {7,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^8 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T90.54 : Triangle type {7,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^6 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T90.55 : Triangle type {7,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T90.56 : Triangle type {8,8,31} Group order 248 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-17 * x * y^-1 * x^-1 * y * z^-12 ] T90.57 : Triangle type {8,10,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^-2 * x^3 * z^2 * y^-1, z^-1 * x^-1 * y^-1 * x^2 * z * y * x ] T90.58 : Triangle type {8,10,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, x^8, y^10 ] T90.59 : Triangle type {8,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, z^-1 * y^3 * x * z * x^-1 * y^-1, z^-1 * x^-1 * y * x * z * y^-1 * z^-6 ] T90.60 : Triangle type {9,9,14} Group order 252 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1, x^-9 ] T90.61 : Triangle type {10,21,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6 * z^2 ] T90.62 : Triangle type {10,22,22} Group order 220 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^-9 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-2 * z ] T90.63 : Triangle type {10,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^8 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T90.64 : Triangle type {10,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-4 * y^3 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T90.65 : Triangle type {11,19,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^2 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z^2 ] T90.66 : Triangle type {11,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, z^-1 * y * x^2 * z * y^-1, y * z^-2 * y * z^-1 * y * z^-3 * y^5 * z^-1 * y^4 * z^-1 ] T90.67 : Triangle type {11,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z^-2 * x^-1 * y^-2, y^-4 * z * y^-4 * z * y^-1 * z * y^-8 ] T90.68 : Triangle type {11,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * y * x^-1 * z * y^-1, y^-2 * z^5 * y^-1 * z^2 * y^-1 * z^4 * y^-1 * z^4 ] T90.69 : Triangle type {11,20,20} Group order 220 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, z^-2 * x^2 * y^-2, y * z^-3 * y^4 * z^-1 * y * z^-1 * y^4 * z^-3 * y^2 ] T90.70 : Triangle type {11,20,20} Group order 220 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-11, y^2 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^7 * z^-1 ] T90.71 : Triangle type {11,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^6 * z^-3 * y^9 ] T90.72 : Triangle type {11,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^4 * z^-1 * y * z^-5 * y * x^-1 * y^6 ] T90.73 : Triangle type {11,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T90.74 : Triangle type {11,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T90.75 : Triangle type {11,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T90.76 : Triangle type {12,12,19} Group order 228 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y * z^-1 * x * z^2, x^-12 ] T90.77 : Triangle type {12,12,19} Group order 228 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, z * y * x^2 * z^-1 * x^-1, z^-1 * y * z^-1 * x * z^-2, x^-2 * y * x^-8 * y ] T90.78 : Triangle type {12,12,19} Group order 228 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^4 * y^-1 * x * y^-1 * x * y^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^3 ] T90.79 : Triangle type {13,16,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-1 * z * y^-1 * z^5 * y^-1 * z^5, x^3 * y^-5 * x * z^-5 * x^4 ] T90.80 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^2 * y^-4 * x^2, y^-5 * x * y^-1 * z^5 * y^-4 ] T90.81 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^2 * y^-4 * x^2, y^5 * z^-4 * y * x^-1 * y^5 ] T90.82 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T90.83 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^3 * z^-3, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T90.84 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-5 * y^6, x^5 * z^-4 * x^2 * y^-4 * x^2 ] T90.85 : Triangle type {13,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^2 * y^-4 * x^2, z^-10 * y * z^-4 ] T90.86 : Triangle type {14,14,16} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, (x^-1 * y * x^-1 * y * x^-1 * y * x^-1)^2, z^16 ] T90.87 : Triangle type {14,14,105} Group order 210 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^-8 * x^-1 * z^3 * y^-1 * z^-3 ] T90.88 : Triangle type {14,14,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^-2 * x^-1 * z * y * z^-3 * x^-1 * y * z^-3 * x^-1 * z^2 * y * z^-1 ] T90.89 : Triangle type {14,14,105} Group order 210 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, y * z^-4 * x^-1 * z * y^-1 * z^-3 * x^-1 * z^5 ] T90.90 : Triangle type {14,15,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1, x^-1 * z * x^-2 * z * x^-4 * z * x^-1 * z * x^-1 * z ] T90.91 : Triangle type {14,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T90.92 : Triangle type {14,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-2 * z^3 * y^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T90.93 : Triangle type {14,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y^6, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T90.94 : Triangle type {15,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T90.95 : Triangle type {15,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * y * z^-4, y^5 * z^-3 * y^2 * x^-6 * y^3 ] T90.96 : Triangle type {15,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^2 * z^-4, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T90.97 : Triangle type {16,16,52} Group order 208 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, y * z^-1 * x^-2 * z * y * z^-1 ] T90.98 : Triangle type {16,16,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, y * z^-4 * x^-1 * z * y * z^-1 * x^-1 * z^5 ] T90.99 : Triangle type {16,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T90.100 : Triangle type {16,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T90.101 : Triangle type {16,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T90.102 : Triangle type {16,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^6 * z^-3 * x^4 * y^-3 * x^3 ] T90.103 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T90.104 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-3 * x^4 * y^-7 ] T90.105 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-2 ] T90.106 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T90.107 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, z^-4 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T90.108 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^3 ] T90.109 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T90.110 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T90.111 : Triangle type {19,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^8 * z^-4 * x^2 * y^-4 * x^5 ] T90.112 : Triangle type {21,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-21 ] T90.113 : Triangle type {21,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^-2 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 ] T90.114 : Triangle type {21,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T90.115 : Triangle type {21,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T90.116 : Triangle type {21,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T90.117 : Triangle type {22,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-5 * x^-1 * y * z^-3 ] T90.118 : Triangle type {22,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-3 * x^2 * y^-3, z^3 * y^-1 * z^-1 * x * z^4 ] T90.119 : Triangle type {22,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-3)^2, z^2 * y^-1 * z^-2 * x * z^4 ] T90.120 : Triangle type {22,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1, z * y^-1 * z^-3 * x * z^4 ] T90.121 : Triangle type {22,22,99} Group order 198 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-4 * x * z^4, z^-6 * y * x * z^-4 ] T90.122 : Triangle type {24,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^-7 * z * y, y^4 * x^-1 * y * z^-1 * y * z^-1 ] T90.123 : Triangle type {24,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y * z^-1 * y * z^-1 * y * z^-3, x^-7 * z * y ] T90.124 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1, y^4 * z^-3 * y^7 ] T90.125 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T90.126 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.127 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * z * y^-2, z^-5 * x * z^-4 * x * y * z^-4 ] T90.128 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * y^-1 * x^7 * z^-1 * x * z^-1 * x * y^-3 * x^5 * z^-2 * x^5 ] T90.129 : Triangle type {27,63,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^6 * z^-4 * y * x^-6 * y * x^-1 * y^2 ] T90.130 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^4 * z^-1 * y * z^-5 * y * x^-1 * y^6 ] T90.131 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T90.132 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T90.133 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-7, z^-4 * x * z^-4 * x^2 * z^-4 ] T90.134 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^4 * x^-1 * z^2 * x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.135 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-7 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.136 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T90.137 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^9 * y^-6 * x^3 ] T90.138 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T90.139 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T90.140 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^10 * x^-7 * y^2 * x^-6 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.141 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T90.142 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T90.143 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^3 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.144 : Triangle type {31,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^18 * y^-2 * x^6 * z^-2 * x^5 ] T90.145 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * z^-3 * y^10 ] T90.146 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-5 * x * y^-1 * z^5 * y^-4 ] T90.147 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-3 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T90.148 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^-1 * z^8 * y^-2 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.149 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x^2 * y^-6 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.150 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^6 * z^-4 * y * x^-5 * y^4 ] T90.151 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^5 * z^-1, y^3 * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T90.152 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z^14 * x^-1 * z * x^-1 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T90.153 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-3 * y * x^-1 * y^6 * x^-3 * z^2 * x^-6 ] T90.154 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y * x^-1 * y^6 * x^-3 * z^2 * x^-5 ] T90.155 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, z^-9 * y^2 * z^-4 ] T90.156 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^-2 * y^6 * x^-4 * z * x^-3 ] T90.157 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^13 * y^-1 * x^9 * y^-1 * x^8 * y^-2 * x * y^-1 * x^3 ] T90.158 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^4 * z^-5 * y^6 ] T90.159 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^5 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.160 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^-11 * z * y^-9 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.161 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, z^-10 * y * z^-4 ] T90.162 : Triangle type {37,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-2 * y * x^-1 * y * x^-1 * z^4 * x^-3 * z^3 * x^-7 ] T90.163 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-2 * x^-1 * y * x^-1 * y * x^-1 * y^5 ] T90.164 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * z * y ] T90.165 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * y^-1 * x * y^-1 * x * y^-1 * z^-2, z * y^-3 * x * z^3 ] T90.166 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, x * z^-2 * x * z^-2 * x * z^-2 * y * z^-1 ] T90.167 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T90.168 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z * y^-3 * x^-1 * z^3 ] T90.169 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y^-1 * x * z^2, z^-1 * x^5 * z^-2 * x * z^-1 ] T90.170 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, z * x^-1 * z * x^-5 * z^2 * x^-2 * z^3 ] T90.171 : Triangle type {38,38,95} Group order 190 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-6 * x^2 * z^-4 * x * z^-1 * y * z^-1 ] T90.172 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T90.173 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^2 * z^-4)^2, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T90.174 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T90.175 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^14 * y^-5 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T90.176 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^12 * y^-2 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.177 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T90.178 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-6 ] T90.179 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T90.180 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^29 * x^-1 * z * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T90.181 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^5 * z^-2 * x^3 * y^-6 * x^3 ] T90.182 : Triangle type {46,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^11 * y^-4 * x^10 ] T90.183 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^26 * y^-4 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.184 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.185 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^9 * x^-6 * y * x^-1 * y^2 ] T90.186 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-3 * y^5 * x^-3 * z^2 * x^-4 ] T90.187 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T90.188 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-4 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T90.189 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T90.190 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^-9 * z^2 * y^-4 ] T90.191 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^17 * x^-1 * z^13 ] T90.192 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-11 * y^5 * z^-2 ] T90.193 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^23 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.194 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^-2 * y^6 * x^-2 * z^3 * x^-4 ] T90.195 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4, x^-2 * y^5 * x^-3 * z^2 * x^-3 ] T90.196 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T90.197 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T90.198 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^-3 * y^6 * x^-2 * z^3 * x^-5 ] T90.199 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-6 * x^5 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T90.200 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 ] T90.201 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^11 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.202 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^5 * z^-4 * y * x^-1 * y^5 ] T90.203 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^11 * y^-3 * x^-1 * z^13 ] T90.204 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T90.205 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-61 ] T90.206 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x^2 * z^-4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T90.207 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^7 * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T90.208 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^8 * x^-3 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T90.209 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^17 * y^-1 * x^7 * y^-2 * x^5 ] T90.210 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T90.211 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T90.212 : Triangle type {61,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^6 * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T90.213 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^7 * x^-1 * y * x^-1 * y * x^-3 * y^4 ] T90.214 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-2 * z * y^-1 * x * y^-4 * z * y^-2 ] T90.215 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, y^2 * x^-1 * y * x^-1 * y^3 * z^-1 ] T90.216 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * x * z^2 * y^-1, x^7 * y^-1 * z^-2 ] T90.217 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * y * x^-1 * z, z^-1 * y * z^-2 * y^3 * z^-4 ] T90.218 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3, x^8 * y^-2 ] T90.219 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-2 * z^3 * x^-1 * z^3 * x^-1 * z^2 * y^-1 * z^3 ] T90.220 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, x^-1 * y * z^-2 * y * z^-1 * y^5 * z^-1 * y^2 ] T90.221 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^5 * z^-1 * y * z^-1, x^-1 * z * x^-3 * z^4 ] T90.222 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * y * z^-2 * y^2 * x * z^-4 ] T90.223 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x * y^-1 * x * y^-1 * x * y^-3, z^-1 * x^5 * z^-2 * x * z^-1 ] T90.224 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3, x^6 * y^-4 ] T90.225 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^-2 * y^2 * x^-5 * z^2 * x^-2 * z * x^-1 ] T90.226 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^7 * z^-1 * x * z^-1 * x^5 * z^-1 * x * z^-1 * x^4 ] T90.227 : Triangle type {62,62,93} Group order 186 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^12 * y^-1 * z * y^-1 * z * x^-1 * z^3 * x^-3 * y^-1 * z^4 * x^-1 * z^6 ] T90.228 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T90.229 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T90.230 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^5 * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T90.231 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^12 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.232 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-17 * z * y^-1 * z * y^-8 * z^2 * y^-8 ] T90.233 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^32 * y^-1 * z^13 ] T90.234 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^7 * z^-3 * x^6 * y^-1 * x^3 ] T90.235 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^8, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T90.236 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-26 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T90.237 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T90.238 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T90.239 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-7 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T90.240 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^7 * z^-4 * x^8 ] T90.241 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^3 ] T90.242 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^12 * y^-5 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T90.243 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T90.244 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T90.245 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-10 * z * y^-1 * z * y^-5 * x * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T90.246 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-56 * x * z^-4 ] T90.247 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^6 * z^-3 * y^2 * x^-4 * y^5 ] T90.248 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-14 * z * x^-10 * y * x^-1 * y * x^-1 * y * x^-2 ] T90.249 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^8 * y^-6 * x^2 ] T90.250 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-7 * x * z^-1 * x * z^-4 * x^5 * z^-2 * y * z^-1 * y * z^-1 ] T90.251 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T90.252 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T90.253 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T90.254 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T90.255 : Triangle type {91,182,182} Group order 182 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^91, y * z^-1 ] T90.256 : Triangle type {92,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^3 * z^-1 * y * z^-1 * y * z^-1 * y^4 * x^-1 * y * x^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T90.257 : Triangle type {92,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^-1 * y * x^-1 * y^3 * x^-1 * y^5 * z^-1 * y^3 ] T90.258 : Triangle type {92,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3, x * y^-3 * x * y^-1 * x * y^-2 * z * y^-3 ] T90.259 : Triangle type {92,92,92} Group order 184 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x^3 * y^-4, z^-3 * x * z^-1 * x * z^-4 ] T90.260 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x^-2 * y^-1, y^71 * x^-1 * y^19, x * z^-1 ] T90.261 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^50 * x^-2 * y^9 ] T90.262 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-27 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y^3 ] T90.263 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^10 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y^3 ] T90.264 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-3 * y * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^12 * x^-1 * y * x^-1 * y * x^-1 * y ] T90.265 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-2 ] T90.266 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T90.267 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-3 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T90.268 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T90.269 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-3 * x^6 * y^-8 ] T90.270 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^-3 * y^5 * x^-8 ] T90.271 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^5 * z^-4 * y * x^-5 * y^3 ] T90.272 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T90.273 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T90.274 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^6 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^5 ] T90.275 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-10 * z^2 * y^-5 ] T90.276 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T90.277 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2, y^-4 * x^2 * y^-7 ] T90.278 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-2 * z * y^-1 * z * y^-16 ] T90.279 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T90.280 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x^-3 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T90.281 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T90.282 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T90.283 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^2 * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T90.284 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-3 * z * y^-3 * z * y^-1 * z * y^-8 * z^2 * y^-8 ] T90.285 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^3 * z^-3, y^9 * x^-6 * y * x^-1 * y^2 ] T90.286 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-4, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T90.287 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T90.288 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^8 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T90.289 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T90.290 : Triangle type {181,181,181} Group order 181 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-13 * z * y^-3 * z * y^-1 * z * y^-5 * x * y^-12 ] Genus 91 T91.1 : Triangle type {2,3,21} Group order 1512 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-6 * x * z^2 * y^2 * x * z^3 * y^-1 * z^-1, y * z^-1 * x * z * y * x * z^2 * y * x * z^2 * y * x * y^-1 * z^-2 * x * z, z^2 * y * x * z^4 * y * x * z^2 * y^2 * x * y^-1 * z^-1 * x * z^2 ] T91.2 : Triangle type {2,3,30} Group order 1350 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^17 * y * z^-5 * x * z^2 * y^-1 * z^-6 * x * z^4 ] T91.3 : Triangle type {2,3,36} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1, z^-8 * x * z^2 * y^-1 * x * z^5 * y^-1 * z^-1 ] T91.4 : Triangle type {2,3,36} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^5 * y^-1 * z^-6, z * y * x * z * y * z^-1 * x * z^2 * y * x * z * y * x * z * y^-1 * z^-2 * x ] T91.5 : Triangle type {2,4,5} Group order 3600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^2 * z^-2 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 ] T91.6 : Triangle type {2,4,8} Group order 1440 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2)^4, x * z * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T91.7 : Triangle type {2,4,8} Group order 1440 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, (y * z^-2)^4 ] T91.8 : Triangle type {2,4,8} Group order 1440 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 * y * x * y^-1 * z^-2 * y * x * y^-1 * z^-1 * x ] T91.9 : Triangle type {2,4,8} Group order 1440 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y^-1 * z * y * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 * y * x * y^-1 * z^-2 * y * x * y^-1 * z^-1 * y ] T91.10 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1 ] T91.11 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, (z^-2 * y * z^-1)^3 ] T91.12 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z^-2 * y * x * z * y^-2 * z^-2 * y * z^-2 * y, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2, x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T91.13 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, y^-1 * z * y * z^-2 * y * x * y^-1 * z^-1 * x * y^-1 * z^3 ] T91.14 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^-1 * x * z^3 * y * x * y * z^-1 * x * z^2 * y^-1 * z^-2, y * z^-1 * y * z^-1 * y * z^-1 * x * y^2 * z^-1 * y * z^-1 * y * z^-2, y * z^-3 * y * z^-1 * x * y^-1 * z^2 * y^-1 * z^-1 * y * z^-2 ] T91.15 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^3 * y * x * y * z^-1 * x * z^2 * y^-1 * z^-2, z^-2 * y * z^-1 * y * z^-1 * x * y^-1 * z^2 * y^-1 * z * y^-1 * z^-2 ] T91.16 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5 ] T91.17 : Triangle type {2,4,8} Group order 1440 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y^-1 * z^2 * y^-1 * z * y^-1 * z^-2 * x * z * y^-1 * z ] T91.18 : Triangle type {2,4,10} Group order 1200 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z^10, (y * z^-1)^6, y * z^-1 * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T91.19 : Triangle type {2,4,12} Group order 1080 Chiral action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, y * z^-1 * y * x * y^-1 * z^-2 * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T91.20 : Triangle type {2,4,12} Group order 1080 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, x * z * y^-1 * z * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * y * z^-1 * y ] T91.21 : Triangle type {2,4,24} Group order 864 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z * y^-2 * z^-4 * y, z^-1 * x * z * y * z^-2 * x * z * y * z^-2 * x * z^2 * y * z^-3 * x * z * y^-1 * z^-1 * x * z^3 * y^-1 * z^-2 ] T91.22 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y * z^-1)^6, x * z^2 * y * x * z^3 * y * z^-1 * x * z^3 * y * x * z^7 * y^-1 * z^-4 ] T91.23 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y * z^-1)^6, z^-3 * x * z^2 * y * z^-8 * x * z^4 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 ] T91.24 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T91.25 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-2 * x * z^3 * y^-1 * x * z * y^-1 * z^-4 ] T91.26 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, (y * z^-1)^6 ] T91.27 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, x * z * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y ] T91.28 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, (y * z^-1)^6 ] T91.29 : Triangle type {2,4,24} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, z^2 * y * z^-1 * x * z^2 * y^-1 * z^3 * y^-1 * z ] T91.30 : Triangle type {2,4,40} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2, x * z^6 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-9 ] T91.31 : Triangle type {2,4,40} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-11 * x * z * y * z^-1 * x * z^12 * y * x * z * y * x * z^7 * y^-1 * z^-3 ] T91.32 : Triangle type {2,4,40} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, x * y^-1 * z * y * z^-6 * y * x * z * x * z^4 * y^-1 * z^-1 * y * z^-2 ] T91.33 : Triangle type {2,4,40} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, x * z^2 * y * z^-6 * y * x * z * x * z^4 * y^-1 * z^-1 * y * z^-1 * y ] T91.34 : Triangle type {2,4,44} Group order 792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y * z^-1)^6, x * z * y * z^-8 * x * y^-1 * z^-6 * x * z^2 * y^-1 * z^-2 ] T91.35 : Triangle type {2,4,76} Group order 760 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-17 * x * z^6 * y * z^-1 * x * y^-1 * z^-1 * x * z^7 * y^-1 * z^-3 ] T91.36 : Triangle type {2,4,184} Group order 736 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-184 ] T91.37 : Triangle type {2,4,184} Group order 736 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-74 * x * z^8 * y * x * z * y^-1 * z^-7 ] T91.38 : Triangle type {2,4,364} Group order 728 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-43 * x * y^-1 * z^-138 ] T91.39 : Triangle type {2,5,5} Group order 1800 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, z^2 * y^2 * z^-1 * x * z * y^2 * x * z * y^-2 * z^-1 * x ] T91.40 : Triangle type {2,6,8} Group order 864 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, z^2 * y^-1 * z^2 * y * z^-2 * y * z^-2 * x * z * y^-1 * z^-1 * x ] T91.41 : Triangle type {2,6,8} Group order 864 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^8, z * y * x * z * y^2 * x * y^-1 * z^2, (z^-1 * y^2 * z^-1)^3 ] T91.42 : Triangle type {2,6,12} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * z^-1 * x * z * y^-2 * z * y^-1 * z^-2 * y ] T91.43 : Triangle type {2,6,12} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^-1 * z^-4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T91.44 : Triangle type {2,6,18} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-3 * x * y^-2 * z^-5, z^-1 * y * z^-2 * x * z^2 * y^-1 * z^2 * y^-1 * z^-2 ] T91.45 : Triangle type {2,6,33} Group order 594 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-11 * x * z^2 * y * z^-1 * x * z^6 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-3 * x * y^-1 * z^-2 ] T91.46 : Triangle type {2,6,93} Group order 558 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^76 * y * x * y * z^-7 * x * z^2 * y^-1 * z^-3 * x * z^2 ] T91.47 : Triangle type {2,6,273} Group order 546 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^74 * y * x * y * z^-6 * x * z * y^-1 * z^-3 * x * z^4 ] T91.48 : Triangle type {2,8,8} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, x * y^-1 * z^2 * y^2 * x * y^-1 * z^-2 ] T91.49 : Triangle type {2,8,8} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^8, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-1 * z * y^-4 * z^-1 * x * z^3, x * z^2 * y^-3 * z^-1 * y^2 * z^-2 ] T91.50 : Triangle type {2,8,8} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y * x * y^-1 * z^2 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T91.51 : Triangle type {2,8,8} Group order 720 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y * x * z * y^-1 * z * y^2 * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z ] T91.52 : Triangle type {2,8,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, z^8, y * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, (z^-1 * y)^5 ] T91.53 : Triangle type {2,8,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-2, (y^3 * z^-1)^3, z^-1 * x * y^-1 * z * y^3 * x * y^-2 * z^-2 ] T91.54 : Triangle type {2,8,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, z^8, y * x * z * y^4 * z^-1 * x * y^-2 * z^-1 ] T91.55 : Triangle type {2,8,8} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^8, z^8, x * y^-1 * z * y^-2 * z^-2 * y * z^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T91.56 : Triangle type {2,8,16} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * y^-3 * z^-5, z^-2 * x * z * y^-2 * z^3 * y^-1 * z^-1 ] T91.57 : Triangle type {2,8,16} Group order 576 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x, z * y * z^-2 * x * y^-1 * z^-1 * x * z^2 ] T91.58 : Triangle type {2,8,16} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z ] T91.59 : Triangle type {2,8,16} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, (y * z^-1)^6 ] T91.60 : Triangle type {2,10,10} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^10, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T91.61 : Triangle type {2,12,12} Group order 540 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z^-1 * x * z * y * x * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T91.62 : Triangle type {2,12,12} Group order 540 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y^-1 * z * y^-3 * z^-2 * x * y^-1, z * y * x * z * y^-1 * z * y^2 * z^-1 * x * z * y^-2 * z^-1 * x ] T91.63 : Triangle type {2,12,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, y^12 ] T91.64 : Triangle type {2,12,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, y^12 ] T91.65 : Triangle type {2,15,30} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-9 * z * x * y^-5 ] T91.66 : Triangle type {2,16,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-3 * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y^3 * x * y^-1, z^-10 * x * z^7 * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-3 ] T91.67 : Triangle type {2,16,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-2 * x * z^10 * y * z^-2 * x * y * x * z^9 * y^-1 * z^-2 ] T91.68 : Triangle type {2,16,208} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, x * z^7 * y^-1 * x * z^4 * y^-1 * z^-13 ] T91.69 : Triangle type {2,16,208} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, z^-2 * x * z^5 * y * x * z^3 * y^-1 * z^-14 ] T91.70 : Triangle type {2,18,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^-1 * z * y^-4 * z * y^-1 * z * y^-1 * z * y^-3 * z^4 ] T91.71 : Triangle type {2,18,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y^-3 * z^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T91.72 : Triangle type {2,24,24} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, x * y^-4 * z^-3 * y, y^-2 * z^2 * y^-3 * z^2 * y^-11 * z * y^-2 * z ] T91.73 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T91.74 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, z^-1 * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T91.75 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * y^6 * z^-5 ] T91.76 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z^-1 * y^6 * z^-5 ] T91.77 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-1 * x * z * y^3 * x * y^-1 * z^-2 ] T91.78 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T91.79 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^2 * z^-2 * y * z^-3 * y * z^-1 * y^4 * z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T91.80 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T91.81 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y^9 * z^-2 * y^2 * z^-2 * y ] T91.82 : Triangle type {2,24,24} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * y^5 * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-6 ] T91.83 : Triangle type {2,30,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^8 * y^-2 * z^5 ] T91.84 : Triangle type {2,40,40} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y^18 * z^-4 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y * z^-2 ] T91.85 : Triangle type {2,40,40} Group order 400 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-13 * z * y^-1 * z^2 * y^-1 ] T91.86 : Triangle type {2,40,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-2 * z^3 * y * x * y^-3 * z^-1 * x * y^-1 * z^-3 * x ] T91.87 : Triangle type {2,40,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-6 * z^4 * y^-4 * z^4 ] T91.88 : Triangle type {2,40,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-2 * z^3 * y * x * y^-3 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T91.89 : Triangle type {2,40,40} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y * z^-2 * y^2 * z^-1 * y^13 * z^-3 * y * z^-15 * y * z^-1 ] T91.90 : Triangle type {2,44,44} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-5 * y * z^-1 * y^4 * z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y ] T91.91 : Triangle type {2,49,49} Group order 392 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-2 * y, y^-3 * z^28 * y^-1 * z * y^-1 * z^2 * y^-13 ] T91.92 : Triangle type {2,54,189} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-14 * z^4 * y^-6 * z^3 ] T91.93 : Triangle type {2,63,126} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^-28 * y^2 * z^-1 * y^10 * z^-4 * y * z^-17 ] T91.94 : Triangle type {2,76,76} Group order 380 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y * z^-1 * y^16 * z^-4 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y * z^-1 ] T91.95 : Triangle type {2,183,366} Group order 366 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^124 * y^-58 ] T91.96 : Triangle type {2,184,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-57 * y^32 * z^-1 * y ] T91.97 : Triangle type {2,184,184} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^59 * z^-124 * y ] T91.98 : Triangle type {2,364,364} Group order 364 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^58 * z^-123 * y ] T91.99 : Triangle type {3,3,15} Group order 675 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^5 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x * z^4 ] T91.100 : Triangle type {3,3,18} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * z^2 * y * z^-1, y * x^-1 * z^2 * y^-1 * x * z * y * x * z ] T91.101 : Triangle type {3,3,18} Group order 648 Chiral action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 * x ] T91.102 : Triangle type {3,3,18} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x, y^-1 * z^-4 * x * z^4 ] T91.103 : Triangle type {3,3,18} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * y * x * z * y * x * z^-1 * x^-1 * y^-1 * z^-1 * x ] T91.104 : Triangle type {3,3,18} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, x * z * x^-1 * z * x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * z * y ] T91.105 : Triangle type {3,3,63} Group order 567 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^7 * y^-1 * x^-1 * z * y * z^-2 * x * z^3 ] T91.106 : Triangle type {3,3,63} Group order 567 Chiral action Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1, y^-1 * z^-2 * x * y^-1 * x * z^2 * y^-1 * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1, z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 ] T91.107 : Triangle type {3,3,183} Group order 549 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^5 * y^-1 * z^-3 * x^-1 * z^2 * y * z^-1 * x * z^3 ] T91.108 : Triangle type {3,4,6} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y, x * z * y * x^-1 * y^-1 * z * x^-1 * z * y * x * z^-1 * y ] T91.109 : Triangle type {3,4,6} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^6, (y * z^-1)^4 ] T91.110 : Triangle type {3,4,24} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y * z^-2 * x^-1 * z^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T91.111 : Triangle type {3,4,24} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, x^-1 * y * x * z^2 * y^-1 * z^-2 * x * y^-1 * x * z * y * z^-1 ] T91.112 : Triangle type {3,6,7} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y^-1 * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 * x^-1 ] T91.113 : Triangle type {3,6,10} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y^-1 ] T91.114 : Triangle type {3,6,10} Group order 450 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^10 ] T91.115 : Triangle type {3,6,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * x * y^-1 * x * z * y^-1 * z^-1, y * z^-1 * y * z^-1 * x^-1 * z^4 ] T91.116 : Triangle type {3,6,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y * x^-1 * y^3 * x * y^-1 ] T91.117 : Triangle type {3,6,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T91.118 : Triangle type {3,6,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * z^-2 * x * z^-1 * x * z^2 * y^-1 ] T91.119 : Triangle type {3,6,42} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^2 * x^-1 * y^-1 * x * z * y^-2, z^-1 * x * y^-2 * x * z * y * z^-1 ] T91.120 : Triangle type {3,6,42} Group order 378 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, x * y^-2 * z^-1 * x * z^3 * y * z^-3 ] T91.121 : Triangle type {3,6,122} Group order 366 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, x * y^-2 * z^-1 * x * z^4 * y * z^-2 ] T91.122 : Triangle type {3,8,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y, y * z^-1 * y * x^-1 * y^-1 * z^2, (x * z * y^2)^2 ] T91.123 : Triangle type {3,8,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^8, z^-1 * y^2 * z^-1 * y * z^-2 * x^-1 * z^-3 * y^2 ] T91.124 : Triangle type {3,8,8} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-1 * y)^2, y^8, y^-1 * z^-2 * y * x * z * y * x ] T91.125 : Triangle type {3,10,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-1 * z^-1 * y * x * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T91.126 : Triangle type {3,12,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^3 * x^-1 * z^3, x^-1 * z * y^-2 * x * y^-1 * z^2 ] T91.127 : Triangle type {3,12,12} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, x^-1 * z * y^-2 * x * y^-1 * z^2, z^-1 * y^4 * z^-3 ] T91.128 : Triangle type {3,12,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T91.129 : Triangle type {3,12,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * y^2 * z^-3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-1 * x * z^2 * y^-1 * x * z^2 * y^-1 * z^-1 ] T91.130 : Triangle type {3,12,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-3 * x^-1 * z^2 * y^-1, y * z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T91.131 : Triangle type {3,12,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^3 * z^-1 * y^5 * x * z^-1 * y^2 ] T91.132 : Triangle type {3,12,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^-1 * z * y^-1 * z * x^-1 * y^-2 * x * y^-1 * z * y^-1 * z ] T91.133 : Triangle type {3,13,13} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^-1 * y^-3, y^3 * z^-2 * y^5 * z^-3 ] T91.134 : Triangle type {3,13,13} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z * y^-2, y^2 * z^-3 * y * z^-2 * y^2 * z^-1 * y^2 ] T91.135 : Triangle type {3,32,96} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-14 * y * z^-2 * y^12 * z^-2 ] T91.136 : Triangle type {3,33,33} Group order 297 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-13 * y * z^-3 * y^8 * z^-2 * y^5 ] T91.137 : Triangle type {3,92,276} Group order 276 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-76 * z * y^-10 * z * y^-3 * z ] T91.138 : Triangle type {3,93,93} Group order 279 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^5 * z^-1 * y^10 * z^-1 * y^75 * z^-1 ] T91.139 : Triangle type {3,273,273} Group order 273 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^4 * z^-1 * y^10 * z^-1 * y^75 ] T91.140 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, (x * y^-1)^4, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T91.141 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, (x * y^-1)^4 ] T91.142 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * y^-1)^4, (x * z^-1)^4, y^-2 * z^-1 * x^-2 * z * y^-1 * z * x^-1, z^-1 * x^-1 * z * y * x^-1 * y * x * z * y^-1 ] T91.143 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * y^-1)^4, z^-1 * x^-1 * z * y * x * z^2 * y ] T91.144 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^2 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x * z^-1 * x ] T91.145 : Triangle type {4,4,4} Group order 720 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y^-1 * z ] T91.146 : Triangle type {4,4,4} Group order 720 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (y^-1 * x)^3, (x * z * y^-1 * z^-1)^2, z^-1 * y * x * z^-1 * x^2 * z * x^-1 * y^-1 * z^-1 ] T91.147 : Triangle type {4,4,4} Group order 720 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z, (z^-1 * x^-1 * y^-1)^3, (y^-1 * x)^5 ] T91.148 : Triangle type {4,4,4} Group order 720 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * x^-1 * y^-1)^2, (y * z^-1)^4, (z^-1 * x^-1 * y)^3, (z * x^-1 * y^-1)^3, z^-1 * y * x^-1 * y * x^2 * z * x^-1 * z * y^-1 ] T91.149 : Triangle type {4,4,4} Group order 720 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * x^-1 * y^-1)^2, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x ] T91.150 : Triangle type {4,4,5} Group order 600 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-2)^2, (z * x^-1 * y^-1)^3, y^-1 * x * z * x^-1 * y^-1 * x * y^-1 * z^-1 * y * x ] T91.151 : Triangle type {4,4,6} Group order 540 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y^-1 * z * y * x * z^-1 * y * x^-2 * y^-1 * z * y * x^-1 * y * x^-1 ] T91.152 : Triangle type {4,4,6} Group order 540 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, z^6, y^2 * x * z * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 ] T91.153 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T91.154 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * z * y^-1 * x * y^-1 * z^-2, x^-1 * z^2 * y^-1 * x * z * y^-1 * z^-1 ] T91.155 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y * x^2 * z * y^-1 * z, (x * y^-1)^4, y^-1 * z * y^-2 * x * z * y * x^-1 ] T91.156 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * z * x^-1 * z, z^-1 * x * y^-1 * x * z^2 * y^-1 * z^-3 * x * z^2 * y * z^-1 ] T91.157 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, z^-1 * x^-1 * y * x^2 * z * y * x, z^12 ] T91.158 : Triangle type {4,4,12} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-2 * x^2 * z^2 * y^-1, (x * y^-1)^4 ] T91.159 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1 ] T91.160 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z^2 * x^-1 * y * x^2 * z^2 * x^-1 * z ] T91.161 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T91.162 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T91.163 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T91.164 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T91.165 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T91.166 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-3 * x^-1 * z^2 * y^-1 ] T91.167 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (z^-1 * x^-1 * y^-1)^3 ] T91.168 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * x^-1 * y^-1 ] T91.169 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, z * y * z^-5 * x * z^5 ] T91.170 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^3 * x^-1 * z^2 * y^-1 ] T91.171 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x, z^6 * y^-1 * x^-1 * z^5 ] T91.172 : Triangle type {4,4,12} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (z * x^-1 * y^-1)^3 ] T91.173 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * x * z^-1 * x^-1 * y^-1 * z^-1, z * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * x * z^5 ] T91.174 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y * x^-1 * z * y^2 * z^-1 * x^-1 * z * y^-1, y * z^-1 * x^-1 * z^2 * y * x^-1 * z^5 ] T91.175 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^-3, z^-5 * x^-1 * z^4 * y^-1 ] T91.176 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1, y * z^-1 * y * x^2 * z^3 ] T91.177 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, x * z^-1 * x^-2 * z * y^-1 * z^-1 ] T91.178 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T91.179 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, x^-1 * z * y * z^-1 * y * x * z * y * z^-1 * y, z^4 * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x^-1 ] T91.180 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-5 * x * z^3 * y^-1 * z^-1 * x * y * x^-1 * z^8 * y ] T91.181 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^8 * y * x^-1 * y * x^-1 * z^5 * y * x * z^4 ] T91.182 : Triangle type {4,4,20} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, y^-1 * z^-1 * y * x^2 * y^-1 * z * y^-1 ] T91.183 : Triangle type {4,4,20} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^4 * y * x^-1 * z^5 ] T91.184 : Triangle type {4,4,20} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-5 * x^-1 * z^4 * y^-1 ] T91.185 : Triangle type {4,4,20} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-1 * z^-1 * x * z^-1 * x * z^3 * y^-1 * z ] T91.186 : Triangle type {4,4,22} Group order 396 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x, z^5 * y * x * y^-1 * x * y^-1 * z^-1 * x^-1 * z^2 ] T91.187 : Triangle type {4,4,38} Group order 380 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^4 * y^-1 * z^-4 * x * z^2 * y * x^-1 * z^4 * y * z^-2 * x^-1 ] T91.188 : Triangle type {4,4,92} Group order 368 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^30 * y * z^-4 * x * z^2 * y^-1 * z^-8 * x ] T91.189 : Triangle type {4,4,92} Group order 368 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^30 * y * z^-4 * x * z^2 * y^-1 * z^-8 * x^-1 ] T91.190 : Triangle type {4,4,92} Group order 368 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-78 * x * y * z^-13 ] T91.191 : Triangle type {4,4,182} Group order 364 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^77 * y^-1 * x * z^13 ] T91.192 : Triangle type {4,6,6} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, z^6, z * x^-1 * y * x^-1 * z^2 * y^-1, y * z^-1 * y * x^-1 * y^-1 * z^2 ] T91.193 : Triangle type {4,6,6} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^6, z^-2 * x^-1 * y^-1 * x * z^-1 * x * z^-1 ] T91.194 : Triangle type {4,6,6} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * x * z^-1 * x * z * y^-1, (z^-1 * y)^3, y^-1 * z^-1 * y^2 * x * y^-1 * z * x^-1 ] T91.195 : Triangle type {4,6,6} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, y * x * z * y * x^2 * z * x^-1 * y^-1 * z^-1 ] T91.196 : Triangle type {4,6,6} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^6, y * x * z^-1 * x^-1 * y^-1 * x * z, y^2 * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1 ] T91.197 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y^2 * x^-2 * y^-1 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T91.198 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^6, z * y * x^-1 * z * y * x * z * y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T91.199 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z, (y * x^-1 * z)^3 ] T91.200 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y^2 * x^-2 * y^-1 * z * x^-1, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (x^-1 * z^2 * y)^2 ] T91.201 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^6, y * z^-1 * x^-2 * z^2 * x^-1, y * x * z^-1 * x^-1 * y^-1 * x * z ] T91.202 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^6, y * z^-1 * x^-2 * z^2 * x^-1, z * y * x^-1 * y^-1 * x * y^-2 * x ] T91.203 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, y * z^-1 * x^-2 * z^2 * x^-1 ] T91.204 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T91.205 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^6, y^-1 * z^-2 * y * x^-1 * z * x^-1 * z ] T91.206 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^6, y^-1 * z^-2 * y * x^-1 * z * x^-1 * z ] T91.207 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^6, y * z^-1 * x^-2 * z^2 * x^-1 ] T91.208 : Triangle type {4,6,6} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^6, y * z^-1 * x^-2 * z^2 * x^-1 ] T91.209 : Triangle type {4,6,12} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T91.210 : Triangle type {4,6,12} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T91.211 : Triangle type {4,6,12} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T91.212 : Triangle type {4,6,21} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-3 ] T91.213 : Triangle type {4,6,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-2 * x^-1 * z^5 * y^-1 * z^-4 ] T91.214 : Triangle type {4,6,156} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^9 * y * z^-1 * x^-1 * z^2 * y * z^-4 * x^-1 * z^8 ] T91.215 : Triangle type {4,7,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-7, z^3 * y^-1 * x * z^3, x^-1 * z * y^2 * x * z * y * z^-1 ] T91.216 : Triangle type {4,7,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (z^-1 * x)^3, z * y * x^-1 * y^-1 * x * y^-2 * x ] T91.217 : Triangle type {4,7,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1 * y)^2, (y * z^-2)^2, z * y^2 * x^-1 * y^-1 * z^-1 * x ] T91.218 : Triangle type {4,8,8} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z^-1 * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x * z ] T91.219 : Triangle type {4,8,8} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z^-1 * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x^-1 * z ] T91.220 : Triangle type {4,8,8} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * y^-2 * x * y^-1 * z^-1, y^-1 * z^2 * x^-1 * z^2 * y^-1 ] T91.221 : Triangle type {4,8,8} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1, y * z^-2 * x^-1 * y^-2 * z ] T91.222 : Triangle type {4,8,8} Group order 360 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x^-1 * y^-2 * z ] T91.223 : Triangle type {4,8,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4, x^-1 * z * y * z^-1 * y * x * z * y * z^-1 * y ] T91.224 : Triangle type {4,8,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^2 * y^2 * x^-1 * z^2 * y^-1 * z, y * z^-3 * x^-1 * z^4, x^-1 * z * y * z^-1 * y * x * y^-1 * z^-2 * y ] T91.225 : Triangle type {4,8,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T91.226 : Triangle type {4,8,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y^2 * x * y^-1 * x * z * y * z^-1 ] T91.227 : Triangle type {4,9,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y^-1 * z * y^-1 * z^-1 * x^-1 * z * y^-1 * z^2, y^-9 ] T91.228 : Triangle type {4,9,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, y^-9 ] T91.229 : Triangle type {4,9,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-2 * y ] T91.230 : Triangle type {4,9,12} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, y^-9 ] T91.231 : Triangle type {4,10,140} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1, y^10 ] T91.232 : Triangle type {4,12,15} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T91.233 : Triangle type {4,12,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z * x^-1 * y * x^2 * z^3 ] T91.234 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3 ] T91.235 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x * y^-1 * x * y^-1 * x * y^-1 * z * y ] T91.236 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T91.237 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T91.238 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^4 * x^-1 * y^-1 * z^-3 ] T91.239 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^-2 * z * x^-1 * y^-3, z^-4 * x^-1 * z^3 * y^-1 ] T91.240 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^4 * x^-1 * z * y * z^-2 ] T91.241 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^4 * x * z^-1 * x * z^-1 ] T91.242 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^-1 * z^3 * y^-4 * x * y^-2 * z^2, y^-12 ] T91.243 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-1 * z^3 * y^-3 * z * x^-1 * z * y^-3, y^-12 ] T91.244 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-4 * x * y^-2 * z^2 * y^-1, y * x^-1 * z * y * z^-3 * x * z^4 * y * x * z ] T91.245 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^3 * y^-3 * z * y^-2 * z^2 * y^-1, y * x^-1 * z * y * z^-3 * x * z^4 * y * x * z ] T91.246 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-4 * x * y^-2 * z^2 * y^-1, z^-6 * y^2 * x^-1 * z^3 * y^-1 * z^-2 ] T91.247 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^4 * y^-1 * z^-3 * x * z^4 ] T91.248 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-6 * x^-1 * z^4 * y * x * z * y * z^-3 * x * y^-1 * z^-7 ] T91.249 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-4 * x * y^-2 * z^2 * y^-1, z^-6 * y^2 * x^-1 * z^4 * y * z^-1 ] T91.250 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-2 * z * x^-1 * y^-3, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z^2 * y, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T91.251 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-2 * z * x^-1 * y^-3, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, x^-1 * z^2 * y * x * z * y^-1 * z^-1, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T91.252 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, y^4 * x * z^-1 * x * z^-1, z^-5 * x^-1 * z * y^-1 * z^-5 ] T91.253 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-12, z^4 * y * z^-1 * x^-1 * y * x^-1 * y^-3 * z^-3 * x^-1 * z ] T91.254 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-12, x^-1 * z^3 * y * x^-1 * z * y * x^-1 * y * x * y^-3 * z^-4 ] T91.255 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^6 * x * y^-2 * z^-1 * x * y^-2 * z^-1, z^5 * y * x^-1 * y * x^-1 * z^5 ] T91.256 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-10 * x^-1 * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * y^-1 * z^-7 ] T91.257 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-12, z^4 * y * z^-1 * x^-1 * y * x^-1 * y^-3 * z^-3 * x * z ] T91.258 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1, z^-2 * y^3 * z^-2 * y ] T91.259 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, z * y^2 * x^-1 * z * y^-1 * z, y^-2 * z * y * x^-1 * y^-2 * z^2 ] T91.260 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y^2 * z^-1 * x^-1 * z * y^-1 * z^-1 ] T91.261 : Triangle type {4,12,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T91.262 : Triangle type {4,12,69} Group order 276 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^11 * y * x * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x ] T91.263 : Triangle type {4,14,28} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, (y^-2 * z * y^-1 * z^3)^2 ] T91.264 : Triangle type {4,16,16} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y^-1 * z * y^-1, y^4 * x^-1 * z^2 * y^-1 * z, z^-1 * y^3 * x^-1 * y^2 * z^-2 ] T91.265 : Triangle type {4,16,16} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y * x^-1 * y^-1 * z^2, z^-2 * y^3 * z^-1 * y * z^-1 ] T91.266 : Triangle type {4,16,16} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T91.267 : Triangle type {4,16,16} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T91.268 : Triangle type {4,20,130} Group order 260 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, y * z^-3 * y^3 * z^-3, y * x^-1 * z^3 * y^-1 * z^-3 * x^-1 * z^5 ] T91.269 : Triangle type {4,26,52} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * x * z * y^-1 * z^3 ] T91.270 : Triangle type {4,36,126} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * y^2 * z^-3 ] T91.271 : Triangle type {4,42,84} Group order 252 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^2 * z^-1 * y^3 * x^-1 * z^-1 * y^2 * z^-7 * y^2 * z^-1 ] T91.272 : Triangle type {4,62,124} Group order 248 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-32 * z^3 * y^-1 * z * y^-1 * z^2 * y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T91.273 : Triangle type {4,122,244} Group order 244 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-34 * z * y^-1 * z * y^-2 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T91.274 : Triangle type {6,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6, y^-1 * z^-1 * y * x^2 * z^-1 * y * x ] T91.275 : Triangle type {6,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6, (x * y^-2 * x)^2, y^-1 * z^-1 * y * x^2 * z * x^-1 * y^-1 ] T91.276 : Triangle type {6,6,6} Group order 360 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, z^6, (x * y^-2 * x)^2, y^-1 * z^-1 * y * x^2 * z * y * x ] T91.277 : Triangle type {6,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, y * x^-3 * z * x^-2, (x * z^2 * y^-1)^2 ] T91.278 : Triangle type {6,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-2 * x^-2 * z * x^-1 * y^-1 ] T91.279 : Triangle type {6,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T91.280 : Triangle type {6,6,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-2 * x^-2 * z * x^-1 * y ] T91.281 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y, z^-4 * x^-1 * z^3 * y^-1 ] T91.282 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T91.283 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z^-1 * y, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T91.284 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, (z^-1 * y)^3, y * x * y^-2 * x * y^-2 * z^-1 ] T91.285 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T91.286 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, x^-1 * z * y * x^-1 * z * x^-1 * z, z * y^-2 * x^2 * y^-1 * z * y^-1 ] T91.287 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T91.288 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-1 * x * y^-1 * x * z^2 ] T91.289 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y, z^-3 * x^-1 * z^2 * y^-1 ] T91.290 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^3 * x^-1 * z^2 * y^-1, y^8, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (x^-1 * z^2 * y)^2 ] T91.291 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, x * z^4 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T91.292 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, x^-1 * z^4 * y * x^-1 * z * y * x^-1 * y * x * z * y * z^-2 ] T91.293 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, (y * z^-2)^2, y^8, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (x^-1 * z^2 * y)^2 ] T91.294 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T91.295 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, y^8, (x * z^-1 * y^2)^2, y * x^-1 * z * y * x^-1 * z^3 ] T91.296 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, x^-1 * y * x^-2 * y^-2 * z, y * x^-1 * z * y * x^-1 * z^3 ] T91.297 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z^4 * y * x^-1 * z * y * x^-1 * y * x^-1 * y^-1 * z^-3 * x ] T91.298 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^4 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x ] T91.299 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T91.300 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, y^-1 * x * y^-1 * x * z^2 ] T91.301 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, x^-1 * z * x^-2 * y^-1 * z^-2, y^8 ] T91.302 : Triangle type {6,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^-2 * y^-1 * z * x^-1, z * y * x^-2 * y * x^-1 * y^-1, z^2 * y * x^-1 * z * y^-2 ] T91.303 : Triangle type {6,10,15} Group order 270 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2, z^-1 * x * y^-1 * x^2 * y^-1 * z^-1 * x, z^-1 * x * z^-1 * x^-2 * z * x^-1 * y^-1 * x ] T91.304 : Triangle type {6,12,28} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * y^-2, (z^-1 * y)^3, y * x^-3 * z * x^-2 ] T91.305 : Triangle type {6,18,117} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^-2 * x * y^-1 * z^-1 * x * z^7 * y * z^-1 ] T91.306 : Triangle type {6,18,117} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^-2 * x * y^-1 * z^-4 * x^-1 * z * y * z^-4 ] T91.307 : Triangle type {6,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y * x^-3 * z * x^-2, y^2 * x^-2 * y * z^-2 ] T91.308 : Triangle type {6,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, y * z^-1 * y^5 * z^-1 * y * z^-1 ] T91.309 : Triangle type {6,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y * z^-1 * y ] T91.310 : Triangle type {6,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2, y * x^-3 * z * x^-2 ] T91.311 : Triangle type {6,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, y * z^-2 * x^-1 * y^-2 * z, z^-1 * y^4 * z^-3 ] T91.312 : Triangle type {6,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T91.313 : Triangle type {6,26,39} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z^4 * y^-1 * z^3 * y^-1 * z^2 ] T91.314 : Triangle type {6,74,111} Group order 222 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T91.315 : Triangle type {8,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z * y^-1, x^-1 * z * y^-1 * x * y^-1 * z, y^3 * x^-1 * z^3 ] T91.316 : Triangle type {8,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3 ] T91.317 : Triangle type {8,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3, z^-1 * y * x^-2 * y * x^-1 * y ] T91.318 : Triangle type {8,8,8} Group order 288 Chiral action Defining relators: [ x * y * z, y^-1 * z * y^-1 * x * z * x^-1, z^-1 * x^-3 * y * z^-2, z * x^-3 * y^-3 ] T91.319 : Triangle type {8,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T91.320 : Triangle type {8,8,8} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 ] T91.321 : Triangle type {8,12,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x * z * x^-2 * y^-1 * z^-2, x * z^-2 * x^-1 * z * x^-1 * y^-1, x^8 ] T91.322 : Triangle type {8,12,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x * z * x^-2 * y^-1 * z^-2, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T91.323 : Triangle type {8,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, y * z^-3 * x^-1 * z * y^-1 * z^-3 * x * z^5 ] T91.324 : Triangle type {8,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-4 * x^-1 ] T91.325 : Triangle type {8,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z * y * z^-4 * x^-1 * z^8 ] T91.326 : Triangle type {8,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z * y * x^-1 * z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-3 * x * z^2 ] T91.327 : Triangle type {8,27,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-5 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T91.328 : Triangle type {8,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^4 * y^-5 * z * y^-2 * z ] T91.329 : Triangle type {8,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, z^-3 * y * z^-1 * y * z^-1 * y^3 * z^-1 * y^3 ] T91.330 : Triangle type {8,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^19 * y^-6 * z * y^-1 ] T91.331 : Triangle type {8,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^6 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^11 * z^-1 ] T91.332 : Triangle type {8,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, y^-1 * z * y^-5 * z * y^-1 ] T91.333 : Triangle type {8,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, z^2 * y^-3 * z^4 ] T91.334 : Triangle type {8,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-2 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T91.335 : Triangle type {8,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^3 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^4 ] T91.336 : Triangle type {8,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T91.337 : Triangle type {9,24,72} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-9 * z * y^-4 * z^2 * y^-5 * z^3 ] T91.338 : Triangle type {9,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T91.339 : Triangle type {9,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-3 * y^2 * z^-3, x^-9 ] T91.340 : Triangle type {9,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y * z^-1 * y^3 * z^-1 * y * z^-1, x^-9 ] T91.341 : Triangle type {9,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3, x^-9 ] T91.342 : Triangle type {9,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x * z^-1 * y * x * z^-2, (z^-1 * y)^3, y^4 * x^-1 * y^-2 * z * y ] T91.343 : Triangle type {9,69,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6 * z^3 ] T91.344 : Triangle type {9,69,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^7 * y^-1 * z^5 * y^-7 * z^3 ] T91.345 : Triangle type {10,12,15} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, z^-1 * y^2 * x^-1 * y^-3, x * y^-1 * x^3 * y^-1 * x * y^-1 ] T91.346 : Triangle type {10,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^2 * y^-3, (x * z^-3)^2, z^-2 * x^-1 * y * x^-1 * z^2 * y * z^-1 ] T91.347 : Triangle type {10,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-2 * x * z^3, x^10 ] T91.348 : Triangle type {10,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z * y * x^-1 * y * x^-1 * z^4 ] T91.349 : Triangle type {12,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * z^-1 * x^-1 * z * y^-1 * z, y^-1 * x^4 * y^-3 ] T91.350 : Triangle type {12,12,12} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z * x^-2 * y^-1 * z^-2, x * z^-2 * x^-1 * z * x^-1 * y^-1, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T91.351 : Triangle type {12,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^3 * x^-1 * y^2 * z^-1, x^-1 * z * x^-1 * z^2 * x^-4 * z^3 ] T91.352 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^2 * z^-3, y^-2 * x^4 * y^-4 ] T91.353 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3, x^-1 * y^3 * x^-7 * y^3 ] T91.354 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-1 * y^2 * x^-6 * y^3 ] T91.355 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y * z^-3 * y * z^-1 * y^3 * x * z^-1 * y * z^-2 * y * x^-1 * y * z^-1 * y^2 ] T91.356 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-2 * x * z^-1 * x * z^-3, y^-1 * x^2 * y^-1 * x^2 * y^-4 ] T91.357 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, z^5 * y^-1 * z^5 * y^-5 * z^2 ] T91.358 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^-12 ] T91.359 : Triangle type {12,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, y^-2 * x^4 * y^-4 ] T91.360 : Triangle type {12,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * z * y^-1 * x * y^-1 * z, y^2 * x^3 * z^2 * x^-1, y^-1 * z^-1 * x^3 * y^-2 * x, y * x^-1 * y^-1 * x^2 * z^-1 * x^-1 * z ] T91.361 : Triangle type {12,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * y^-1, z * y * x^2 * z^2, x^-12 ] T91.362 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, (z^-1 * y)^3 ] T91.363 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, x^-3 * z * x^-7 * y * x^-1 ] T91.364 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (z^-1 * y)^3 ] T91.365 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-2 * y * x^-9 * z ] T91.366 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^-12 ] T91.367 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^-1 * z * y * x^-1 * y^-3, x^4 * y^-1 * z^-1 * x^4 * z^-2 * x^2 ] T91.368 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, (z^-1 * y)^3 ] T91.369 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, z * y * z^-1 * x^-1 * z * y^-1 * z ] T91.370 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^2 * x^-1 * y * x^-1 * z^2 * y * x^-1 ] T91.371 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * z^-1 * y * x^-1 * y^-1 * z * y, z * y * z^-1 * x^-1 * z * y^-1 * z ] T91.372 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y^2 * x^-3 * y^4, z^2 * x^-3 * z^4 ] T91.373 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^2 * x^-3 * y^4, z^2 * x^-3 * z^4 ] T91.374 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, x^-4 * y * x^-1 * y, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^-1 * z * y * x^-1 * y^-3 ] T91.375 : Triangle type {12,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * x^-3 * y^-1 * x^2, y^2 * z^-1 * x^-1 * y * z^-1 * y ] T91.376 : Triangle type {12,34,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x * y^-5 ] T91.377 : Triangle type {12,51,68} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z ] T91.378 : Triangle type {14,15,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^9 * y^-1 * z^5, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T91.379 : Triangle type {14,16,16} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, y^-6 * z * y^-1 * z * y^-4 * z * y^-1 * z, x^5 * z * y^-1 * z * x^-4 * y * z^-1 * y * x^2 ] T91.380 : Triangle type {14,16,16} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^-14 ] T91.381 : Triangle type {14,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-9 * y * z^-4, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T91.382 : Triangle type {14,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T91.383 : Triangle type {14,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-3 * y^7, x^5 * z^-3 * x^4 * y^-3 * x^2 ] T91.384 : Triangle type {15,15,15} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, z^15, y^-4 * z * y^-1 * z^5 * y^-1 * x^5 * y^-1 * x * y^-2 ] T91.385 : Triangle type {15,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y^2 * z^-4, x^6 * z^-4 * x^2 * y^-4 * x^3 ] T91.386 : Triangle type {15,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x * y * z^-4, y^5 * z^-4 * y * x^-5 * y^3 ] T91.387 : Triangle type {16,16,104} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-3 * x^3 * z^-3, z^-2 * x * z^2 * y^-1 * z^-3 * x^-1 * z^3 * y^-1 * z^-1 ] T91.388 : Triangle type {16,16,104} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-3 * x^3 * z^-3, y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 * x^-1 * z^5 ] T91.389 : Triangle type {16,16,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, x^-1 * y^-1 * x * z^3 * y * z^-1 * x * z^3 * y^-1 * z^-3 ] T91.390 : Triangle type {18,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z * y^-1 * z^-1 ] T91.391 : Triangle type {18,18,18} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, z * y * x^-2 * z * y * x ] T91.392 : Triangle type {18,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * z^-2 * x^5 * y^-1 * x ] T91.393 : Triangle type {18,18,18} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T91.394 : Triangle type {18,33,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-2, x^7 * z^-3 * x^4 * y^-3 * x^4 ] T91.395 : Triangle type {18,33,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^-3 * x^6 * y^-8 ] T91.396 : Triangle type {20,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y^3 * x^-1 * y^8 * x^-1 * y ] T91.397 : Triangle type {20,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * y^2 * x^-1 * z * x^-6 * y ] T91.398 : Triangle type {20,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^-2 * x * y^-1 * x * y^-2 * z ] T91.399 : Triangle type {20,40,40} Group order 200 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^-20 ] T91.400 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1, x^-1 * z * y * x^-1 * z * x^-7 * z * x^-1 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T91.401 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^6 * y^-4 * x^2 * z^-4 * x^8 ] T91.402 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x^-6 * z * x^-1 * z ] T91.403 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^5 ] T91.404 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^3 * z^-1 * x^-1, x^-2 * y^6 * x^-3 * y^4 ] T91.405 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z * x^-8 * y, z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z^2 ] T91.406 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^4 * z^-1 * x^-5 * y^-1, x^5 * y^-1 * x^2 * y^-1 * x^2 ] T91.407 : Triangle type {20,40,40} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-2 * z^4, y^3 * x^-4 * y^6 * x^-1 * y ] T91.408 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3, z^-1 * y^4 * x^-1 * y^3 * z^-2 * y^2 ] T91.409 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * x^2 * y^-3, z^-1 * x^5 * z^-1 * x * z^-1 * x ] T91.410 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z, y^-1 * x * y^-4 * x * y^-1 * x^4 * y^-1 * x * y^-1 * x^2 * y^-1 * x ] T91.411 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, x^-2 * z * x^-5 * z * x^-1 * z * x^-1 ] T91.412 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1, y^-1 * z * y^-5 * z * y^-1 ] T91.413 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-7 * y * x^2 * z^-1 * x * z^-3 ] T91.414 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^-6 * y^3, z^-2 * x^4 * z^-4 ] T91.415 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^-6 * y * x^-2 * z^2 * x^-7 * y * x^-5 ] T91.416 : Triangle type {22,33,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-4 * y^3, y^-1 * z * x^-1 * z * x^-1 * z^6 ] T91.417 : Triangle type {24,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-3 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-6 ] T91.418 : Triangle type {24,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2, y * z^-1 * y * z^-1 * y * z^-5 * y * x^-1 * y^5 ] T91.419 : Triangle type {24,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T91.420 : Triangle type {24,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^11 * y^-6 * x * y^-1 * x * y^-1 * x^2 ] T91.421 : Triangle type {24,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, x^3 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x ] T91.422 : Triangle type {24,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * x^2 * z^-4, y^-3 * x * y^-1 * x * y^-4 ] T91.423 : Triangle type {27,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^2 * y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T91.424 : Triangle type {27,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^5 * z^-4 * y * x^-3 * y^4 ] T91.425 : Triangle type {27,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, z^3 * x^-5 * z^11 ] T91.426 : Triangle type {27,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-3 ] T91.427 : Triangle type {27,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^2 * y^-1 * x^6 * y^-6 * x^2 ] T91.428 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-1 * z * y * x^-1 * y * x^-1 * z * y * x^-7 * z * x^-3 ] T91.429 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x * y^-9 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x ] T91.430 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-3 * y * x^-1 * z * y * x^-6 * z^2 * x^-1 * y * x^-2 ] T91.431 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x^9 * y^-6 * x^3 ] T91.432 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^4 * y^-4, x^2 * z^-2 * x^4 * z^-4 ] T91.433 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T91.434 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^-8 * z^4 * y^-6 ] T91.435 : Triangle type {32,48,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x^3 * y^-4, z^-1 * x * z^-2 * x^4 * z^-1 * x * z^-2 ] T91.436 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-8 * x * y^-11 * x * y^-11 ] T91.437 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T91.438 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^27 * y^-4 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T91.439 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^4 * x^-1 * z^7 * y^-3 * x^-1 * z^13 ] T91.440 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x^-3 * y^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T91.441 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^-3 * y^5 * x^-3 * z^2 * x^-4 ] T91.442 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^5 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T91.443 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, (y^-5 * x * y^-1)^2 ] T91.444 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^10 * y^-6 * x^4 ] T91.445 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^4 * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T91.446 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^2 * y^-1 * z * y^-3 * z^11 ] T91.447 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^5 * z^-1 * x * z^-1 * x * z^-4 * x^9 ] T91.448 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-5 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T91.449 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^8 * x^-7 * y^2 * x^-6 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T91.450 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-5 * y, z^-3 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-3 ] T91.451 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, z^-10 * y * z^-4 ] T91.452 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-6 * x^4 * y^-6 * x * y^-1 * x * y^-2 ] T91.453 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^23 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T91.454 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T91.455 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-2, x^4 * z^-3 * x^7 ] T91.456 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-3 * x^7, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T91.457 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T91.458 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-5 * z^3 * x^-14 ] T91.459 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^-5 * x * y^-1 * z^5 * y^-4 ] T91.460 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T91.461 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * z^2 * x^-3, z^-3 * y * z^-5 * y^2 * z^-4 ] T91.462 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-3 ] T91.463 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^47 * y^-1 * x^9 * y^-1 * x * y^-1 * x^3 ] T91.464 : Triangle type {62,93,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T91.465 : Triangle type {63,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * z * y^-5 * z^2 * y^-1 ] T91.466 : Triangle type {63,63,63} Group order 189 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * y * x^-1 * y^2, x^-1 * z^2 * x^-2 * z^4 ] T91.467 : Triangle type {63,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^18 * x^-2 * z^4 * x^-1 * z^8 ] T91.468 : Triangle type {63,63,63} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-5 * y^2 * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T91.469 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T91.470 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2 ] T91.471 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^10 * y^-18 * x * y^-1 * x * y^-1 * x * y^-2 ] T91.472 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-48 * x^2 * y^-12 ] T91.473 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^3 * z^-1 * x^4 * y^-5 * x^2 ] T91.474 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z * y^-2 * z^9 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T91.475 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T91.476 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T91.477 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-4 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T91.478 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, y^5 * z^-4 * y * x^-3 * y^4 ] T91.479 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T91.480 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-3 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T91.481 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-12 * y^6 * z^-1 * y * z^-2 ] T91.482 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^6 * z^-4 * y * x^-6 * y * x^-1 * y^2 ] T91.483 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^3 * x^-5 * z^11 ] T91.484 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T91.485 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y^-7 * z^4 * y^-5 ] T91.486 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^-7 * z^4 * y^-5 ] T91.487 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-13 * z^2 * y^-3 * z * y^-1 * z * y^-5 * x * y^-12 ] T91.488 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T91.489 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^12 * y^-1 * x^12 * y^-1 * x^67, y * z^-1 ] T91.490 : Triangle type {92,184,184} Group order 184 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^40 * y^-2 * x^5 ] T91.491 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x^-2 * y^-1, y^72 * x^-1 * y^19, x * z^-1 ] T91.492 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^10 * y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x^3 ] T91.493 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x * y^-1 * x^7 * y^-1 * x^10 * z^-1 * x * y^-1 * x * y^-1 * x^3 ] T91.494 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-4 * y * x^-1 * y^6 * x^-3 * z^2 * x^-7 ] T91.495 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^3 * z^-3, x^-4 * y^6 * x^-1 * z^4 * x^-1 * z * x^-5 ] T91.496 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^-3 * y^5 * x^-8 ] T91.497 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^3 * z^-3, x^4 * z^-3 * x^2 * y^-5 * x^2 ] T91.498 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, z^-4 * y * z^-5 * y^6 * z^-1 ] T91.499 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x * y * z^-4, y^5 * z^-4 * y * x^-3 * y^4 ] T91.500 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-5 * x^3 * y^-6 * x * y^-2 ] T91.501 : Triangle type {183,183,183} Group order 183 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^3 * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^4 ] Genus 92 T92.1 : Triangle type {2,3,12} Group order 2184 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, y * z^-1 * x * z^2 * y * z^-1 * x * z * y * z^-1 * y^-1 * z^-3 * x * z^2, y * x * z * y * x * z * y * x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z, z * y * z^-2 * x * z * y * z^-2 * x * z * y * z^-1 * x * z^2 * y^-1 * z^-2 * x ] T92.2 : Triangle type {2,3,12} Group order 2184 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, x * z * y * z^-2 * x * z * y * z^-1 * y * z^-3 * x * y^-1 * z^-1 ] T92.3 : Triangle type {2,4,6} Group order 2184 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, (y^-1 * z * y^-1 * z^2)^3, z^-1 * x * z * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z^-1 * y ] T92.4 : Triangle type {2,4,186} Group order 744 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-186 ] T92.5 : Triangle type {2,4,368} Group order 736 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-44 * x * y^-1 * z^-139 ] T92.6 : Triangle type {2,6,6} Group order 1092 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T92.7 : Triangle type {2,6,6} Group order 1092 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-2 * y * z^-1 * y)^2, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * z * y^-1 ] T92.8 : Triangle type {2,6,6} Group order 1092 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y * z^-1 * x * z * y^-1 * z^-2 * x * z^2 * y^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-3 * y * z^-2 * y * z^-2 * y * z^-1 * x ] T92.9 : Triangle type {2,6,6} Group order 1092 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, x * z * y^-1 * z^2 * y^-1 * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * y * z^-2 * y * z^-2 * y * z^-2 * y * z^-2 ] T92.10 : Triangle type {2,6,6} Group order 1092 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^2 * z^-1 * x * z * y^-1 * z^-1, z * y^2 * x * z * y^2 * x * y^-1 * z^-1 * y * x ] T92.11 : Triangle type {2,6,16} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^4 * y^2 * x * z^3, z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z ] T92.12 : Triangle type {2,6,16} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^4 * y^2 * x * z^3, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T92.13 : Triangle type {2,6,24} Group order 624 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-2 * x * z * y^-2 * z * y^-1 * z^-3, y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T92.14 : Triangle type {2,6,24} Group order 624 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y^-2 * z * y^-2 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T92.15 : Triangle type {2,6,42} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^-2 * z * y^-2 * z^-1 * y * x * y^-2 * z^-1 * x, x * z^4 * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-4 ] T92.16 : Triangle type {2,6,42} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * z * y^-1, z^-2 * x * z * y * z^-4 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T92.17 : Triangle type {2,6,94} Group order 564 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-57 * x * z^15 * y * z^-1 * x * y^-1 * z^-19 ] T92.18 : Triangle type {2,6,276} Group order 552 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^74 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 * x * z^2 ] T92.19 : Triangle type {2,8,33} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-23 * x * y^-1 * z^-6 * x * z * y^-1 * z^-1 ] T92.20 : Triangle type {2,8,124} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-38 * x * z^3 * y * x * z^8 * y^-1 * z^-11 ] T92.21 : Triangle type {2,10,48} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-34 * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-5 ] T92.22 : Triangle type {2,10,230} Group order 460 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^30 * y * z^-9 * x * z * y^-1 * z^-3 * x * z ] T92.23 : Triangle type {2,18,18} Group order 468 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * z * y * x * y^-1 * z^-2 * x * z^2, z * y^-2 * z * y^-1 * z^3 * y^-5 * z * y^-1 * z * y^-1 * z ] T92.24 : Triangle type {2,18,207} Group order 414 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, x * z^11 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T92.25 : Triangle type {2,30,30} Group order 420 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-2 * z * y^-6 * z^4 * y^-1 * z * y^-11 * z * y^-1 * z * y^-1 ] T92.26 : Triangle type {2,94,188} Group order 376 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-59 * y^32 * z^-1 * y ] T92.27 : Triangle type {2,185,370} Group order 370 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^125 * y^-58 * z ] T92.28 : Triangle type {2,186,186} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^60 * z^-126 ] T92.29 : Triangle type {2,368,368} Group order 368 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^59 * z^-125 ] T92.30 : Triangle type {3,3,6} Group order 1092 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z^2 * x^-1 * y^-1 * x * z * y^-1 * x * z, x^-1 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-1 * x * z ] T92.31 : Triangle type {3,3,6} Group order 1092 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, (z^-1 * x^-1 * y^-1)^3, z * y^-1 * z^-2 * x * y^-1 * x^-1 * z * y * z^-2 * x^-1, x^-1 * y^-1 * z^-1 * x * z * y * x^-1 * z * y * x^-1 * z * y ] T92.32 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z^-1 * x^-1 * z * y * x * z * y^-2 ] T92.33 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * y ] T92.34 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z^-1 * x^-1 * z * y * x * y^-1 * x * y^-1 * z^-1 * y * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x * z * y ] T92.35 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * z * y^-1 * z * y^-1 * x * y^-1 * z^-1 * y * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T92.36 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y * z^-2 * y^2 * z^-1 * y * z^-1 ] T92.37 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y^-1 * z^-2 * y * x^-1 * y^-1 * z^2 * y^-1 ] T92.38 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z * y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T92.39 : Triangle type {3,6,6} Group order 546 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z * y^-1 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T92.40 : Triangle type {3,24,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 * y^-1 ] T92.41 : Triangle type {3,24,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T92.42 : Triangle type {3,24,24} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^2 * x * y^-1 * x * y^-2 * z^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T92.43 : Triangle type {3,42,42} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * y^-1 * z^2, y^-3 * z^3 * y^-3 * z * y^-1 * z^3 ] T92.44 : Triangle type {3,42,42} Group order 294 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^-1 * z * y^-2 * z * y^-1 * z * y^-2 * x * y^-1 * z^2 * y^-2 ] T92.45 : Triangle type {3,94,94} Group order 282 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^75 * y^-14 * z^3 * y^-1 ] T92.46 : Triangle type {3,276,276} Group order 276 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-76 * z * y^-15 ] T92.47 : Triangle type {4,4,93} Group order 372 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-79 * x * y * z^-13 ] T92.48 : Triangle type {4,4,184} Group order 368 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-78 * x * y^-1 * z^-13 ] T92.49 : Triangle type {4,6,24} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y^2 * x^-1 * z * y^-2 * z, z^-1 * y * z^-1 * y * x^-1 * z^3 * y^-1, y * z^-2 * y * x^-1 * y^-1 * z^3 ] T92.50 : Triangle type {4,6,24} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, y^-3 * z^-1 * x^-1 * z * y^-2 * z ] T92.51 : Triangle type {4,8,38} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^23 * y * z^-1 * x^-1 * y * z^-5 * x^-1 * z^7 ] T92.52 : Triangle type {4,12,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z * y * x^-1 * z * y * x^-1 * y^-1 * z^-2 * x^-1 * z ] T92.53 : Triangle type {4,12,138} Group order 276 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^11 * y * x * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1 ] T92.54 : Triangle type {4,16,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^2 * y * x * z * y * z^-7 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z ] T92.55 : Triangle type {4,22,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, z^-1 * y * z^-1 * y * z^-2 * y^3 * z^-3 * y^9 * z^-1 ] T92.56 : Triangle type {4,33,33} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^18 * y^-5 * z^2 * y^-6 * z ] T92.57 : Triangle type {4,124,124} Group order 248 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-29 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-13 ] T92.58 : Triangle type {5,47,235} Group order 235 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T92.59 : Triangle type {5,48,48} Group order 240 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^-32 * z^3 * y^-1 * z * y^-2 * z * y^-6 * z * y^-1 ] T92.60 : Triangle type {5,48,48} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y * z^-14 * y^3 * z^-1 * y^12 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^2 * z^-1 * y^6 ] T92.61 : Triangle type {5,230,230} Group order 230 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^12 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T92.62 : Triangle type {5,230,230} Group order 230 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^15 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T92.63 : Triangle type {6,6,8} Group order 336 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, y^6, x * z^-1 * y^2 * x * y^-1 * z * y, z^8 ] T92.64 : Triangle type {6,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * y^-1 * x^2 * z^2, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z ] T92.65 : Triangle type {6,6,8} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * y^-1 * x^2 * z^2, z * y^-1 * z^-1 * x^-2 * z * y^-1 * z^-1 * x ] T92.66 : Triangle type {6,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * x^-2 * y * x * y^-1, x * z * x^-2 * y^-1 * z^-2, y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T92.67 : Triangle type {6,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-1 * y^2 * x^-1 * y^-2 * z^-2 ] T92.68 : Triangle type {6,6,12} Group order 312 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^-1 * y^2 * x^3 * y^-1 * z^-1 * x^-1 * y^-1 ] T92.69 : Triangle type {6,6,21} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z^-1, z * x^-1 * y^-1 * x * y^-1 * z, y * z^-1 * x^-1 * y * x^-1 * z^4 ] T92.70 : Triangle type {6,6,21} Group order 294 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T92.71 : Triangle type {6,6,47} Group order 282 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-31 * x * y^-1 * x * y^-1 * x * z^4 * y^-1 * z^-9 ] T92.72 : Triangle type {6,6,138} Group order 276 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-23 * x^-1 * y^-1 * z^-1 * x * z^5 * y^-1 * z^-1 * x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T92.73 : Triangle type {6,18,18} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * y * z^-2, z * y^-1 * z * x^-1 * z * y^-2, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T92.74 : Triangle type {6,18,18} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^2 * z^-3, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T92.75 : Triangle type {6,20,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x * z^-1 * x^-1, y * z^-1 * y^5 * z^-1 * y * z^-1 ] T92.76 : Triangle type {6,20,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, y^6 * z^-4 ] T92.77 : Triangle type {6,24,30} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * x^-1 * y^-4, z^-3 * x^-1 * z * y^-1 * z^-5 ] T92.78 : Triangle type {6,38,114} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^10 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T92.79 : Triangle type {6,111,222} Group order 222 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^9 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T92.80 : Triangle type {8,8,62} Group order 248 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-17 * x * y^-1 * x * y^-1 * z^-12 ] T92.81 : Triangle type {8,10,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, y^10 ] T92.82 : Triangle type {8,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, z^4 * y^-1 * z^-2 * x^-1 * z^3 ] T92.83 : Triangle type {8,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * x * z, z^-1 * y^2 * x^-1 * y^-3, y^-2 * x^3 * z * y^-2 ] T92.84 : Triangle type {9,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x * z * y * x^-1 * y * x * z^-1, x^-9 ] T92.85 : Triangle type {9,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, y * x^-1 * y * x^-1 * y * x * z ] T92.86 : Triangle type {9,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, y * z^-2 * x^-1 * y^-2 * z, z * y^3 * x^-1 * z * y^-1 * z * y^-1 ] T92.87 : Triangle type {9,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, y^-1 * z * y * x^-1 * y^-3, y * z^-2 * y^2 * z^-1 * y * z^-1, x^-9 ] T92.88 : Triangle type {9,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 ] T92.89 : Triangle type {9,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^8 * x^-1 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T92.90 : Triangle type {10,10,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^10 * y^-1 * x * y^-1 * x * y * x^-1 * y * x^-1 * z^10 ] T92.91 : Triangle type {10,10,115} Group order 230 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^10 * y^-1 * z^-4 * x * y^-1 * z^-1 * x^-1 * z^6 ] T92.92 : Triangle type {10,10,115} Group order 230 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-4 * x * z^3 * y * z^-1 * x * z^2 * y * z^-3 * x^-1 * z * y * z^-3 * x * z^2 * y^-1 ] T92.93 : Triangle type {10,20,44} Group order 220 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^-2, z^-1 * x * y^-1 * x * y^-2 ] T92.94 : Triangle type {10,20,44} Group order 220 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * y^-2, x^-1 * z * y^-1 * x * z^-1 * y, y^2 * z^-1 * x^-1 * y^2 * z^-1 ] T92.95 : Triangle type {10,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^7 * x^-2 * y * z^-5 * y * z^-1 * y * z^-1 * y^4 ] T92.96 : Triangle type {12,27,27} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, y^-1 * z * y^-3 * x^-1 * z * y^-2 * z ] T92.97 : Triangle type {12,51,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-4 * z * y^-1 * z^5 * y^-1 * x^2 * y^-5 ] T92.98 : Triangle type {12,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^5 * x^-3 * y * z^-5 * y * z^-1 * y^4 ] T92.99 : Triangle type {15,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * y^-1 * z, z^2 * x^-3 * z^4 ] T92.100 : Triangle type {15,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * y^-1 * z, y^2 * x^2 * z^2, x^-15 ] T92.101 : Triangle type {15,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x^-4 * y^-1 * x * z, z * y^2 * x^-1 * z^2 * y^-1, y^2 * x^-3 * y^4 ] T92.102 : Triangle type {15,30,30} Group order 210 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, y * z^-1 * y^2 * z^-2, x^-2 * z^2 * y * x^-1 * z * x^-6 * z * y * x^-3 ] T92.103 : Triangle type {18,66,99} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T92.104 : Triangle type {18,66,99} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-3 * y^7, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-2 ] T92.105 : Triangle type {20,50,50} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * y^2 * z^-4, x^-1 * z * y * x^-8 ] T92.106 : Triangle type {20,50,50} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-4, x^-1 * z * y * x^-8 ] T92.107 : Triangle type {24,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^6 * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T92.108 : Triangle type {24,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^-6 * x * y^-2 * z^3 * y^-5 ] T92.109 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, (y^-3 * z * y^-6)^2 ] T92.110 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x * z^-1 * x * z^-1 * x * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 * x * z^-1 * x ] T92.111 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z^3 * y^-6 * z^11 ] T92.112 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, z^-10 * y * z^-4 ] T92.113 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^7 * y^-5 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x^3 ] T92.114 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-2, x^-2 * y^6 * x^-4 * z * x^-3 ] T92.115 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-2 * z^3 * x^-7 ] T92.116 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-10 * x^3 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.117 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, y^-5 * x * y^-1 * z^5 * y^-4 ] T92.118 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^5 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T92.119 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-21 * z^2 * x^-6 * y^2 * x^-9 ] T92.120 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-9 * z^2 * y^-4 ] T92.121 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^-4 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T92.122 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^18 * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x * y^-1 * x^3 ] T92.123 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, x^-2 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T92.124 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^2 * z^-4, y^-3 * x^5 * y^-6 * x * y^-1 ] T92.125 : Triangle type {38,95,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^-13 * x * y^-1 * x * y^-1 ] T92.126 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-8 * z^2 * y^-3 * x^3 * y^-3 * z * y^-1 * z * y^-5 ] T92.127 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^8 * y^-18 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.128 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T92.129 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^15 * y^-5 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T92.130 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^6 * z^-3 * x^2 * y^-6 * x * y^-1 * x^2 ] T92.131 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T92.132 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^3 ] T92.133 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-6 * x * z^-1 * x * z^-4 * x * y^5 * z^-1 * y * z^-2 ] T92.134 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^6 * x^-4 * y^-1 * z^5 * y^-1 * z^7 ] T92.135 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x * y^-1 * x^6 * y^-7 ] T92.136 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^15 * y^-4 * x^6 ] T92.137 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T92.138 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T92.139 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-14 * x^5 * y^-10 ] T92.140 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T92.141 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^6 * z^-4 * x^7 ] T92.142 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y^6 * z^-4 * y * x^-3 * y^5 ] T92.143 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T92.144 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T92.145 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^22 * z^-1 * x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 * x * z^-1 * x ] T92.146 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, y^9 * x^-6 * y * x^-1 * y^2 ] T92.147 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T92.148 : Triangle type {47,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-47 ] T92.149 : Triangle type {48,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^2 * y^-1 * x^2 * y^-1 * x^5 * y^-4 * x * y^-2 ] T92.150 : Triangle type {48,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-3 * y^2 * z^-3, y * x^-4 * y * x^-1 * y^2 ] T92.151 : Triangle type {48,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, x^-1 * z * x^-1 * z^3 * x^-1 * z * x^-2 * z * x^-1 * z^2 ] T92.152 : Triangle type {48,64,64} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z * x^-3 * z^3, y^-3 * x * y^-1 * x * y^-4 ] T92.153 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-35 * x * y^-11 ] T92.154 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^11 * x^-6 * y * x^-1 * y^4 ] T92.155 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T92.156 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^13 * y^-5 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.157 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^6 * z^-3 * y^9 ] T92.158 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-11 * y^6 * z^-1 * y * z^-1 ] T92.159 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^6 * z^-4 * x^4 * y^-2 * x^2 ] T92.160 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^9 * y^-6 * x^3 ] T92.161 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6, y^4 * z^-4 * y^6 ] T92.162 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^2 * y^-1 * z^9 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T92.163 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^-1 * x * y^-1 * x^6 * y^-8 ] T92.164 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^4 * y^-7, z^-9 * y * z^-4 ] T92.165 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^4 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T92.166 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, z^3 * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T92.167 : Triangle type {93,186,186} Group order 186 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^93, y * z^-1 ] T92.168 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-32 * z * y^-7 * z * y^-7 ] T92.169 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^11 * y^-18 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.170 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-5 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.171 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-5 * x^5 * y^-6 * x * y^-3 ] T92.172 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x^2 * z^-4, y^-6 * x * y^-6 * x * y^-2 ] T92.173 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, y^-3 * x^4 * y^-7 ] T92.174 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^3 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T92.175 : Triangle type {94,94,94} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T92.176 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x^-2 * y^-1, y^72 * x^-1 * y^20, x * z^-1 ] T92.177 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^7 * z^-3 * y^2 * x^-2 * y^7 ] T92.178 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-2 * y^4 ] T92.179 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-49 * x * y^-12 ] T92.180 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-4 * x^2 * y^-7 ] T92.181 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^2 * y^-1 * z * y^-4 * z^5 * y^-1 * z^5 ] T92.182 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^11 * y^-1, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T92.183 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^28 * y^-4 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T92.184 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T92.185 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-2, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T92.186 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T92.187 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T92.188 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T92.189 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, z * x^-12 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T92.190 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x^-2 * z^4 * y^-1 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T92.191 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^4 ] T92.192 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^7, y^5 * z^-4 * y * x^-5 * y^3 ] T92.193 : Triangle type {185,185,185} Group order 185 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^13 * z^-2 * x^9 * y^-1 * x^3 ] Genus 93 T93.1 : Triangle type {2,4,96} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-32 * x * z^8 * y^-1 * z^-7 ] T93.2 : Triangle type {2,4,96} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-78 * x * z^8 * y * x * z * y^-1 * z^-7 ] T93.3 : Triangle type {2,4,96} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-78 * x * z^11 * y^-1 * z^-6 ] T93.4 : Triangle type {2,4,96} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-29 * x * z^11 * y * z^-1 * x * y^-1 * z^-5 ] T93.5 : Triangle type {2,4,188} Group order 752 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-188 ] T93.6 : Triangle type {2,4,372} Group order 744 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-45 * x * y^-1 * z^-140 ] T93.7 : Triangle type {2,7,12} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-2 * y^3 * z^-2 * y * z^-1 * y, x * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T93.8 : Triangle type {2,8,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-6 ] T93.9 : Triangle type {2,8,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, y * x * y^-3 * z^-1 * y * z^-2, z^2 * y * x * z^2 * y * z^-7 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T93.10 : Triangle type {2,8,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z^3 * y * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 ] T93.11 : Triangle type {2,8,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, z^-3 * x * z^3 * y^-2 * z * y * z^-5 * x * z^2 * y^-1 * z^-2 ] T93.12 : Triangle type {2,8,18} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y * x * y^-1 * z * y^3 * x * y^-2 * z^-1 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * z^3 ] T93.13 : Triangle type {2,8,64} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-5 * x * z^3 * y * x * z^4 * y^-1 * z^-2 ] T93.14 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^40 * y * x * z * y * x * y * z^-8 * x * y^-1 * z^-3 * x * z^8 ] T93.15 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-28 * x * z^20 * y * z^-15 ] T93.16 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-7 * x * z * y * z^-1 * x * z^4 * y * z^-2 * x * z^2 * y^-1 * z^-12 ] T93.17 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-9 * x * z^2 * y * x * z^5 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-4 ] T93.18 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-3 * x * z^3 * y * z^-3 * x * z^4 * y * z^-2 * x * z^2 * y^-1 * z^-12 ] T93.19 : Triangle type {2,8,64} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-4 * x * z^2 * y * z^-1 * x * z^11 * y^-1 * z^-12 ] T93.20 : Triangle type {2,8,248} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^47 * y * z^-7 * x * z * y^-1 * z^-3 * x * z^2 ] T93.21 : Triangle type {2,8,248} Group order 496 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^48 * y^-1 * z^-6 * x * z * y^-1 * z^-3 * x * z^2 ] T93.22 : Triangle type {2,11,22} Group order 506 Chiral action Defining relators: [ x^2, x * y * z, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-11, x * y^-5 * z^-3 * y^2 ] T93.23 : Triangle type {2,11,22} Group order 506 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-3 * y, y * x * y^-1 * z * y^2 * z^-1 * x * z^2, y^-11 ] T93.24 : Triangle type {2,11,22} Group order 506 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y * z^-1 * y, y^-11 ] T93.25 : Triangle type {2,11,22} Group order 506 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * x * y^-1 * z^2 * y^-1 * z^-1, y * x * z * y^3 * x * y^-2 * z, y^-11 ] T93.26 : Triangle type {2,11,22} Group order 506 Chiral action Defining relators: [ x^2, x * y * z, y^-2 * z * y^3 * x * y^-1 * z^-1 * x, z * y * x * z * y^2 * z^-1 * x * y^-1 * z, y^-11 ] T93.27 : Triangle type {2,12,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * z^2 * y^-2 * z^-3 * y, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y^12, z^-2 * x * z * y * x * y^-1 * z^-5 ] T93.28 : Triangle type {2,12,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y, z^5 * y * z^-1 * x * y^-2 * z * y^-1 * z^-1 * x ] T93.29 : Triangle type {2,12,76} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-4 * x * z^11 * y * x * z * y * x * y * z^-9 * x * y^-1 * z^-9 ] T93.30 : Triangle type {2,14,217} Group order 434 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-4 * y^5 * z^-4, z^-11 * x * z^4 * y^-1 * z^-15 ] T93.31 : Triangle type {2,64,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-19 * z^4 * y^-6 * z^2 * y^-1 ] T93.32 : Triangle type {2,64,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-27 * y^13 * z^-2 * y^20 * z^-1 ] T93.33 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-6 * z^3 * y^-10 * z^2 * y^-1 * z^2 ] T93.34 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, z^2 * y^-45 * z ] T93.35 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-92 * z * y^-1 ] T93.36 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-60 * y^35 ] T93.37 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-10 * y^12 * z^-4 * y^19 * z^-2 ] T93.38 : Triangle type {2,96,96} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-30 * z^3 * y^-13 ] T93.39 : Triangle type {2,187,374} Group order 374 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^126 * y^-60 ] T93.40 : Triangle type {2,188,188} Group order 376 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^61 * z^-126 * y ] T93.41 : Triangle type {2,372,372} Group order 372 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^60 * z^-125 * y ] T93.42 : Triangle type {3,8,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y^-1 * z * y, y^8 ] T93.43 : Triangle type {3,8,16} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3, y^8 ] T93.44 : Triangle type {3,12,28} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-1 * x^-1 * y * z^-3, y * z^-3 * x^-1 * z^2 * y * z^-1 ] T93.45 : Triangle type {3,94,282} Group order 282 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-77 * z * y^-10 * z * y^-4 * z ] T93.46 : Triangle type {3,279,279} Group order 279 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^5 * z^-1 * y^87 ] T93.47 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^15 * y * x^-1 * z^2 * y^-1 * z^-5 * x^-1 ] T93.48 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^9 * y^-1 * z^-1 * x * z^4 * y * z^-1 * x^-1 * z * y^-1 * z^-5 * x ] T93.49 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-41 * x * y * z^-6 ] T93.50 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^12 * y^-1 * z^-5 * x^-1 * y^-1 * x * z^5 ] T93.51 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-12 * x * z^2 * y * z^-3 * x^-1 * y * x * z^2 * y^-1 * z^-2 ] T93.52 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^38 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-5 * x^-1 * z ] T93.53 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-15 * x * z^2 * y^-1 * z^-2 * x^-1 * z^3 * y ] T93.54 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^15 * y * z^-1 * x * y^-1 * x * y^-1 * z^-2 * x * z^3 ] T93.55 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-15 * x * z^2 * y^-1 * z^-2 * x^-1 * z^3 * y^-1 ] T93.56 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-35 * x * z^4 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-5 ] T93.57 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^13 * y * z^-6 * x^-1 * z^4 ] T93.58 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-10 * x^-1 * z^6 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-4 ] T93.59 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-13 * x^-1 * z^3 * y * z^-3 * x^-1 * z^3 * y^-1 ] T93.60 : Triangle type {4,4,48} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-12 * x * z^4 * y * z^-3 * x^-1 * z^3 * y ] T93.61 : Triangle type {4,4,94} Group order 376 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-80 * x * y * z^-13 ] T93.62 : Triangle type {4,4,186} Group order 372 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-79 * x * y^-1 * z^-13 ] T93.63 : Triangle type {4,6,28} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-4 * x^-1 * z * y * x^-1 * z^2 * y * x^-1 * z^2 * y^-1 * z^-2 ] T93.64 : Triangle type {4,6,28} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-5 * x * z^8 * y * z^-2 * x^-1 * z * y * x^-1 * y * x * z * y * z^-7 ] T93.65 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x^2 * z * y * z^-1 ] T93.66 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, z^-2 * y * x^2 * z * y * z^-1, y^8 ] T93.67 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, y^8, x * z * y^2 * x * z^-3 ] T93.68 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^-3 ] T93.69 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z^-4 * x^-1 * z * y^-1 * z^-2 ] T93.70 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^2 * y * x^-1 * z * y^-2, y^8, x^-1 * z * y^2 * x^-1 * z^3 ] T93.71 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, z^-4 * x^-1 * z * y^-1 * z^-2 ] T93.72 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, z^3 * y^2 * x * z^-1 * x * z^2 ] T93.73 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z * y * z^-1 * y * x^2 * z^4 ] T93.74 : Triangle type {4,8,20} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, (x * y^-1)^4, x^-1 * z * y^2 * x^-1 * z^3 ] T93.75 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 * y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * z^3 ] T93.76 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^12 * y^-1 * z^-4 * x^-1 * z^3 ] T93.77 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-13 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-2 * x * z * y ] T93.78 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-11 * x * z^4 * y * z^-4 ] T93.79 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T93.80 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y * z^-4 ] T93.81 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^2 * y^-1 * z^-1 * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x ] T93.82 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^8, z^3 * y * x^-1 * y * x^-1 * z^5 ] T93.83 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * z^-2 * x^-1 * y * x^-1 * z^3 * y^-1 * z^-1 ] T93.84 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * y * x^-1 * z^5 ] T93.85 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-4 * x * z^3 * y * z^-5 * x * z^5 ] T93.86 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^4 * y * z^-1 * x^-1 * z^8 * y * z^-5 * x^-1 ] T93.87 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^6 * y * z^-1 * x * z^5 * y^-1 * z^-6 * x^-1 ] T93.88 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^6 * y^-1 * z^-5 * x * z * y^-1 * z^-1 * x^-1 * z^5 ] T93.89 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-11 * x^-1 * z^3 * y^-1 * z^-5 ] T93.90 : Triangle type {4,8,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^9 * y^-1 * z^-2 * x^-1 * z^2 * y^-1 * x * z^5 ] T93.91 : Triangle type {4,18,18} Group order 288 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * z * y^-1, y * x * y^-1 * x * z * y, y^2 * z^-1 * y^5 * z^-1 * y * z^-3 * y * z^-1 * y^2 * z^-1 ] T93.92 : Triangle type {4,18,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-4 * y^2 * z^-2 * y^2 * z^-4 * x^-1 * y ] T93.93 : Triangle type {4,18,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * z^-1 * x^-1 * y^-1 * x * z, z * y^-4 * z * y^-1 * z * y^-1 ] T93.94 : Triangle type {4,18,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-2 * y^8 * z^-3 * y * z^-1 * y ] T93.95 : Triangle type {4,18,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^8 * x * y * z^-1 * y^3 * z^-4 * y ] T93.96 : Triangle type {4,18,18} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^2 * z^-3 * y^2 * z^-5 * y^3 * z^-1 * y^2 ] T93.97 : Triangle type {4,22,132} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * z^-1 * y * z^-2 * y^4 * z^-3 * y^8 * z^-1 ] T93.98 : Triangle type {4,33,44} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^2 * z^-1 * y^4 * z^-2 ] T93.99 : Triangle type {4,63,252} Group order 252 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^35 * z^-1 * y * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T93.100 : Triangle type {4,64,64} Group order 256 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y * z^-1 * y^4 * z^-1 * y^3 * z^-1 * y * z^-1 * y^3 ] T93.101 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 * x^-1 * z^-1 * x * z^-3 * y * z^-1 * y * z^-1 ] T93.102 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y^2 * z^-2 * y^6 * z^-1 * y * z^-2 * y^8 ] T93.103 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-30 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-11 * z * y^-1 ] T93.104 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y^2 * z^-2 * y^9 * z^-1 * y^6 * z^-2 ] T93.105 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 * z^-2 * y * z^-1 * y^11 * z^-1 * y^6 * z^-2 ] T93.106 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, y * z^-8 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y^7 * z^-1 ] T93.107 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^36 * z^-1 * y * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T93.108 : Triangle type {4,64,64} Group order 256 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y^2 * z^-2 * y^9 * z^-1 * y^8 ] T93.109 : Triangle type {4,248,248} Group order 248 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-33 * z^2 * y^-1 * z * y^-1 * z^2 * y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T93.110 : Triangle type {4,248,248} Group order 248 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-36 * z * y^-1 * z^2 * y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T93.111 : Triangle type {6,7,7} Group order 336 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-7, z^2 * y^2 * x^-1 * z * y^-1 * z * y^-1 ] T93.112 : Triangle type {6,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * y * z^-1 * y^5 ] T93.113 : Triangle type {6,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^3 * z^-1 * y * z^-2 * y^5 * x^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y ] T93.114 : Triangle type {6,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * z^4 * y^-1 * z^-1 ] T93.115 : Triangle type {6,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^5 * z^-1 * y * z^-1, z^-3 * x^-1 * z * y * x^-1 * y * x^-1 * z^2 * y * z^-1 ] T93.116 : Triangle type {6,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-2 * x * y^-1 * z, y * x^-3 * z * x^-2 ] T93.117 : Triangle type {6,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y * z^-1 * y^7 * z^-1 ] T93.118 : Triangle type {6,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, z^-1 * y^2 * z^-2 * y * z^-2 * y^2 ] T93.119 : Triangle type {6,76,76} Group order 228 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y^2 * z^-2 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y^10 ] T93.120 : Triangle type {7,32,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^4 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T93.121 : Triangle type {7,33,33} Group order 231 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-2 * y^5 * z^-3 * y * z^-1 ] T93.122 : Triangle type {7,217,217} Group order 217 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^3 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T93.123 : Triangle type {7,217,217} Group order 217 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T93.124 : Triangle type {7,217,217} Group order 217 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^3 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T93.125 : Triangle type {8,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, x^8, z^4 * y^-1 * x^-1 * z^4 ] T93.126 : Triangle type {8,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1 * x)^2, y * z^-1 * x^2 * z * y, (x * y^-2)^2, x^8, z^4 * y^-1 * x^-1 * z^4 ] T93.127 : Triangle type {8,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^-1 * y * x^-2 * y^-2 * z, x^8, z^4 * y^-1 * x^-1 * z^4 ] T93.128 : Triangle type {8,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z^4 * y^-1 * x^-1 * z^4 ] T93.129 : Triangle type {8,8,9} Group order 288 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, x^8, z^4 * y^-1 * x^-1 * z^4 ] T93.130 : Triangle type {8,8,32} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^8, y^-1 * z^-1 * x^-1 * z * y * x^-1 * z^4 ] T93.131 : Triangle type {8,8,32} Group order 256 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^8, y^8, y^-1 * z^-1 * x^-1 * z * y * x^-1 * z^4 ] T93.132 : Triangle type {8,8,32} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, x^8, y^-1 * z^-3 * x^-1 * z^4 ] T93.133 : Triangle type {8,8,32} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, x^8, z * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T93.134 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^3 * y * z^-2 * x * z^2 * y^-1 * z^-1 * x^-1 * z^6 ] T93.135 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^4 * y * z^-3 * x^-1 * y^-1 * x * y^-1 * z^-6 * x^-1 ] T93.136 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^-5 * x^-1 * y^-1 * z^-1 * x^-1 * z^3 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T93.137 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-18 * x * y^-1 * x^-1 * y * z^-12 ] T93.138 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, y^-1 * z^-1 * x * z^3 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x^-1 * z^3 ] T93.139 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^9 * y * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-5 * x^-1 * y^-1 * z^-5 * x^-1 ] T93.140 : Triangle type {8,8,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^-7 * x^-1 * z^3 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T93.141 : Triangle type {8,8,124} Group order 248 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^9 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-5 * x^-1 * y * z^-4 * x^-1 * z ] T93.142 : Triangle type {8,8,124} Group order 248 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^13 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 * x * y^-1 * z^-5 * x^-1 ] T93.143 : Triangle type {8,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, y^10 ] T93.144 : Triangle type {8,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, y^10 ] T93.145 : Triangle type {8,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^8, y^4 * x * z^-1 * x * z^-1, z^-2 * x^-1 * z^2 * y^-1 * x * y^-1 * z^-4 ] T93.146 : Triangle type {8,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^8, y^4 * x * z^-1 * x * z^-1, z^3 * y * z^-1 * x^-1 * z^5 ] T93.147 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-1 * z * y^-1 * z^3 * y^-8 ] T93.148 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-1 * z * y^-1 * z^3 * y^-4 * z^4 ] T93.149 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^21 * y^-2 * z * y^-1 * z^2 ] T93.150 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-5 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T93.151 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^-1 * z * y^-1 * z^3 * y^-3 * x * y^-4 * z ] T93.152 : Triangle type {8,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^2 * y^-1 * z^3 * y^-2 * z^3 * y^-2 ] T93.153 : Triangle type {8,54,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 ] T93.154 : Triangle type {10,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * y * x * z^-1 * x^-1, y^3 * x^-1 * y^-1 * z * y ] T93.155 : Triangle type {10,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^3 * z^-1 * x^-1, z * y^2 * x^-1 * z^3 ] T93.156 : Triangle type {10,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * z * x^-1, (x * z * y^-1)^2, (z^-1 * y)^3 ] T93.157 : Triangle type {10,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, y * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z^3 ] T93.158 : Triangle type {10,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^10, y * x * y^-2 * z * x^-1 * y^-1 * z * x^-1 * z * x * z^-1 * x * z^-1 * y^3 ] T93.159 : Triangle type {10,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^2 * x^-1 * y * x^-1 * y^3 * z^-1, z * x^-1 * z^2 * x^-1 * z^4 ] T93.160 : Triangle type {10,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3, x^10 ] T93.161 : Triangle type {10,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * x * z^2 * y^-1, x^10 ] T93.162 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, y^2 * x^-2 * y * x^-1 * y, x * z^-1 * x^-2 * y^-1 * x * z^-1 ] T93.163 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, x^-4 * z * y^-1 * z, z^-1 * y * x^-2 * y^-1 * x * y^-1, z^2 * x^-2 * z * y * x, x^-1 * y^2 * x^-1 * y * z^-1 * y ] T93.164 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, y^2 * x^-2 * y * z^-1 * y, z^-2 * x^-2 * y^-1 * x^2 ] T93.165 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, y * x^-1 * y^-1 * x * z * x^-1, z^-2 * y * x * z * y^-1, z^-1 * y * x^-2 * z * y^-2, y^-2 * x^3 * z^2 * y^-1 ] T93.166 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, x * z^-1 * x^-1 * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * y ] T93.167 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, z^2 * y^-1 * x * y^-1 * z, z * y^3 * z^-1 * x^-1 ] T93.168 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^2, y^2 * x^-2 * z^2 * y ] T93.169 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * y^-1 * x, y * x^-3 * y * x * z^-1 ] T93.170 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, y^-2 * x^2 * z^-1 * x, y^2 * x^2 * y^-1 * z^-1 ] T93.171 : Triangle type {11,11,11} Group order 253 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * z, x^-1 * y * x^-2 * y * x * z^-1 ] T93.172 : Triangle type {12,12,15} Group order 240 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2 ] T93.173 : Triangle type {12,12,15} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, y * x^-1 * y * x^-1 * z^3 ] T93.174 : Triangle type {12,12,15} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T93.175 : Triangle type {12,12,38} Group order 228 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, z^-2 * y * x^2 * z^2 * y ] T93.176 : Triangle type {12,12,38} Group order 228 Chiral action Defining relators: [ x * y * z, (y^-1 * x)^3, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * y * x^-1 * z, z^-1 * y^2 * x^2 * z^-3 ] T93.177 : Triangle type {12,12,38} Group order 228 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-2, z^4 * y^-1 * x * y^-1 * x * y^-1 * x * z^12 ] T93.178 : Triangle type {12,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-3 * z^3 ] T93.179 : Triangle type {18,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y * z^-4, y^-2 * x * y^-1 * x^6 * y^-6 * x * y^-2 ] T93.180 : Triangle type {18,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, z^2 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.181 : Triangle type {18,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-7, z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T93.182 : Triangle type {20,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-3 ] T93.183 : Triangle type {20,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z * y^-3 * x^5 * y^-2, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-3 * z^3 ] T93.184 : Triangle type {20,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * z^5)^2, x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y^2 ] T93.185 : Triangle type {20,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^2 * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T93.186 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T93.187 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-8 * y^2 * z^-4, x * y^-1 * x^6 * y^-6 * x ] T93.188 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4 * z * y^-1, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-4 ] T93.189 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^-6 * x^2 * y^-6 * x * y^-1 * x * y^-1 ] T93.190 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T93.191 : Triangle type {28,49,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-5 * z * x^-4 * y * x^-18 ] T93.192 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, x^-1 * z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.193 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T93.194 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x * y^-4 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^12 * y^-1 * x * y^-1 * x^3 ] T93.195 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T93.196 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-16 * y^2 * x^-6 * z^2 * x^-8 ] T93.197 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-1 * y, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T93.198 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^7 * z^-4 * y * x^-3 * y^6 ] T93.199 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-6 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-4 ] T93.200 : Triangle type {32,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^6, (y^-5 * x * y^-1)^2 ] T93.201 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-31 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T93.202 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T93.203 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T93.204 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^6, z^-2 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T93.205 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-5 * y^2, z^-4 * x * z^-4 * x^2 * z^-4 ] T93.206 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-9 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-4 * x * z^-2 ] T93.207 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.208 : Triangle type {48,64,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-4 * z * y^-6 * z^5 * y^-8 ] T93.209 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-32 * y^2 * x^-6 * y^2 * x^-8 ] T93.210 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-5 * z * x^-14 * y * x^-4 ] T93.211 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-8 * y^2 * x^-4 * y^4 * x^-1 * z * x^-1 * z * x^-6 ] T93.212 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-5 * z * x^-1 * y * x^-1 * z * y * x^-7 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T93.213 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-1 * x^4 * y^-5 * x^2, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T93.214 : Triangle type {48,96,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3, x^-1 * z * y * x^-6 * z^2 * x^-1 * z^2 * x^-1 ] T93.215 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-5 * x * z^-1 * x * z^-4 * x * y^5 * z^-1 * y * z^-1 ] T93.216 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^39 * z^-1 * x^18 * y^-1 * x^5 ] T93.217 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T93.218 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^4 * z^-2, y^-6 * x^3 * y^-6 * x * y^-3 ] T93.219 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-2 * x^6 * y^-7 ] T93.220 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x * y^-3 * x * y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^12 * y^-1 * x * y^-1 * x^3 ] T93.221 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^7 * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T93.222 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^6 * z^-4 * y * x^-5 * y^4 ] T93.223 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x^-3 * y^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T93.224 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-19 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 * x * z^-2 ] T93.225 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^-9 * z^2 * y^-4 ] T93.226 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-3 ] T93.227 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^28 * y^-4 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T93.228 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^9 * x^-3 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^4 ] T93.229 : Triangle type {63,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4, y^-2 * x^6 * y^-7 ] T93.230 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3, y^-1 * x^5 * y^-1 * x * y^-1 * x ] T93.231 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, x^3 * z^-2 * x^5 * z^-2 ] T93.232 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^-10 * z * y^-3 * x * y^-1 * x * y^-6 ] T93.233 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-3 * x^-1 * z^2 * y^-1, y^-7 * x * y^-2 * z^2 ] T93.234 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * x * z^2 * y^-1, z^-2 * x^4 * z^-4 ] T93.235 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, z^-1 * y * x^-1 * y^-2, y^-2 * z^2 * y^-3 * x^3 * y^-1 * x * y^-2 * x * y^-1 ] T93.236 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, y^-1 * z^2 * y^-2 * x^-1 * z^4 ] T93.237 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * y^2 * z^-5 ] T93.238 : Triangle type {64,64,96} Group order 192 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^14 * x^-1 * z^2 * x^-1 * z^4 * x^-1 * z * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T93.239 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-8 * z^2 * y^-5 * z^3 * y^-8 ] T93.240 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-50 * x * y^-12 ] T93.241 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-3 * y^7, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T93.242 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T93.243 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T93.244 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T93.245 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^4 * y^-3 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.246 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^24 * y^-1 * z^13 ] T93.247 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-2 ] T93.248 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^7 * z^-3 * x^8 * z^-1 * x ] T93.249 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y * z^-1 * y * z^-1 * y * z^-5 * y^3 * z^-3 ] T93.250 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-5 * x * z^-4 * x * y * z^-4 ] T93.251 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^3 * z^-3, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T93.252 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^3 * z^-3, y^5 * z^-4 * y * x^-3 * y^4 ] T93.253 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T93.254 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^6 * z^-3 * x^2 * y^-5 * x^4 ] T93.255 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T93.256 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-3 ] T93.257 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^10 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T93.258 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] T93.259 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-11 * y^5 * z^-2 ] T93.260 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-6 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T93.261 : Triangle type {94,188,188} Group order 188 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^13 * y^-1 * x^12 * y^-1 * x^68, y * z^-1 ] T93.262 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x^-2 * y^-1, y^73 * x^-1 * y^20, x * z^-1 ] T93.263 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-1 * z * x^-1 * z * x^-3 ] T93.264 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, z^2 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.265 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^2 * z^-4, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T93.266 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^2 * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T93.267 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, z^-5 * x^4 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] T93.268 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-49 * x^2 * y^-12 ] T93.269 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^10 * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T93.270 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-2 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T93.271 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * z^-1, z^-11 * y^6 * z^-1 * y * z^-1 ] T93.272 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-3 * y * x^-1 * y * x^-1 * z^3 * x^-4 * z^3 * x^-8 ] T93.273 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-10 * y * z^-4 ] T93.274 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T93.275 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^12 * x^-4 * z^13 ] T93.276 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^9 * z^-1 * x^7 * z^-2 * x * y^-1 * x * y^-1 * x^3 ] T93.277 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * z, z^4 * y^-1 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T93.278 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^30 * y^-4 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T93.279 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^23 * x^-2 * y^-1 * z^13 ] T93.280 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T93.281 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-1 * y, x^-3 * y^6 * x^-2 * z^3 * x^-5 ] T93.282 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-12 * x^3 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * y^-1 * x^10 * z^-1 * x * z^-1 * x ] T93.283 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * x^-5 * y^2, z^-9 * y * z^-4 ] T93.284 : Triangle type {187,187,187} Group order 187 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] Genus 94 T94.1 : Triangle type {2,3,12} Group order 2232 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3 * x * z, z * y * z^-1 * x * z^2 * y * z^-1 * x * z * y * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T94.2 : Triangle type {2,4,35} Group order 840 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, (y * z^-1)^6, z * y * z^-2 * y * z^-1 * y * z^-2 * x * z^2 ] T94.3 : Triangle type {2,4,66} Group order 792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y * z^-1)^6, z^-2 * x * z^5 * y * z^-3 * x * z^3 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 ] T94.4 : Triangle type {2,4,190} Group order 760 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-190 ] T94.5 : Triangle type {2,4,376} Group order 752 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-46 * x * y^-1 * z^-141 ] T94.6 : Triangle type {2,6,6} Group order 1116 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, x * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T94.7 : Triangle type {2,6,6} Group order 1116 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y^-1 * z^2 * y^-1 * z^-2 * x * z^2 * y * z^-2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-3 * y * z^-2 * y * z^-1 * x ] T94.8 : Triangle type {2,6,12} Group order 744 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y * x * z * y * x * z * y^-1 * z^2 * y^-1 * z^2 * y^-1 * z^-2 ] T94.9 : Triangle type {2,6,12} Group order 744 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * z^2 * y^-1 * z^-5, y^-2 * z^2 * y * x * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T94.10 : Triangle type {2,6,96} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-14 * x * z^11 * y^-1 * x * z^3 * y^-1 * z^-2 ] T94.11 : Triangle type {2,6,96} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-58 * x * z^19 * y * z^-1 * x * y * z^-6 * x * z * y^-1 * z^-8 ] T94.12 : Triangle type {2,6,96} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^74 * y * z^-5 * x * z^16 ] T94.13 : Triangle type {2,6,282} Group order 564 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^77 * y * x * y * z^-6 * x * z * y^-1 * z^-3 * x * z^4 ] T94.14 : Triangle type {2,9,18} Group order 558 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z^2 * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T94.15 : Triangle type {2,10,10} Group order 620 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, y^10, (y * z^-1 * y^3)^2 ] T94.16 : Triangle type {2,10,10} Group order 620 Chiral action Defining relators: [ x^2, x * y * z, y^10, (y * z^-1 * y^3)^2, (y * z^-3 * y)^2, x * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-1 ] T94.17 : Triangle type {2,10,235} Group order 470 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-8 * x * z^23 * y * z^-9 * x * z^2 * y^-1 * z^-3 ] T94.18 : Triangle type {2,12,21} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-4 * z^-1 * y^3, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^2 * y^-1 * z^-4 * x * z^8 * y^-1 * z^-3 ] T94.19 : Triangle type {2,12,21} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-4 * z^-1 * y^3, z^3 * y^3 * x * z^3 ] T94.20 : Triangle type {2,12,114} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^24 * y * z^-1 * x * y^-1 * z^-8 * x * z^3 ] T94.21 : Triangle type {2,18,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, x * y^-6 * z^-1 * y^5, y^-1 * z * y^-1 * z * y^-4 * z * y^-1 * z * y^-2 * z^2 * y^-1 * z^2 ] T94.22 : Triangle type {2,18,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, y * x * z^11 * y * z^-4 * x * y * z^-5 * x * z ] T94.23 : Triangle type {2,18,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, (z * y^-1 * z)^3, x * z^3 * y^-1 * z^-4 ] T94.24 : Triangle type {2,24,36} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y^-3 * z^-1 * x * z^2 ] T94.25 : Triangle type {2,24,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z * y * x * z^5 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x ] T94.26 : Triangle type {2,24,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^9 * z^-1 * y * z^-1, z^-1 * x * z^3 * y * z^-4 * x * z^2 * y^-1 * z^-6 ] T94.27 : Triangle type {2,30,42} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^-8 * z^-1 * y * x, z^-5 * x * z^3 * y^-1 * z^-5 ] T94.28 : Triangle type {2,35,35} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^2 * z^-1 * y^3 * z^-1 * y * x * z ] T94.29 : Triangle type {2,66,66} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-4 * z * y^-2 * z^2 * y^-7 * z^4 * y^-1 * z ] T94.30 : Triangle type {2,66,66} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^2 * z^-29 * y^2 * z^-1 * y^8 * z^-1 * y * z^-4 * y * z^-17 ] T94.31 : Triangle type {2,189,378} Group order 378 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^127 * y^-60 * z ] T94.32 : Triangle type {2,190,190} Group order 380 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^62 * z^-128 ] T94.33 : Triangle type {2,376,376} Group order 376 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^61 * z^-127 ] T94.34 : Triangle type {3,3,6} Group order 1116 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z * y * x * z * x^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * x * z * y * x ] T94.35 : Triangle type {3,4,21} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-1 * x * z * y * x^-1 * y^-1 * z^-3 ] T94.36 : Triangle type {3,4,21} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-2 * x^-1 * z^3 ] T94.37 : Triangle type {3,5,15} Group order 465 Chiral action Defining relators: [ x^3, x * y * z, y^-5, z^-2 * x^-1 * y^-1 * x * z^2 * y, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1 ] T94.38 : Triangle type {3,5,15} Group order 465 Chiral action Defining relators: [ x^3, x * y * z, y^-5, x^-1 * z * y^2 * x * y^-2 * z^-1, x^-1 * y^-1 * z^-1 * y * x^-1 * z^2 * y ] T94.39 : Triangle type {3,5,15} Group order 465 Chiral action Defining relators: [ x^3, x * y * z, y^-5, z^-1 * y * x * y^-1 * x * z * y^-1 * z^-1, z^-3 * y * x^-1 * y^-1 * z^-1 * y ] T94.40 : Triangle type {3,5,15} Group order 465 Chiral action Defining relators: [ x^3, x * y * z, y^-5, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^2 * x^-1 * y * x^-1 * y^-1 * x * z^2 ] T94.41 : Triangle type {3,6,6} Group order 558 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z * y ] T94.42 : Triangle type {3,6,6} Group order 558 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * z^-1 * y * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T94.43 : Triangle type {3,6,6} Group order 558 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * x * z ] T94.44 : Triangle type {3,6,6} Group order 558 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, z * y^-1 * z * y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-2 * z^-1 * x^-1 ] T94.45 : Triangle type {3,6,6} Group order 558 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T94.46 : Triangle type {3,12,12} Group order 372 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x * z * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 ] T94.47 : Triangle type {3,12,12} Group order 372 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, y * z^-1 * y * z^-1 * y * z^-1 * x * y^3 * z^-1 * y * z^-1 ] T94.48 : Triangle type {3,12,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * z * y, y^-5 * x^-1 * z^4 ] T94.49 : Triangle type {3,12,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * z^3 ] T94.50 : Triangle type {3,15,105} Group order 315 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^2 * z^-1 * x^-1 * z^3, y * z^-3 * y * z^-1 * y^5 * z^-2 * y^2 ] T94.51 : Triangle type {3,95,285} Group order 285 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^6 * z^-1 * y^10 * z^-1 * y^76 * z^-1 ] T94.52 : Triangle type {3,96,96} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-78 * z * y^-10 * z * y^-5 * z ] T94.53 : Triangle type {3,96,96} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^76 * y^-14 * z^4 * y^-1 ] T94.54 : Triangle type {3,96,96} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-14 * y * z^-2 * y^14 ] T94.55 : Triangle type {3,282,282} Group order 282 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-77 * z * y^-10 * z * y^-5 ] T94.56 : Triangle type {4,4,33} Group order 396 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, z * y^-1 * z^-2 * x * z * y * x^-1 * z^5 ] T94.57 : Triangle type {4,4,95} Group order 380 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-5 * x * z^3 * y^-1 * z^-2 * x^-1 * z^2 * y * z^-3 * x^-1 * y * x^-1 * y ] T94.58 : Triangle type {4,4,95} Group order 380 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-81 * x * y * z^-13 ] T94.59 : Triangle type {4,4,188} Group order 376 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-80 * x * y^-1 * z^-13 ] T94.60 : Triangle type {4,6,12} Group order 372 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z^2 * y * x * z * y^-1 * z * y^-1 * z^-1 * x^-1 * z * y^-1 * z * y^-1 * z^-2 * x^-1 ] T94.61 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * x * z^-1 * x^-1 * z * x^-1 * z, z * y * z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z^6 ] T94.62 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T94.63 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, z * y^-1 * z^-1 * x * z^2 ] T94.64 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, y^2 * z^-1 * y * x^-1 * z^3 ] T94.65 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, (x * z * y)^2, x^-1 * y * z^-1 * x^-1 * z * y * z^-1 ] T94.66 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (y^-1 * x)^3, y^6 ] T94.67 : Triangle type {4,6,15} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z * y^-1 * z^-4 * x^-1 * y * x * z^3, y * z^-1 * x * z * y * z^-2 * x^-1 * z^-3 * x * z ] T94.68 : Triangle type {4,8,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * y^-1 * z * y^-1, z^3 * y^-1 * x * z^3 ] T94.69 : Triangle type {4,8,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3, z^3 * y^-1 * x * z^3 ] T94.70 : Triangle type {4,8,76} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^23 * y * z^-1 * x^-1 * y * z^-5 * x * z^7 ] T94.71 : Triangle type {4,12,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, y^-2 * z * x^-1 * y^-3, y * z^-3 * x^-1 * z^4 ] T94.72 : Triangle type {4,12,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-6 * x^-1 * z^4 * y * x * z * y * z^-3 * x^-1 * y^-1 * z^-7 ] T94.73 : Triangle type {4,12,48} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-10 * x^-1 * y^-1 * z^-1 * x * z * y * z^-2 * x * y^-1 * z^-7 ] T94.74 : Triangle type {4,14,70} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-1 * z^-2 * x^-1 * y * z^-2 * x^-1 * z, y^-4 * z^3 * y^-1 * z^4 * y^-1 * z ] T94.75 : Triangle type {4,20,28} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^5 * x^-1 * y^-3 * z * y, z^-3 * x * z^2 * y * x^-1 * z * y * x^-1 * y * x * y^-1 * z^-4 ] T94.76 : Triangle type {4,33,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-2 * z * y^-7 * z * y^-1 ] T94.77 : Triangle type {4,52,65} Group order 260 Chiral action Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^-2 * z * y^-2 * z^4 * x * z * y^-3 ] T94.78 : Triangle type {4,52,65} Group order 260 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, z^-1 * x^-1 * z * y^-1 * z^-3 * x^-1 * z^2 * y^-1 * z^-1, y^-3 * z * y^-4 * z^4 * y^-1 ] T94.79 : Triangle type {4,126,252} Group order 252 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^35 * z^-1 * y * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T94.80 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, x * z * y * x * z^-2, y^-1 * z^-1 * x^-2 * y * x * y^-1 ] T94.81 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, (y * z^-2)^2, z * y^3 * x^-1 * z * y * x ] T94.82 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-2 * y * x * y^-1, z * x^-1 * y * x^-1 * y^2 * x ] T94.83 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, (y * z^-2)^2, (x * z^-1 * y^2)^2, z^-1 * x * z * y * x * z^2 * y ] T94.84 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, y^2 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * z * x^-1 * z, y^-1 * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T94.85 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z^-1, y^2 * x^-2 * z^2 * x^-1 ] T94.86 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T94.87 : Triangle type {5,10,10} Group order 310 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, z^-2 * y^2 * z^-1 * y ] T94.88 : Triangle type {5,48,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-18 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-13 * z * y^-1 * z * y^-1 * z ] T94.89 : Triangle type {5,235,235} Group order 235 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^19 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T94.90 : Triangle type {5,235,235} Group order 235 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^14 * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T94.91 : Triangle type {6,6,6} Group order 372 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, z * y * z^-1 * y * z^-1 * x^-1 * z * x^-1 * z * y * x ] T94.92 : Triangle type {6,6,6} Group order 372 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, y^-1 * z * y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z ] T94.93 : Triangle type {6,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-2 * x * y^-1 * x * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-2 * x * z * y^-1 * z^-3 ] T94.94 : Triangle type {6,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, z * y^-1 * x * z^2 * y * x^-1 * z^3 * y^-1 * z^-2 * x^-1 * z^3 * y * z^-1 * x^-1 ] T94.95 : Triangle type {6,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^5 * y * x^-1 * z^3 * y^-1 * z^-3 ] T94.96 : Triangle type {6,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-32 * x * y^-1 * x * y^-1 * x * z^4 * y^-1 * z^-9 ] T94.97 : Triangle type {6,6,48} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^24 * y * z^-2 * x * z^5 * y^-1 * x * y^-1 * z^-4 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T94.98 : Triangle type {6,6,141} Group order 282 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^26 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x^-1 * z^5 * y * z^-1 * x^-1 ] T94.99 : Triangle type {6,12,22} Group order 264 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^4 * y^-1 * z^-1 * x * z^4 * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^5 ] T94.100 : Triangle type {6,12,84} Group order 252 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * y)^3, z^-2 * y * x^-1 * y * z^-2 ] T94.101 : Triangle type {6,14,42} Group order 252 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y * z^-2 * x^-1 * z^3, y^-2 * z^2 * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z ] T94.102 : Triangle type {6,14,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3 * y^-1 * z * y^-2 * z^2 * y^-1 ] T94.103 : Triangle type {6,14,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^3 * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 ] T94.104 : Triangle type {6,20,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, z^-1 * y * z^-1 * y^3 * z^-4 ] T94.105 : Triangle type {6,21,21} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, z * y^-1 * z^7 * y^-6 * z^2 * y^-2 * z^2 ] T94.106 : Triangle type {6,24,60} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * x^-1 * y^-4, y * z^-2 * x^-1 * z * y * x^-1 * y * z^-1 * x * z^3 ] T94.107 : Triangle type {6,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, z^-1 * y^5 * z^-2 * y * z^-1 ] T94.108 : Triangle type {6,39,78} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y * z^-2 * y^3 * x^-1 * y^2 * z^-5 ] T94.109 : Triangle type {6,39,78} Group order 234 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y * z^-2 * y^3 * z^-1 * y * z^-4 ] T94.110 : Triangle type {6,39,78} Group order 234 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^9 * z^-7 * y * z^-1 * y^6 * z^-6 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T94.111 : Triangle type {6,76,228} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^9 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T94.112 : Triangle type {6,114,114} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^9 * z^-7 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T94.113 : Triangle type {8,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z * x^-1 * y^-1 * z * y^-1, z^4 * y^-1 * z^-5 * x ] T94.114 : Triangle type {8,108,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^4 ] T94.115 : Triangle type {8,108,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-3 ] T94.116 : Triangle type {9,9,9} Group order 279 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^-1 * x^-1 * y ] T94.117 : Triangle type {9,18,26} Group order 234 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, z^-1 * x^-3 * y^-1 * x^2, x^-9 ] T94.118 : Triangle type {9,72,72} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-9 * z * y^-4 * z^2 * y^-4 * z * y^-1 * z^2 ] T94.119 : Triangle type {9,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^4 * z^-3, x^-9 ] T94.120 : Triangle type {9,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^-9, y^-1 * z * y^-1 * z * x^-1 * z^4 ] T94.121 : Triangle type {9,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T94.122 : Triangle type {10,12,24} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^10 ] T94.123 : Triangle type {10,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T94.124 : Triangle type {10,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-8 ] T94.125 : Triangle type {10,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-3 * y^5 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T94.126 : Triangle type {10,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-4 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-3 ] T94.127 : Triangle type {12,12,57} Group order 228 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-4 * x * z * y^-1 * x * z^2 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1 ] T94.128 : Triangle type {12,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-3 * x^-1 * z * y^-2 * z ] T94.129 : Triangle type {12,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-3 * x^-1 * y^-1 * z^3 ] T94.130 : Triangle type {12,36,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, y^3 * x^-1 * y * z^-1 * y ] T94.131 : Triangle type {12,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^2 * z^-3 ] T94.132 : Triangle type {12,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * y * z^-2, y^-3 * x^2 * y^-3 ] T94.133 : Triangle type {12,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-1 * y^4 * x^-1 * y * z^-1 * y * z^-4 * y * z^-1 * y^3 ] T94.134 : Triangle type {12,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, y^-1 * x * z * x^-2 * y^-1 * z * y^-1 * z ] T94.135 : Triangle type {12,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-12, y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T94.136 : Triangle type {14,16,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^4 * x^-1 * y^-3 * z^-1, x * z^-1 * x * z^-1 * x * z^-2 * x * z^-1 * x * z^-1 * y * x^2 * z^-1 ] T94.137 : Triangle type {14,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-5 * z, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T94.138 : Triangle type {15,30,70} Group order 210 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^2, y^-1 * z^-1 * y * x * z * x^-1, y * x^-4 * z^2 * x^-1 * z ] T94.139 : Triangle type {15,30,70} Group order 210 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, z^-1 * x^-1 * y^-1 * x * y^-2, z * x^-2 * z^2 * x^-1 * z^5 ] T94.140 : Triangle type {15,30,70} Group order 210 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * y)^3, x^-1 * y * x^-2 * z * y^2 ] T94.141 : Triangle type {15,42,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, y^-2 * z^4 * y^-8 ] T94.142 : Triangle type {16,26,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-3 * z^3, x^4 * y^-4 * x^2 * z^-4 * x^6 ] T94.143 : Triangle type {18,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, x^-4 * z * x^-1 * y, y * z^-1 * y * x^-1 * y^3 ] T94.144 : Triangle type {18,18,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (z^-1 * x)^3, (z^-1 * y)^3, y^-1 * z^-1 * x^-2 * z^2 * y^-1 ] T94.145 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-2 * y^-1 * x^2 * z * y^-1 * z, x^7 * z^-1 * x * z^-1 ] T94.146 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y * x^-6 * y^5 ] T94.147 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-4 * y * x * z^-1, z^-4 * y^2 * z^-4 ] T94.148 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-1 * y * x^-6 * y^3 * z^-1 * y, x^-2 * z^2 * x^-3 * z * x^-1 * z^3 ] T94.149 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8 * y^-2, y * z^-5 * x^-1 * z * y * z^-1 * x * z^3 ] T94.150 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1 * z^-3 * x^-1 * z^3 * y^-1 * z^-1, (x * z^-4)^2 ] T94.151 : Triangle type {18,18,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, (z^-1 * x)^3 ] T94.152 : Triangle type {18,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^-4 * y * x * z, y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-4 ] T94.153 : Triangle type {18,24,24} Group order 216 Chiral action Defining relators: [ x * y * z, y^-2 * x^2 * z * y^-1, z^-2 * x^2 * z^-1 * y ] T94.154 : Triangle type {18,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z * x^-1 * y^-1 * x * z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T94.155 : Triangle type {18,24,24} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, z^-1 * y^4 * z^-3, x * z * y^-1 * x * z * x^-5 * y^-1 ] T94.156 : Triangle type {20,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * y * z^-1 * y * z^-4, x^-1 * z * y * x^-8 ] T94.157 : Triangle type {20,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^5 * z^-1 * y * z^-2, x^-1 * z * y * x^-8 ] T94.158 : Triangle type {21,30,30} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * z * x^-2, x^5 * z * x^-1 * y, y^8 * z^-2 ] T94.159 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T94.160 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-4 ] T94.161 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x ] T94.162 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T94.163 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-2 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T94.164 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^6 * y^-7, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T94.165 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-3 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T94.166 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-3 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-5 ] T94.167 : Triangle type {22,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x^2 ] T94.168 : Triangle type {25,40,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-7 * y^3 * x^-6 ] T94.169 : Triangle type {25,40,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^4 * y^-2, z^10 * y^-1 * z^5 ] T94.170 : Triangle type {25,40,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^6 * x^-4 * y^6 * x^-1 * y^4 ] T94.171 : Triangle type {25,40,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-4 * z^2, y^5 * x^-1 * y * z^-5 * y * z^-1 * y^3 ] T94.172 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^3 * y^-4 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T94.173 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-2, x^2 * y^-1 * x^6 * y^-6 * x^2 ] T94.174 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4 * z * y^-2, z^-4 * x * z^-1 * x * z^-4 * x * y * z^-4 ] T94.175 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^-5 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T94.176 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-4 ] T94.177 : Triangle type {28,98,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-2 * z * x^-1 * z^4 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T94.178 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^2 * x^-1 * y * z^-1 * y, x^-1 * z * y * x^-9 ] T94.179 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y^-2 * x * y^-1 * x * y^-3, z^2 * x^-3 * z^4 ] T94.180 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-1 * z * y * x^-9 ] T94.181 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-2 * y * x^2 * z^-3, y^-1 * x^2 * y^-1 * x^2 * y^-4 ] T94.182 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-1 * z * y * x^-9 ] T94.183 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-4 * y^-1 * x * z, y^-2 * x * y^-2 * z * y^-3 * x^3 * y^-5 * x^2 * y^-1 ] T94.184 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^2 * x^-3 * z^4, y^4 * x^-1 * y * z^-1 * y * z^-1 ] T94.185 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, y * x^-1 * y^3 * x^-6 * y * x^-2 * y ] T94.186 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-4 * y * x^-1 * y, z^-4 * y^2 * z^-4 ] T94.187 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-19 * y^2 * x^-8 * y * x^-1 * z * x^-3 ] T94.188 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^6 * z^-3 * y^9 ] T94.189 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-8 * x^3 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T94.190 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^6 * y^-5 * x^2, z^-4 * x * z^-4 * x^2 * z^-4 ] T94.191 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^3 * z^-1 * x * z^-1 * x * z^-4 * x^7 ] T94.192 : Triangle type {33,66,66} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-17 * z^2 * x^-6 * y^2 * x^-8 ] T94.193 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x * z^-1 * x * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-4 * x * z^-2 ] T94.194 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^5 * z^-4 * y * x^-1 * y^5 ] T94.195 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-3 * y * x^-1 * y^6 * x^-3 * z^2 * x^-6 ] T94.196 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-20 * y * x^-1 * y^2 * x^-7 * y^2 * x^-8 ] T94.197 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-2 ] T94.198 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-4 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T94.199 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^3 * z^-1 * x * z^-4 * x^6 ] T94.200 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-7, z^-3 * y * z^-5 * y^2 * z^-4 ] T94.201 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-5, z^-12 * y^5 * z^-3 ] T94.202 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y ] T94.203 : Triangle type {39,65,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-10 * x^4 * y^-2 * z * y^-7 ] T94.204 : Triangle type {48,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^16 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T94.205 : Triangle type {48,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-3 ] T94.206 : Triangle type {48,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-11 * y^6 * z^-1 * y * z^-1 ] T94.207 : Triangle type {48,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-3 * y^7, x^6 * z^-4 * x^7 ] T94.208 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-44 * y * x^-1 * y * x^-9 * y * x^-8 ] T94.209 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-7 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x^3 ] T94.210 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T94.211 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x ] T94.212 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^4 * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^4 ] T94.213 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^2 * z^-4, y^-9 * z^2 * y^-4 ] T94.214 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-9 * z^5 * y^-1 * z * y^-5 ] T94.215 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, x^4 * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T94.216 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, z * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T94.217 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * z^2 * x^-3, z^-10 * y * z^-4 ] T94.218 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-17 * z * y^-7 * z * y^-7 ] T94.219 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^-13 * x * y^-1 * x * y^-1 ] T94.220 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-4 * x^6 * y^-6 * x * y^-1 * x * y^-1 ] T94.221 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^6, x^4 * z^-3 * x^7 ] T94.222 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-16 * x * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 * x * z^-2 ] T94.223 : Triangle type {64,96,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^4 * x^-5 * z^4 * x^-1 * z * x^-1 * z^6 ] T94.224 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-35 * x^3 * y^-11 ] T94.225 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^3 ] T94.226 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-6, z^-4 * y * z^-5 * y^2 * z^-4 ] T94.227 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^4 * z^-3 * y^2 * x^-4 * y^3 ] T94.228 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-50 * x^2 * y^-12 ] T94.229 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, y^-5 * x * y^-2 * z^3 * y^-4 ] T94.230 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T94.231 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^6, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T94.232 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T94.233 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-7, z^-9 * y * z^-4 ] T94.234 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-2 * z^28 * x^-2 * z * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T94.235 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^2 * y^-1 * z * y^-3 * z^11 ] T94.236 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^8 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T94.237 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^-2 * z * y^-9 * z * y^-5 ] T94.238 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^11 * y^-1 * z * y^-1 * z^4 * x^-1 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T94.239 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x^2 ] T94.240 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T94.241 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^6 * z^-4 * x * y^-6 * x^3 ] T94.242 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^8 * x^-14 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T94.243 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, x^5 * z^-4 * x * y^-6 * x^2 ] T94.244 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-5 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T94.245 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T94.246 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-5 ] T94.247 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-12 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-6 ] T94.248 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^8 * z^-4 * x^2 * z^-4 * x * y^-1 * x * y^-1 * x^2 ] T94.249 : Triangle type {95,190,190} Group order 190 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^95, y * z^-1 ] T94.250 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-20 * x * y^-11 ] T94.251 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-20 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-5 * x * z^-2 ] T94.252 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y ] T94.253 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y^5 * z^-4 * y * x^-1 * y^5 ] T94.254 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 ] T94.255 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x^-2 * y^-1, y^73 * x^-1 * y^21, x * z^-1 ] T94.256 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T94.257 : Triangle type {189,189,189} Group order 189 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^4 * z^-2, y^3 * z^-1 * y * z^-5 * y * x^-1 * y^5 ] Genus 95 T95.1 : Triangle type {2,4,192} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-192 ] T95.2 : Triangle type {2,4,192} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-78 * x * z^9 * y^-1 * z^-8 ] T95.3 : Triangle type {2,4,380} Group order 760 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-47 * x * y^-1 * z^-142 ] T95.4 : Triangle type {2,6,285} Group order 570 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-57 * x * z^19 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-6 ] T95.5 : Triangle type {2,8,128} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^40 * y * x * z * y * x * z^21 ] T95.6 : Triangle type {2,8,128} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-27 * x * z^21 * y * z^-1 * x * y^-1 * z^-13 ] T95.7 : Triangle type {2,12,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3)^2, z^2 * y * z^-1 * y^2 * z^-1 * x * z^5 ] T95.8 : Triangle type {2,12,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3)^2, x * z^2 * y * x * z * y^-1 * z^-5 ] T95.9 : Triangle type {2,12,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-7 * x * z * y * x * z^3 * y * x * z^4 * y * x * z * y * x * y * z^-9 * x * y^-1 * z^-9 ] T95.10 : Triangle type {2,12,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, x * z^8 * y * x * y * z^-5 * x * z * y^-1 * z^-3 ] T95.11 : Triangle type {2,12,228} Group order 456 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^22 * y * z^-3 * x * z^7 * y^-1 * z^-3 * x * z ] T95.12 : Triangle type {2,16,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, x * z * y * z^-1 * x * z^11 * y * x * y * x * z^9 * y^-1 * z^-2 ] T95.13 : Triangle type {2,16,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-3 * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y^3 * x * y^-1, z^-9 * x * z^9 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T95.14 : Triangle type {2,20,44} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^3 * x * y^-3 * z * y * x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y^5, z^-2 * x * z^3 * y * x * z^9 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T95.15 : Triangle type {2,22,209} Group order 418 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^9 * y * z^-3 * x * z^6 ] T95.16 : Triangle type {2,78,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y * z^-1 * y^11 * z^-4 * y^20 * z^-2 ] T95.17 : Triangle type {2,191,382} Group order 382 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^128 * y^-62 ] T95.18 : Triangle type {2,192,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-60 * y^33 * z^-2 ] T95.19 : Triangle type {2,192,192} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^63 * z^-128 * y ] T95.20 : Triangle type {2,380,380} Group order 380 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^62 * z^-127 * y ] T95.21 : Triangle type {3,285,285} Group order 285 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^6 * z^-1 * y^88 ] T95.22 : Triangle type {4,4,96} Group order 384 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-83 * x * y * z^-12 ] T95.23 : Triangle type {4,4,96} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^33 * y * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-5 * x * z ] T95.24 : Triangle type {4,4,96} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^33 * y * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-5 * x^-1 * z ] T95.25 : Triangle type {4,4,96} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-35 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * y * z^-6 ] T95.26 : Triangle type {4,4,190} Group order 380 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-81 * x * y^-1 * z^-13 ] T95.27 : Triangle type {4,6,42} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, y * x^-1 * z * y * x^-1 * z^4 ] T95.28 : Triangle type {4,8,152} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-25 * x * z^3 * y * z^-9 ] T95.29 : Triangle type {4,8,152} Group order 304 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-25 * x * z * y * z^-11 ] T95.30 : Triangle type {4,10,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^2 * z^-1, z^16 ] T95.31 : Triangle type {4,10,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1 * y)^2, y^3 * x^-1 * y^2 * z^-1, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-2 * x^-1 * z^4 ] T95.32 : Triangle type {4,10,16} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, y^10 ] T95.33 : Triangle type {4,10,16} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, z^-4 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-3 * x * y^-1 * z^-2 ] T95.34 : Triangle type {4,14,140} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-1 * z^-2 * x^-1 * y * z^-2 * x * z, (y^-4 * z^2 * y^-1)^2 ] T95.35 : Triangle type {4,44,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * z^-1 * y * z^-2 * y^2 * x * z^-4 * y^9 * z^-1 ] T95.36 : Triangle type {4,52,130} Group order 260 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-2 * z^-3 * x^-1 * z^-1 * x^-1 * z^2, z^-1 * x^-1 * z * y^-1 * z^-3 * x^-1 * z^2 * y^-1 * z^-1, y^-3 * z * y^-3 * x * y^-2 * z^3 * y^-1 ] T95.37 : Triangle type {4,128,128} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-31 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-13 ] T95.38 : Triangle type {4,128,128} Group order 256 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^36 * z^-1 * y * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T95.39 : Triangle type {6,24,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^3 * z^-2 * y, z^4 * y * x^-1 * z^5 ] T95.40 : Triangle type {6,24,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * y^3 * z^-2 * y, z * y^-1 * z^-3 * x * z^5 ] T95.41 : Triangle type {6,40,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, (y^2 * z^-2 * y)^2 ] T95.42 : Triangle type {6,40,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, y^6 * z^-1 * y^2 * z^-1 ] T95.43 : Triangle type {6,40,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^3 * z^-2 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 ] T95.44 : Triangle type {6,40,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y^-3 * z^3 * y^-1 * z * x^-1 * y^-3 * z^3 * y^-1 * z^3 ] T95.45 : Triangle type {6,228,228} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^10 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T95.46 : Triangle type {8,8,64} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^10 * y * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 * x * y * z^-4 * x^-1 * z ] T95.47 : Triangle type {8,8,64} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-18 * x * y^-1 * x * y^-1 * z^-12 ] T95.48 : Triangle type {8,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^8, z^-1 * x^-1 * z^4 * y^-1 * z^-4 ] T95.49 : Triangle type {8,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^8, z^3 * y * z^-1 * x^-1 * z^5 ] T95.50 : Triangle type {8,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * y * x * z^-1 * y, z^-1 * x^-3 * z * y^-1 * z^-1 ] T95.51 : Triangle type {8,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * z^2, z^-2 * y * x * z^-1 * y ] T95.52 : Triangle type {8,20,24} Group order 240 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (y * z^-2)^2, x^8, y * z^-1 * y * x^2 * z^-1 * y^2, y * x * z * y * x^-1 * z^3 ] T95.53 : Triangle type {8,20,24} Group order 240 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, (y * z^-2)^2, x^8, y * z^-1 * y * x^2 * z^-1 * y^2, z^-1 * x * z * y^-1 * x * y^-1 * z^-2 ] T95.54 : Triangle type {8,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^-3 * z * x^-1 * z * x^-1 * y^-5 ] T95.55 : Triangle type {8,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, x^8, y^-3 * z * x^-1 * z * x^-1 * y^-5 ] T95.56 : Triangle type {8,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^4 * y^-4 * x * y^-2 * z * y^-2 ] T95.57 : Triangle type {8,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^4 * y^-4 * z * y^-1 * z^3 ] T95.58 : Triangle type {8,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^19 * y^-4 * z * y^-1 * z^2 ] T95.59 : Triangle type {8,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y^12 ] T95.60 : Triangle type {10,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x^-1 * y^-3, x^-1 * z * y * x^-1 * y^-1 * z^2, y^-2 * x * y^-1 * x * y^-1 * z^2 ] T95.61 : Triangle type {10,44,44} Group order 220 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x^-3 * y^2 * z^-1 * y * z^-1 * y^10 ] T95.62 : Triangle type {11,20,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^-2 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T95.63 : Triangle type {11,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^6 * x^-2 * y * z^-5 * y * z^-1 * y * z^-1 * y^3 ] T95.64 : Triangle type {11,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^-3 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T95.65 : Triangle type {11,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z^2 ] T95.66 : Triangle type {11,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^11 * y^-6 * z^2 ] T95.67 : Triangle type {11,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^4 * y^-5 ] T95.68 : Triangle type {12,12,20} Group order 240 Chiral action Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, y^2 * x^2 * z^2, x^12 ] T95.69 : Triangle type {12,12,20} Group order 240 Chiral action Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y * z^-1 * x^2 * z * y, (x * y^-1 * x * y^-3)^2 ] T95.70 : Triangle type {12,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, (x * y^-2)^2, z * y^-1 * z^-1 * x^-1 * z * y * x ] T95.71 : Triangle type {12,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, (x * y^-2)^2, x * z * y * x^-1 * y^-1 * z^-2 ] T95.72 : Triangle type {12,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^-12, x * z * y^-1 * z^-3 * x^-1 * z * y^-1 * x * y^-1 * z^-1 * x * y^-1 ] T95.73 : Triangle type {12,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^-12, z^-3 * x^-1 * z * y * x^-1 * y^-1 * x * y^-1 * z^-3 ] T95.74 : Triangle type {12,12,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-8 * y, z^-9 * x^-1 * y * x^-1 * y * x * y^-1 * x * y^-1 * z^-7 ] T95.75 : Triangle type {12,12,114} Group order 228 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^4 * y^-1 * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-4 * x * z^2 ] T95.76 : Triangle type {14,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x * y^-1 * x * y^-1 * x * z * y^-1 * z^-1, (x * z^-3)^2 ] T95.77 : Triangle type {14,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, y^-2 * x^9 * y^-2 * x^2 * y^-2 * x ] T95.78 : Triangle type {14,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^2, y^-2 * x^4 * y^-4 ] T95.79 : Triangle type {14,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z * x^-1 * z^2 * y^-1 * z * x^-1 * z^4 * x^-1 ] T95.80 : Triangle type {14,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-2)^2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * z * y ] T95.81 : Triangle type {15,42,70} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^5 * y^-6, x^4 * y^-5 * x * z^-5 * x^5 ] T95.82 : Triangle type {16,16,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z^-2 * x * z^3 * y^-1 * z^-1 * x^-1 * z * y * z^-5 ] T95.83 : Triangle type {16,16,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y^2 * x^-1, z^-2 * x * y^-1 * x * y^-1 * x * z^5 * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T95.84 : Triangle type {20,20,22} Group order 220 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, y^2 * x^2 * z^-2, y * x^-5 * y^4 ] T95.85 : Triangle type {20,20,22} Group order 220 Chiral action Defining relators: [ x * y * z, y * x^-1 * y^-1 * x * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y * x^-5 * y^4 ] T95.86 : Triangle type {20,20,22} Group order 220 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^-1 * z * y^-1 * x * z * y, x^-7 * y^2 * x^-1 * z ] T95.87 : Triangle type {20,20,22} Group order 220 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z^-1 * y, y * x^-1 * y^-1 * x * z^-2, x^-6 * y^2 * x^-1 * y ] T95.88 : Triangle type {20,20,22} Group order 220 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * z^-1 * x * z * y^-1 * z^-4 * x * y^-1 * x * y^-1 * x * y^-1 ] T95.89 : Triangle type {20,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^2 ] T95.90 : Triangle type {20,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-5 * y^3 * z^-2 * y^3, z^-1 * x^6 * z^-5 * x * z^-4 ] T95.91 : Triangle type {20,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^2 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^3 ] T95.92 : Triangle type {20,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^5, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-2 ] T95.93 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^8 * z^-4 * y * x^-3 * y^7 ] T95.94 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-1 * z^20 * x^-1 * z * x^-10 * y * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T95.95 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-11 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 * x * z^-2 ] T95.96 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^3 * z^-3, x^-1 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T95.97 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^10, x^-3 * y^2 * x^-4 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-2 ] T95.98 : Triangle type {39,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-4 * y * x^-1 * z^4 * x^-4 * z^2 * x^-7 ] T95.99 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^14 * y^-1 * x^12 * y^-1 * x^69, y * z^-1 ] T95.100 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-32 * y^2 * x^-15 ] T95.101 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-8 * y^2 * x^-4 * y^4 * x^-9 ] T95.102 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T95.103 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^6 * y^-5 * x^2, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y ] T95.104 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-2 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-8 ] T95.105 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-4 * x^6, y^5 * z^-4 * y * x^-3 * y^4 ] T95.106 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-4 * x^5 * y^-6 * x * y^-2 ] T95.107 : Triangle type {96,192,192} Group order 192 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^4 * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T95.108 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x^-2 * y^-1, y^74 * x^-1 * y^21, x * z^-1 ] T95.109 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-51 * x * y^-12 ] T95.110 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^33 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T95.111 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^17 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T95.112 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^7 * y^-5 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T95.113 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^8 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 * x ] T95.114 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^5 * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T95.115 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^6 * z^-1 * y^4 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T95.116 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^2 ] T95.117 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^2 * x^-1 * y^6 * x^-6 * y^3 ] T95.118 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^5 * z^-2 * x^3 * y^-6 * x^3 ] T95.119 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-4 * x^3 * y^-6 * x * y^-1 ] T95.120 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * x^-5 * y^2, z^-4 * x * z^-4 * x * y * z^-4 ] T95.121 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4 * z * y^-2, z^-5 * x * z^-4 * x * y * z^-4 ] T95.122 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T95.123 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-2 * y^8, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-2 ] T95.124 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^4 * y^-6 * z^5 * y^-1 * z * y^-1 * z^5 ] T95.125 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T95.126 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^6 * y^-1 * z * y^-1 * z^4 * x^-2 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T95.127 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^5 * z^-1, y^4 * z^-1 * y * z^-5 * y * x^-1 * y^6 ] T95.128 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-5 * x, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T95.129 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T95.130 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^4 * z^-2, y^4 * z^-1 * y^4 * x^-6 * y^3 ] T95.131 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T95.132 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^7, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T95.133 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-4 * z * y^-7 * z^3 * y^-8 ] T95.134 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-11 * z^3 * x^-6 * z * x^-8 ] T95.135 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^7 * z^-3 * y^10 ] T95.136 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T95.137 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * z^-2 * x^6 ] T95.138 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-21 * y * x^-7 * y^2 * x^-9 ] T95.139 : Triangle type {191,191,191} Group order 191 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^8, y^-9 * z^2 * y^-4 ] Genus 96 T96.1 : Triangle type {2,3,9} Group order 3420 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 * x, x * z * y * z^-1 * x * z^3 * y * z^-1 * x * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 * x * y^-1 * z^-3 ] T96.2 : Triangle type {2,3,9} Group order 3420 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, y * x * z * y * x * z^3 * y * x * z * y * x * z * y^-1 * z^3 * y^-1 * z^-1 * x * z ] T96.3 : Triangle type {2,3,9} Group order 3420 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^3 * y * x * z^2 * y * x * z^2 * y * x * z * y^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T96.4 : Triangle type {2,4,99} Group order 792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-80 * x * z^10 * y * z^-1 * x * y^-1 * z^-6 ] T96.5 : Triangle type {2,4,194} Group order 776 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-194 ] T96.6 : Triangle type {2,4,384} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-48 * x * y^-1 * z^-143 ] T96.7 : Triangle type {2,6,98} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-60 * x * z^17 * y * x * z * y * x * y^-1 * z^-17 ] T96.8 : Triangle type {2,8,66} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-12 * x * z^7 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-6 * x * z * y^-1 * z^-1 ] T96.9 : Triangle type {2,8,66} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-41 * x * z^5 * y * z^-1 * x * y^-1 * z^-17 ] T96.10 : Triangle type {2,10,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, y * x * y^-3 * z^-1 * y * z^-2, y^10, z^-4 * x * z^5 * y^-1 * z^-2 ] T96.11 : Triangle type {2,10,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^10, z^-2 * x * z^3 * y^-1 * z^-6 ] T96.12 : Triangle type {2,10,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y^10, z^-4 * x * z^2 * y^-1 * z^-5 ] T96.13 : Triangle type {2,10,50} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^10, y * z^-1 * y^4 * z^-1 * y * z^-2, z^2 * y * x * z * y * x * y * z^-2 * x * z^2 ] T96.14 : Triangle type {2,10,50} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^10, y * z^-1 * y^4 * z^-1 * y * z^-2, z^2 * y * x * z * y * x * y^-1 * z^-3 * x * z ] T96.15 : Triangle type {2,10,50} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^36 * y^-1 * z^-7 * x * z^2 * y^-1 * z^-3 * x ] T96.16 : Triangle type {2,10,50} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^26 * y * x * z * y * x * y * z^-8 * x * y^-1 * z^-3 * x * z^8 ] T96.17 : Triangle type {2,10,240} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-14 * x * z^20 * y * x * z^3 * y^-1 * z^-9 ] T96.18 : Triangle type {2,14,34} Group order 476 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^14, z^-7 * x * z^4 * y * x * z * y * x * y * x * y^-1 * z^-18 ] T96.19 : Triangle type {2,14,224} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-4 * y^5 * z^-4, z^-1 * x * z^14 * y * z^-4 * x * z^8 * y^-1 * z^-3 ] T96.20 : Triangle type {2,18,26} Group order 468 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-2 * z * y * x * z * y^4 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * x * y^-4, z^15 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^2 ] T96.21 : Triangle type {2,26,208} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-13 * z^4 * y^-5 * z^4 ] T96.22 : Triangle type {2,30,70} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^7 * z^-1 * y * z^-1, z^-5 * x * z^2 * y * z^-6 ] T96.23 : Triangle type {2,34,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-21 * z^4 * y^-5 * z^4 ] T96.24 : Triangle type {2,50,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-12 * y^12 * z^-4 * y^21 ] T96.25 : Triangle type {2,51,68} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, z * y^-1 * z * y^-2 * z * y^-1 * z * y^-4 * z^3 * y^-1 * z ] T96.26 : Triangle type {2,98,196} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-62 * y^33 * z^-2 ] T96.27 : Triangle type {2,99,99} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-95 * z * y^-1 ] T96.28 : Triangle type {2,130,195} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-28 * y^13 * z^-2 * y^19 * z^-1 * y ] T96.29 : Triangle type {2,193,386} Group order 386 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^129 * y^-62 * z ] T96.30 : Triangle type {2,194,194} Group order 388 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^64 * z^-130 ] T96.31 : Triangle type {2,384,384} Group order 384 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^63 * z^-129 ] T96.32 : Triangle type {3,3,98} Group order 588 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^4 * y^-1 * z^-6 * x^-1 * z^5 ] T96.33 : Triangle type {3,3,193} Group order 579 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-4 * x^-1 * y^-1 * z^-5 * x^-1 * z^3 ] T96.34 : Triangle type {3,4,10} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^10 ] T96.35 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^3, z^2 * x^-1 * y^-1 * x * y^-1 * z^2 ] T96.36 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y^-1 * z, z^-2 * x^-1 * y^-1 * x * y^-2 * z^-1, z * x^-1 * z * y^-1 * x * y^-1 * z^2 ] T96.37 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * y * z^-2, z^-1 * y * x * y^-1 * x * z * y^-1 * z^-1 ] T96.38 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-2)^2, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T96.39 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-2)^2, y * z^-1 * y * x^-1 * z^3 ] T96.40 : Triangle type {3,18,18} Group order 342 Chiral action Defining relators: [ x^3, x * y * z, (y * z^-2)^2, y^2 * z^-1 * x^-1 * y^2 * z^-1 ] T96.41 : Triangle type {3,26,52} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y^3 * z^-7 * y^6 * z^-2 * y * z^-1 * y^4 ] T96.42 : Triangle type {3,50,75} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * z^-1 * y * z^-3 * y^11 * z^-3 * y^2 * z^-2 ] T96.43 : Triangle type {3,97,291} Group order 291 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^7 * z^-1 * y^10 * z^-1 * y^77 * z^-1 ] T96.44 : Triangle type {3,98,98} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^77 * y^-14 * z^5 * y^-1 ] T96.45 : Triangle type {3,288,288} Group order 288 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-78 * z * y^-10 * z * y^-6 ] T96.46 : Triangle type {4,4,97} Group order 388 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * z^-3 * x * z^-2 * x * y^-1 * z^4 ] T96.47 : Triangle type {4,4,97} Group order 388 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^84 * y * x * z^12 ] T96.48 : Triangle type {4,4,192} Group order 384 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-83 * x * y^-1 * z^-12 ] T96.49 : Triangle type {4,6,6} Group order 456 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, y^-1 * z^2 * y^-1 * z^-3 * y * x * y^-1 * z^-2 * x * z ] T96.50 : Triangle type {4,6,56} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-5 * x * z^8 * y * z^-2 * x^-1 * z * y * x^-1 * y * x * y^-1 * z^-8 ] T96.51 : Triangle type {4,12,30} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-2 ] T96.52 : Triangle type {4,15,20} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x * z^-2 ] T96.53 : Triangle type {4,15,20} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-3 * y^3 * z^-1 * y^3, y^-15 ] T96.54 : Triangle type {4,16,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^2 * y * x * z * y * z^-7 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x^-1 * z ] T96.55 : Triangle type {4,44,132} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, z^-1 * y * z^-1 * y * z^-2 * y^4 * z^-3 * y^8 * z^-1 ] T96.56 : Triangle type {4,65,260} Group order 260 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^33 * z^-1 * y^5 * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T96.57 : Triangle type {4,66,66} Group order 264 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-1 * z^18 * y^-5 * z^2 * y^-4 * z^2 * y^-1 ] T96.58 : Triangle type {4,66,66} Group order 264 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-33 * z^3 * y^-1 * z * y^-12 * z * y^-7 * z^2 * y^-4 * z * y^-1 ] T96.59 : Triangle type {4,256,256} Group order 256 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^35 * z^-1 * y * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T96.60 : Triangle type {5,10,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, z^-1 * x * y^-1 * x^2 * y^-1 * z^-1 * x ] T96.61 : Triangle type {5,10,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y * x^-1 * z * y, z^-3 * y^2 * z^-3 ] T96.62 : Triangle type {5,10,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, (y^-1 * x)^3, (x * z^-2)^2 ] T96.63 : Triangle type {5,10,15} Group order 300 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, x^-5, y^10 ] T96.64 : Triangle type {5,12,12} Group order 300 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x * y^-1 * x * z * y, y^-1 * z^-1 * y * x^-1 * z * x^-1, y^-5 * z * y^-1 * z * x * y^-3 * z ] T96.65 : Triangle type {5,12,12} Group order 300 Chiral action Defining relators: [ x * y * z, x^-5, x^-1 * y^-2 * x * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-3 * z * x * z * y^-1 * z * y^-1 ] T96.66 : Triangle type {5,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^4 * y^-2 * z^3 * y^-1 * z^2 ] T96.67 : Triangle type {5,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (z * y^-1 * z * y^-2 * z)^2 ] T96.68 : Triangle type {5,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^-6 * z * y^-2 * z * y^-2 ] T96.69 : Triangle type {5,49,245} Group order 245 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z * y^-15 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T96.70 : Triangle type {5,50,50} Group order 250 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * y * z^-3 * y^3 ] T96.71 : Triangle type {5,50,50} Group order 250 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * y * z^-2 * y * z^-1 * y^2 ] T96.72 : Triangle type {5,50,50} Group order 250 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^18 * z^-1 * y^3 * z^-1 * y * z^-1 * y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T96.73 : Triangle type {5,50,50} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^3 * y^-1 * z^2 * y^-1 * z^3 ] T96.74 : Triangle type {5,50,50} Group order 250 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * x^-1 * y * x^-1 * z^-5 ] T96.75 : Triangle type {5,50,50} Group order 250 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z * y^-1 * z^15 * y^-3 * z * y^-6 * z * y^-6 * z * y^-1 * z * y^-11 * z * y^-1 ] T96.76 : Triangle type {5,240,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-19 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-13 * z * y^-1 * z * y^-1 * z ] T96.77 : Triangle type {5,240,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-17 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-13 * z * y^-1 * z * y^-1 * z ] T96.78 : Triangle type {6,6,49} Group order 294 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, y^-1 * z^3 * x^-1 * z^4 ] T96.79 : Triangle type {6,6,49} Group order 294 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-3 * x^-1 * z^4 ] T96.80 : Triangle type {6,6,49} Group order 294 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-40 * x^-1 * y^-1 * z^-8 ] T96.81 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-2)^2, (z^-1 * x)^3, (y * z^-2)^2, y * z^-1 * x^-2 * y * z^-1 * y ] T96.82 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (y * z^-1 * y)^2, (x * z * y)^2, x^-1 * y^-2 * x^2 * y^-1 * z * y ] T96.83 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, x^-1 * z * y^-1 * x^2 * z^2 * y, y^-1 * x * z^-1 * x^2 * y^-1 * z^-1 * x ] T96.84 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * z^2, x^6, y^-2 * x^2 * y^-1 * z, y^-7 ] T96.85 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, z * x^-1 * y^-1 * x * z * x^-1, y * z^-1 * y * x^-1 * z^2 * y ] T96.86 : Triangle type {6,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, (x * z^-1 * y)^2, y^-7 ] T96.87 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, z * y^-2 * x^2 * y^-1 * z * y^-1, z * y * z^-1 * x^2 * y^-3 ] T96.88 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y^2 * x^-1 * z * y^-1 * z, y^5 * x^-1 * z^-1 * y^4 ] T96.89 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (y * z^-2)^2, z * y^2 * x^-1 * y^-1 * x * y^-1 * x * z * x^-1 ] T96.90 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, (x * z^-1 * x)^2, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2 ] T96.91 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, x^-1 * z * x^-2 * z * y * z^-1, y^4 * x^-1 * z * x^-1 * z, z^-2 * y^3 * z^-2 * y ] T96.92 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y * z^-1 * y^4 * z^-1 * y * z^-2, z^10 ] T96.93 : Triangle type {6,10,10} Group order 300 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^10, z^10 ] T96.94 : Triangle type {6,30,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, y^7 * z^-1 * y * z^-1 ] T96.95 : Triangle type {6,40,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^3 * x^-1 * y^-4, z^-2 * y^4 * z^-4 ] T96.96 : Triangle type {7,33,231} Group order 231 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^3 ] T96.97 : Triangle type {7,34,34} Group order 238 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y * z^-3 * y^2 * z^-1 * y * z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 ] T96.98 : Triangle type {7,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T96.99 : Triangle type {7,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^4 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T96.100 : Triangle type {7,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T96.101 : Triangle type {8,8,33} Group order 264 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-19 * x * y^-1 * x^-1 * y * z^-12 ] T96.102 : Triangle type {8,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x * z^-1 * x^-1 * z * x^-1 * z ] T96.103 : Triangle type {8,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-2 * y^4 * z^-4 ] T96.104 : Triangle type {9,9,42} Group order 252 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-2 * x^2 * z^3 ] T96.105 : Triangle type {9,25,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^10 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T96.106 : Triangle type {9,26,26} Group order 234 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^8 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y^8 ] T96.107 : Triangle type {9,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-3 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T96.108 : Triangle type {9,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^8 * x^-2 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T96.109 : Triangle type {9,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^2 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T96.110 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-1 * x)^2, y^2 * x^-2 * z * x^-1 * y, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T96.111 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-1 * x)^2, y^2 * x^-2 * z * x^-1 * y, x * z * y * x^-1 * z^2 * y ] T96.112 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, (x * z^-2)^2, (y * z^-2)^2, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^-1 * x^-1 * y * x^-1 * z * y^-1 * z^-1 ] T96.113 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, (x * z^-2)^2, (y * z^-2)^2, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, x^-1 * z * y * x^-1 * y^-1 * z^-2 ] T96.114 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, z^2 * y * x * z^2, x^10 ] T96.115 : Triangle type {10,10,25} Group order 250 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-2 * x^-1 * z^2, x^10 ] T96.116 : Triangle type {10,10,25} Group order 250 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-7 * x^-1 * z * y * z^-5 * x^-1 * z^10 * y ] T96.117 : Triangle type {10,10,25} Group order 250 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^4 * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y * z^-4 * x^-1 * z^3 * y * z^-3 * x^-1 ] T96.118 : Triangle type {10,10,25} Group order 250 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-10 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * z * y^-1 * z^-9 ] T96.119 : Triangle type {10,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^10 * y^-1 * z^-2 * x^-1 * z^11 ] T96.120 : Triangle type {10,10,120} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-3 * x * z * y * z^-7 * x^-1 * z^5 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T96.121 : Triangle type {10,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z * y^3 * x * y^-1 * z^-1 * x^-1, x^10 ] T96.122 : Triangle type {12,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-5 * y * z^-1 * y^2 * z^-1 ] T96.123 : Triangle type {12,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, y^-1 * z * y^-3 * z * y^-1 * z^2 ] T96.124 : Triangle type {13,17,221} Group order 221 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-5 * x * z^-5 * x^4, z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T96.125 : Triangle type {13,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x, y^2 * x^-1 * z^2, y * z^-1 * y^3 * z^-1 * y * z^-2 * y * z^-1 * y^5 * z^-2 ] T96.126 : Triangle type {13,18,18} Group order 234 Chiral action Defining relators: [ x * y * z, z * x^-2 * y * x^-1, y * z^-1 * x^-1 * y^-1 * z, y * z^-2 * y * z^-2 * y^2 * z^-3 * y^3 * z^-4 ] T96.127 : Triangle type {13,18,18} Group order 234 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-13, y^4 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y^4 ] T96.128 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-1 * z^5 * y^-6, x^3 * y^-5 * x * z^-5 * x^4 ] T96.129 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-2 * z^4, x^3 * y^-5 * x * z^-5 * x^4 ] T96.130 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-5 * x * z^-5 * x^4, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-4 ] T96.131 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6, x^3 * y^-5 * x * z^-5 * x^4 ] T96.132 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-5 * x * z^-5 * x^4, z^4 * y^-1 * z^5 * y^-1 * z^5 ] T96.133 : Triangle type {13,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z, x^3 * y^-5 * x * z^-5 * x^4 ] T96.134 : Triangle type {14,14,17} Group order 238 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-4 * y * x^-8 * y, z^-9 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-3 ] T96.135 : Triangle type {14,14,112} Group order 224 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z^9 * y^-1 * z^-1 * x^-1 * z^5 ] T96.136 : Triangle type {14,14,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x * z^2 * y^-1 * z^-1 * x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z^2 * y * z^-1 ] T96.137 : Triangle type {14,14,112} Group order 224 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, y * z^-4 * x * z * y^-1 * z^-5 * x^-1 * z * y * z^-1 * x^-1 * z ] T96.138 : Triangle type {14,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x * y^-1 * z^-1 * x * y^-1 * x^6 * y^-2 * x^2 * y^-2 ] T96.139 : Triangle type {14,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x * y^-1 * x * y^-1 * x * y^-3, z^-3 * y * z^-1 * y * z^-4 ] T96.140 : Triangle type {14,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * x^-3 * z^4, y^-1 * x * y^-1 * x^3 * y^-1 * x * y^-2 ] T96.141 : Triangle type {14,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x * z^2, x * z^-1 * x^12 * y^-1 ] T96.142 : Triangle type {14,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, (x^-1 * z^5)^2 ] T96.143 : Triangle type {15,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-2 * z^4, x^4 * y^-5 * x * z^-5 * x^5 ] T96.144 : Triangle type {15,70,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, y^-2 * z^4 * y^-4 * z^4 ] T96.145 : Triangle type {15,70,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, y^-2 * z^4 * y^-3 * z * y^-1 * z * y^-1 * z ] T96.146 : Triangle type {16,52,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^7 * y^-1 * z^5, y^-5 * z^2 * y^-3 * x^5 * y^-1 * x * y^-2 ] T96.147 : Triangle type {16,52,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^4 * y^-6, x^4 * y^-4 * x^2 * z^-4 * x^6 ] T96.148 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-4 * z^2, x^5 * y^-5 * x * z^-5 * x^6 ] T96.149 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-8, z^5 * x^-1 * z^5 * x^-5 * z^2 ] T96.150 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x * y^-11, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T96.151 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, y^-5 * z^4 * y^-1 * x^5 * y^-1 * x * y^-1 ] T96.152 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-6, x^5 * y^-5 * x * z^-5 * x^6 ] T96.153 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^2 * y^-8, z^-2 * x^6 * z^-5 * x * z^-5 ] T96.154 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-7, z^4 * x^-1 * z * x^-1 * z^5 * x^-6 * z^2 ] T96.155 : Triangle type {17,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-5 * z, x^5 * y^-5 * x * z^-5 * x^6 ] T96.156 : Triangle type {21,30,70} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^4 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T96.157 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-2 * y^2 * x^-9 * z^3 * x^-6 * y * x^-5 ] T96.158 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-4 * z^2, y^4 * x^-4 * y * z^-5 * y * z^-1 * y * z^-1 * y^2 ] T96.159 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^6 * x^-5 * y^6 * x^-1 * y * x^-1 * y^3 ] T96.160 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-9 * z * x^-4 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T96.161 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-3 * x^5 * y^-1, z^11 * x^-1 * z^5 ] T96.162 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-2 * z^4, y^5 * x^-5 * y^3 * z^-2 * y^6 ] T96.163 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z ] T96.164 : Triangle type {25,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-9 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T96.165 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-2 * x^-1 * z^4, y * z^-1 * x^-1 * y^4 * x^-1 * y * x^-1 * y^5 ] T96.166 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4, y^-2 * x^4 * y^-4 ] T96.167 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6 * y^-2, y^5 * z^-1 * y * z^-1, z^3 * y * x^-1 * z^4 ] T96.168 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-4 * x^-1 * z^3 * y^-1, z^-4 * x^2 * z^-4 ] T96.169 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x^-1 * z^3 * y^-1, x^8 * y^-2 ] T96.170 : Triangle type {26,26,104} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, y * z^-1 * x * z^-5 * y^2 * z^-5 ] T96.171 : Triangle type {30,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^2 ] T96.172 : Triangle type {30,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, z^-1 * y * z^-1 * x * z^-2 ] T96.173 : Triangle type {30,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, (x * y^-2)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2 ] T96.174 : Triangle type {30,30,35} Group order 210 Chiral action Defining relators: [ x * y * z, (y^-1 * x)^3, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x * z^-2 ] T96.175 : Triangle type {30,30,35} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^5 * z^-1 * x * z^-1, y^5 * z^-1 * y * z^-1, z^3 * y * x * z^3 ] T96.176 : Triangle type {30,30,35} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^3 * y * x * z^3 ] T96.177 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^8 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T96.178 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-6 ] T96.179 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x^2 ] T96.180 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T96.181 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-3 * y^2 * x^-4 * y^3, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T96.182 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T96.183 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^8 * z^-4 * y * x^-6 * y * x^-1 * y^4 ] T96.184 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-13 * y * x^-1 * y * x^-11 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T96.185 : Triangle type {33,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-7, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T96.186 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^-3 * z * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * z * y^-1 ] T96.187 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^3 * z^-1 * y^3 * x^-3 * y^3 ] T96.188 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, x^6 * y^-4 ] T96.189 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^6 * y^-2, z^-1 * y^5 * z^-2 * y * z^-1 ] T96.190 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y^-1 * z^2 * x^-1 * z * x^-1 * z^5 ] T96.191 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * z^-1 * x * z^-1, y^-4 * x^2 * y^-4 ] T96.192 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, x^-1 * y^3 * x^-8 * y * x^-1 ] T96.193 : Triangle type {34,34,102} Group order 204 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * y * z^-4 * y * x * z^-2 * y * z^-1 * x * z^-1 ] T96.194 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3, z * y^-4 * x * y^-3 * z ] T96.195 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * y^3, x^-1 * z * x^-1 * z * x^-1 * z^4 ] T96.196 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 ] T96.197 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1, y^-2 * x * y^-1 * x * z * y^-2 ] T96.198 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x * z^-1 * x^13 * z^-1 * x * z^-1 ] T96.199 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y * z^-2, x^-6 * z^3 ] T96.200 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, x^-1 * z * y * x * y^-1 * z^-1, y^-4 * x^2 * y^-5 ] T96.201 : Triangle type {34,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * x^5 * y^-1 * x * y^-1 * x ] T96.202 : Triangle type {40,50,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-3 * z^3, y^-3 * z * y^-1 * z^5 * y^-1 * x^2 * y^-4 ] T96.203 : Triangle type {40,50,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-6, y^8 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T96.204 : Triangle type {40,50,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^15 * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T96.205 : Triangle type {40,50,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x * z^-1 * x * z^-3 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-5 ] T96.206 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^6, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T96.207 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^5 * z^-2 * x^3 * y^-6 * x^3 ] T96.208 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T96.209 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4 * z * y^-2, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T96.210 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T96.211 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-2 * z^30 * x^-2 * z * x^-1 * z * x^-11 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T96.212 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^13 * x^-4 * y^2 * z^-3 * y^6 ] T96.213 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^6, z^-2 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-2 ] T96.214 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y^9, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1 ] T96.215 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, z^-4 * y * z^-5 * y^2 * z^-4 ] T96.216 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^3 * z^-3, x * y^-1 * x * y^-1 * x^6 * y^-6 * x^3 ] T96.217 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-8 * z^4 * x^-2 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T96.218 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-13 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * z^-5 * x * z^-2 ] T96.219 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^17 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.220 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-49 ] T96.221 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-3 ] T96.222 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^9 * z^-4 * y^6 * z^-1 * y^4 ] T96.223 : Triangle type {49,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-3 * y^2 * x^-4 * y^3, x^4 * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T96.224 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-8 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-5 * y * z^-1 * y * z^-5 ] T96.225 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^5 * z^-1 * x * z^-1, y^-2 * z * y^-1 * z^3 * y^-1 * z * y^-4 * z ] T96.226 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-3 * y * x^-1 * y * x^-1 * y * x^-7 * y * x^-2 ] T96.227 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x * z^-1 * x^8 * y^-1 * x^3 * y^-2 * x^3 ] T96.228 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y * z^-1 * y * z^-3, x^-1 * y * x^-3 * y * x^-3 * y * x^-1 * y^3 ] T96.229 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-2, y^-2 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T96.230 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^14 * z^-1 * y^7 * z^-1 * y^3 ] T96.231 : Triangle type {50,50,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^3 * y^-3 * z * x^-1 * z^3 * x^-1 * z * x^-5 * z^3 ] T96.232 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, x^2 * y^-1 * x^6 * y^-8 ] T96.233 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x^7 * z^-1 * x^4 * y^-6 * x * y^-1 * x^4 ] T96.234 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^33 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.235 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-13 * y^6 * z^-1 * y * z^-3 ] T96.236 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^7, y^4 * z^-5 * y^6 ] T96.237 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-17 * y^3 * x^-14 ] T96.238 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^22 * x^-5 * y^8 ] T96.239 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, z^-4 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T96.240 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, z^-3 * y * z^-1 * y * z^-5 * y^4 * z^-1 * y * z^-1 ] T96.241 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T96.242 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-47 * z * x^-8 * z^2 * x^-8 ] T96.243 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x^3 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.244 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-4 * y^2 * z^-9 * y * z^-5 * y * x * z^-5 * y * z^-1 * y ] T96.245 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-4 ] T96.246 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^2 * z^-4, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T96.247 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^2 * z^-4, y * x^-1 * y^6 * x^-6 * y^2 ] T96.248 : Triangle type {65,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^2 * x^-6 * z^4 * x^-1 * z^6 ] T96.249 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-30 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * y^-2 * x * y^-1 * x * y^-1 * x^3 ] T96.250 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^3 * y^-6 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x^3 ] T96.251 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^3 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^9 * z^-2 * x^6 ] T96.252 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^8 * z^-4 * x * y^-6 * x * y^-1 * x * y^-1 * x^2 ] T96.253 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-5 * y^4 * z^-2, x^6 * z^-3 * x^2 * y^-5 * x^4 ] T96.254 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-2, x^5 * z^-3 * x^6 * y^-1 * x ] T96.255 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-2 ] T96.256 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-4 * x^6, z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T96.257 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^-6 * x * y^-6 * x * y^-2 ] T96.258 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^6, y^7 * z^-4 * y * x^-3 * y^6 ] T96.259 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-2 ] T96.260 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-3 * y^2 * x^-4 * y^3, z^-5 * x * z^-4 * x * y * z^-4 ] T96.261 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-4 * z * y^-1 * z * y^-6 * z^5 * y^-8 ] T96.262 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-4 * x^4 * y^-2 * x, y^5 * z^-4 * y * x^-3 * y^4 ] T96.263 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y * x^2 * z^-4 * y * z^-1 * y * z^-1 * y ] T96.264 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^-6 * x^2 * y^-6 * x * y^-1 * x * y^-1 ] T96.265 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-2, y^-5 * x * y^-2 * z^3 * y^-4 ] T96.266 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-11 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^2 * z^-6 ] T96.267 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-4 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.268 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^4 * y^-7, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^5 * y^-1 * x ] T96.269 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, x^-1 * y * x^-1 * y^6 * x^-6 * y^3 ] T96.270 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^4 * z^-1 * x * z^-1 * x * z^-4 * x^8 ] T96.271 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-16 * y * z^-14 * x^3 * z^-7 ] T96.272 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^4 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.273 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-5 * y^2 * z^-4, y^-3 * x^5 * y^-6 * x * y^-1 ] T96.274 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4 * z * y^-2, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T96.275 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^-4 * z * y^-17 ] T96.276 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y^3 * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T96.277 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y^6, x^5 * z^-4 * x^6 ] T96.278 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] T96.279 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-41 * x * z^-7 ] T96.280 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^19 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.281 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x^4 ] T96.282 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^6 * x^-7, y * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T96.283 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-5 ] T96.284 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x^2 * z^-4, x^2 * y^-1 * x^6 * y^-6 * x * y^-1 ] T96.285 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-2 ] T96.286 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-12 * z * y^-1 * z * y^-5 * x * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T96.287 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-7 * y * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T96.288 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^3 * x^-5 * y, z^3 * x^-5 * z^11 ] T96.289 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^4 * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^2 ] T96.290 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y^2 ] T96.291 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-2 * x^4 * y^-4 * x, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^7 ] T96.292 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-5 * y^6, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T96.293 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^8 * z^-4 * x^4 * y^-2 * x^4 ] T96.294 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^11 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T96.295 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^-59 * x * z^-5 ] T96.296 : Triangle type {97,194,194} Group order 194 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^97, y * z^-1 ] T96.297 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.298 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, z^-4 * x * z^-1 * x * z^-4 * x^6 * z^-1 ] T96.299 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-3 * z * y^-6 * z^5 * y^-7 ] T96.300 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-37 * x * z^-4 * x * z^-7 ] T96.301 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-8 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x^3 ] T96.302 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y^2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T96.303 : Triangle type {98,98,98} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4, x^8 * y^-6 * x^2 ] T96.304 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x^-2 * y^-1, y^74 * x^-1 * y^22, x * z^-1 ] T96.305 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-51 * x^2 * y^-12 ] T96.306 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^31 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.307 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-3 * x^15 * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.308 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x^6 * y^-5 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.309 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x^7 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T96.310 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-3 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-2 ] T96.311 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-4 ] T96.312 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^3 * x^-1 * y^6 * x^-6 * y^4 ] T96.313 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, y^5 * z^-2 * y^3 * x^-6 * y * x^-1 * y^2 ] T96.314 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T96.315 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, y^-5 * x^2 * y^-8 ] T96.316 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x * y * z^-4, y^4 * z^-3 * y^2 * x^-6 * y^2 ] T96.317 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-7, z^-5 * x * z^-4 * x * y * z^-4 ] T96.318 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^-4 * x * z^-1 * x * z^-1 * x * z^-4 * x * y^3 * z^-4 ] T96.319 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-3 * y^7, x^-1 * y * x^-5 * z^4 * x^-1 * z * x^-1 * z * x^-2 ] T96.320 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^-3 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-3 ] T96.321 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-4 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 ] T96.322 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-8 * y * z^-5 * y * x^4 * z^-2 * y * z^-3 ] T96.323 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^6, z * y^-6 * z^5 * y^-1 * z * y^-1 * z^2 ] T96.324 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-1 * x * z^-4 * x^5 * z^-1, y^-4 * x^3 * y^-6 * x * y^-1 ] T96.325 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^6, x^7 * z^-4 * x^8 ] T96.326 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-11 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^4 * z^-5 ] T96.327 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^4 * z^-2, x^6 * z^-4 * x^7 ] T96.328 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^3 * z^-3, x^-3 * y^6 * x^-2 * z^3 * x^-5 ] T96.329 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-8 * y^3 * x^-3 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-3 ] T96.330 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-20 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x * z^-7 ] T96.331 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z * y^-3 * z * y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T96.332 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^3 * z^-3, y^9 * x^-6 * y * x^-1 * y^2 ] T96.333 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^2 * z^-4, y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y^2 ] T96.334 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^2 * y^-6 * z^5 * y^-1 * z * y^-1 * z^3 ] T96.335 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^6 * z^-1 * y * z^-5 * y^6 * z^-1 * y^3 ] T96.336 : Triangle type {193,193,193} Group order 193 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^6 * x^-6 * y * x^-1, x^2 * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] Genus 97 T97.1 : Triangle type {2,3,12} Group order 2304 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^12, z^-2 * x * z * y * z^-1 * x * z * y * z^-2 * x * y^-1 * z^-2 * x * y^-1 * z^-1, x * z * y * x * z^2 * y * x * z * y * x * z * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.2 : Triangle type {2,3,12} Group order 2304 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y * z^-1 * x * z^2 * y * x * z * y * z^-1 * x * z * y * x * z^2 * y * z^-1 * x * z * y * x * z * y * z^-1 * x * z^3 * y^-1 * z^-3 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T97.3 : Triangle type {2,3,12} Group order 2304 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z^-1 * x * z^5 * y * z^-2 * y * x * z^3 * y^-1 * z^-1, x * z^2 * y * x * z * y * z^-1 * x * z^2 * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.4 : Triangle type {2,3,12} Group order 2304 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z^-2 * x * z * y * z^-1 * x * z * y * z^-2 * x * y^-1 * z^-2 * x * y^-1 * z^-1, x * z^2 * y * x * z * y * z^-1 * x * z^2 * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.5 : Triangle type {2,3,12} Group order 2304 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^12, z^-2 * x * z * y * z^-1 * x * z * y * z^-2 * x * y^-1 * z^-2 * x * y^-1 * z^-1, z * y * z^-1 * x * z * y * x * z^2 * y * x * z * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-1 * x ] T97.6 : Triangle type {2,3,24} Group order 1536 Chiral action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * x * z^3 * y * x * z^2 * y * x * z^2 * y^-1 * z^-1 * x, x * z^3 * y * x * z * y * x * z^2 * y * x * y^-1 * z^-4 ] T97.7 : Triangle type {2,3,24} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^5 * y^-1 * z^-6, z^2 * y * x * z^3 * y * x * z^2 * y * x * z^2 * y^-1 * z^-1 * x, x * z * y * x * z * y * z^-2 * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T97.8 : Triangle type {2,3,24} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1, z * y * x * z * y * x * z * y * x * z^4 * y * x * z * y * x * y^-1 * z^-1 * x * z^3 ] T97.9 : Triangle type {2,3,24} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-2 * x * z^2 * y^2 * z^-3 * x * z^2, z^2 * y * x * z^3 * y * x * z^2 * y * x * z^2 * y^-1 * z^-1 * x ] T97.10 : Triangle type {2,3,24} Group order 1536 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * x * z^2 * y * z^-2 * x * z^2 * y * x * z^5 ] T97.11 : Triangle type {2,3,30} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * z^-1 * x * z * y * x * z * y^2 * z^-2 * x * y^-1 * z^-1 * x, z * y * z^-1 * x * z^2 * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x, z^5 * y * x * y^-2 * z^-1 * x * y^-1 * z^-3 * x * z^6 ] T97.12 : Triangle type {2,3,30} Group order 1440 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T97.13 : Triangle type {2,4,5} Group order 3840 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z, y * x * z * y * z^-1 * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T97.14 : Triangle type {2,4,5} Group order 3840 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, z^-1 * y * x * z * y * x * z * y^-1 * z * y^-2 * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y, z^2 * y * z^-1 * y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T97.15 : Triangle type {2,4,6} Group order 2304 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^6, z^2 * y * x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-2 * x, y * x * z * y * z^-2 * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-2 ] T97.16 : Triangle type {2,4,6} Group order 2304 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-2)^4 ] T97.17 : Triangle type {2,4,7} Group order 1792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, x * z * y^-1 * z^2 * y^-2 * z^-2 * y * z^-2 * y ] T97.18 : Triangle type {2,4,7} Group order 1792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, (y * z^-2)^4, z * y * z^-1 * y * x * z * y^2 * z^-1 * x * y^-1 * z^2 * y^-1 ] T97.19 : Triangle type {2,4,7} Group order 1792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, (y * z^-1)^4, z^2 * y^-1 * z^3 * y^-1 * z * y * z^-2 * y * z^-3 * y * x ] T97.20 : Triangle type {2,4,10} Group order 1280 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^10, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y^-1 * z^2 * y^-2 * z^-2 * y * z^-2 * y ] T97.21 : Triangle type {2,4,10} Group order 1280 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z^10, (y * z^-2)^4, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^2, y^-1 * z * y * z^-2 * x * z * y^-2 * z^-1 * x * z^3 ] T97.22 : Triangle type {2,4,10} Group order 1280 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^10, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T97.23 : Triangle type {2,4,12} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2 * y * z^-1)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12 ] T97.24 : Triangle type {2,4,12} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12 ] T97.25 : Triangle type {2,4,16} Group order 1024 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2 ] T97.26 : Triangle type {2,4,16} Group order 1024 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T97.27 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2, x * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T97.28 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * y * z^-1, z^-6 * x * z^7 * y^-1 * z^-2 ] T97.29 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, (y * z^-2)^4, y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2, z^-5 * x * z^7 * y^-1 * z^-3 ] T97.30 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * y * z^-1, y^-1 * z * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^3, z^2 * y * x * z * y * z^-2 * x * z^6 * y^-1 * z^-2 * x ] T97.31 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y^-1 * z * y^-1 * z^3 * y^-1 * z)^2, z^-6 * x * z^7 * y^-1 * z^-2 ] T97.32 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * z * y^2 * z^-1 * x * z^2 * y^-1, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z, z^2 * y * x * z * y * x * z^4 * y * x * y^-1 * z^-5 * x ] T97.33 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-2)^4, x * z * y * z^-3 * y * z^-1 * x * z^2 * y^-1 * z^-1 * y, z^-5 * x * z^7 * y^-1 * z^-3 ] T97.34 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, (y * z^-2)^4, z^2 * y * z^-2 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.35 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, (y * z^-2)^4, y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T97.36 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * y * z^-1, z^2 * y * z^-1 * x * z^5 * y^-1 * z * y^-1 ] T97.37 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, (y * z^-2)^4, (y^-1 * z * y^-1 * z^3 * y^-1 * z)^2 ] T97.38 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, x * z * y * z^-3 * y * z^-1 * x * z^2 * y^-1 * z^-1 * y, z^-2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y, x * z * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-4 ] T97.39 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T97.40 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^4 ] T97.41 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.42 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-1 * x * z^3 * y^-1 * z * y^-1 * z^2, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^4 ] T97.43 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-2)^4 ] T97.44 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-2)^4, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^4 ] T97.45 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y * z^-3 * y * z^-1 * x * z^2 * y^-1 * z^-1 * y ] T97.46 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z^4 ] T97.47 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-2)^4 ] T97.48 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (z^4 * y^-1 * z^3)^2 ] T97.49 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^4 * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z ] T97.50 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, (y * z^-2)^4, z^2 * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T97.51 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-6 * y * x * z^6 * y^-1 * z^-1 * y * z^-2 ] T97.52 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * x * z * y^-1 * z^-4 * x ] T97.53 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.54 : Triangle type {2,4,16} Group order 1024 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, (y * z^-2)^4, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-2 ] T97.55 : Triangle type {2,4,20} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-1)^6, x * z^2 * y^-1 * z * y^-2 * z^-3 * y * z^-1 * y ] T97.56 : Triangle type {2,4,20} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2 * y * z^-1)^2, z * y * z^-3 * x * y^-1 * z^-4 * x ] T97.57 : Triangle type {2,4,28} Group order 896 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-2 * y, z^-5 * x * z^8 * y * x * z * y * x * z^7 * y^-1 * z^-2 * x * y^-1 * z^-1 ] T97.58 : Triangle type {2,4,52} Group order 832 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-36 * x * z^7 * y * x * y^-1 * x * z * y^-1 * z^-5 ] T97.59 : Triangle type {2,4,100} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-82 * x * z^7 * y * z^-2 * x * z^2 * y^-1 * z^-5 ] T97.60 : Triangle type {2,4,196} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-196 ] T97.61 : Triangle type {2,4,388} Group order 776 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-49 * x * y^-1 * z^-144 ] T97.62 : Triangle type {2,5,5} Group order 1920 Chiral action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (y * z^-1)^6, x * z * y * x * z * y^2 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-2 ] T97.63 : Triangle type {2,5,5} Group order 1920 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, y^-1 * z * y^2 * z^-2 * y * x * y^-2 * z^-1 * y * z^-2 * y * x, y^-1 * z * y * x * y^-1 * z * y * x * y^-2 * z^-1 * x * y^-2 * z^-1 * x ] T97.64 : Triangle type {2,6,6} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z^2 * y * z^-1 * y^2 * z^-2 * x * y^-1 ] T97.65 : Triangle type {2,6,6} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1 * y)^4, (y * z^-2 * y * z^-1 * y)^2, (y * z^-1 * y * z^-2 * y)^2, x * z * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-2 ] T97.66 : Triangle type {2,6,6} Group order 1152 Chiral action Defining relators: [ x^2, x * y * z, y^6, z^6, z * y^-2 * z * y^-2 * z^-1 * x * z * y^-1 * z, y * x * z * y * z^-1 * y^2 * x * y^-1 * z^-2 * y ] T97.67 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3, y^-1 * z * y^2 * x * z * y^-3 * z^-1 * y^2 * z^-1 * x ] T97.68 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-1 * y)^4, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y^2 * x * z * y^2 * x * y^-1 * z^-1 * y * x ] T97.69 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 * y, z * y^2 * x * z * y^2 * x * y^-1 * z^-1 * y * x ] T97.70 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, (z * y^-1 * z)^3 ] T97.71 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.72 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-3 * z^-2 * y^2, x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z * y * x * z * y^2 * z^-2 * x * z * y^-1 * z^-2 ] T97.73 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2, (y * z^-1 * y)^4 ] T97.74 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.75 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, (y * z^-1 * y)^4, (z^-1 * y^2 * z^-1)^3 ] T97.76 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, (y * z^-1 * y)^4, (y * z^-2 * y * z^-1 * y)^2 ] T97.77 : Triangle type {2,6,6} Group order 1152 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T97.78 : Triangle type {2,6,7} Group order 1008 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-3 * x * y * z^-3, x * z^2 * y^-1 * z * y * x * z * y * z^-2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T97.79 : Triangle type {2,6,9} Group order 864 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, y * x * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^3 * z^-1 * y * x * y^-1 * z^-1 * y * z^-1 * x * z ] T97.80 : Triangle type {2,6,9} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * y^-1 * z^-1 * x * y^-1 * z * y * x * y^-1 * z * y^-2 * z^-1 * y * x * y^-2 * z^-1 * y^2 * z^-1 * y ] T97.81 : Triangle type {2,6,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, z * y^-2 * z * y^3 * z^-1 * x * y^-1 * z^-1 * x ] T97.82 : Triangle type {2,6,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, (y * z^-1 * y)^4 ] T97.83 : Triangle type {2,6,12} Group order 768 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^2 * z^-1 * y * z^-1 * y, z^2 * y^-1 * z * y^3 * z^-1 * x * z^3, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z ] T97.84 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * y^-1 * z, (y * z^-1 * y)^4 ] T97.85 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-1 * y)^4, (y * z^-4 * y)^2 ] T97.86 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1, (y * z^-1 * y)^4 ] T97.87 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-1 * y)^4 ] T97.88 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-3 * z^-3 * y^2, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T97.89 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z^3 * y^-1 * z * y^-1 * z^-2 * x * z * y^-1, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T97.90 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^2 * y^-3 * z^-3 * y^2 ] T97.91 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-3 * z^-3 * y * z^-1, z^-1 * y^2 * x * y^-2 * z^-2 * y * z^-2 ] T97.92 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-5)^2 ] T97.93 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-2 * z^-3 * y, z^-1 * y * z^-1 * x * y^-2 * z^-2 * y * z^-1 * y, (y * z^-1 * y)^4 ] T97.94 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, z * y * x * z * y^-1 * z^-2 * x * z * y * z^-1 * x * z^2 * y^-2 * x * y^-1 * z^-2 * y * z^-1 * x * y^-1 * z^-1 * x ] T97.95 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^2 * z^-1 * y * z^-1 * y, z^2 * y^-1 * z * y^3 * z^-1 * x * z^3, y * z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T97.96 : Triangle type {2,6,12} Group order 768 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^3 * y^2 * z^-1 * y * z^-1 * y, z^2 * y^-1 * z * y^3 * z^-1 * x * z^3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.97 : Triangle type {2,6,15} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z ] T97.98 : Triangle type {2,6,15} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z * y^-1 * z * y^3 * z^-1 * y * z^-1 * x, y * z^-1 * y * z^-1 * y^2 * x * y^-1 * z^2 ] T97.99 : Triangle type {2,6,21} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^2 * y * z^-1 * x * z * y^-2 * z * y^-2 * z * y^-2 ] T97.100 : Triangle type {2,6,27} Group order 648 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * z * y^-3 * z^-1 * x * z * y^-1 * z^-2 ] T97.101 : Triangle type {2,6,27} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-1 * x * z^4 * y * x * z^3 * y * z^-1 * x * z^2 * y * z^-13 ] T97.102 : Triangle type {2,6,75} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z * y * z^-6 * x * z * y * x * y^-1 * z^-6 * x * z * y^-1 * z^-4 ] T97.103 : Triangle type {2,6,99} Group order 594 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-8 * x * z^13 * y * z^-1 * x * z * y^-1 * z^-8 ] T97.104 : Triangle type {2,6,99} Group order 594 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-59 * x * z^14 * y * z^-1 * x * z^7 * y * z^-7 * x * z^2 * y^-1 * z^-6 ] T97.105 : Triangle type {2,6,291} Group order 582 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-57 * x * z^21 * y * z^-1 * x * y * z^-6 * x * z * y^-1 * z^-8 ] T97.106 : Triangle type {2,7,7} Group order 896 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^-3 * x * y * z^-3, x * y^-2 * z * y^-3 * z^-3 * y * z^-2 ] T97.107 : Triangle type {2,7,7} Group order 896 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, z^-3 * x * y * z^-3, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T97.108 : Triangle type {2,7,7} Group order 896 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, z^-3 * x * y * z^-3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T97.109 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^3 * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z ] T97.110 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^3 * y^-1 * z^-1, z^2 * y * z^-3 * x * y^-1 * z * y^-1 * z^3 ] T97.111 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, z^6 * y^3 * x * z^5 ] T97.112 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, y^-1 * z * y * z^-4 * x * y^-1 * z^6 ] T97.113 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^3 * y^-1 * z^-1, y^-1 * z * y^2 * z^-2 * x * y^-1 * z * y^-1 * z^3 ] T97.114 : Triangle type {2,8,24} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^3 * y^-1 * z^-1, z^2 * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-2 * x ] T97.115 : Triangle type {2,10,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^10, (y * z^-1 * y^3)^2, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T97.116 : Triangle type {2,10,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, y^10, (y * z^-1 * y * z^-1 * y)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T97.117 : Triangle type {2,10,10} Group order 640 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^10, (y * z^-2 * y^2)^2, (y * z^-3 * y)^2 ] T97.118 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, y^12, (y * z^-1 * y^4)^2 ] T97.119 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-3 * z^-1 * x * y^-2, x * z^3 * y^-1 * z^-4, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T97.120 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^12 ] T97.121 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^12 ] T97.122 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, y^2 * x * z * y^2 * x * z^3, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^12 ] T97.123 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, z^2 * y^-4 * z^-1 * y * x * z^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T97.124 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^12, (y * z^-1 * y^4)^2 ] T97.125 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, y^12, y^2 * z^-1 * y^4 * z^-3 * y^2 ] T97.126 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1)^4, y^12 ] T97.127 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, y^12, z^-4 * x * z^5 * y^-1 * z^-2 ] T97.128 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x, y^12 ] T97.129 : Triangle type {2,12,12} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, y^12, z^-12 ] T97.130 : Triangle type {2,12,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, x * y^-1 * z * y^-3 * z * y^-2 * z^-1 * y, z^-2 * x * z * y * x * y^-1 * z^-5 ] T97.131 : Triangle type {2,12,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * z^2 * y^-2 * z^-3 * y, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y^12, z^2 * y * x * z * y * x * y * z^-2 * x * z^2 ] T97.132 : Triangle type {2,12,60} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^12, y * x * z^2 * y * z^-1 * x * z^2 * y * z^-3 * x * z^4 * y^-1 * z^-3 * x * z ] T97.133 : Triangle type {2,15,30} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-2 * y * z^-1 * y, y^15 ] T97.134 : Triangle type {2,15,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-3 * y, z^-2 * x * y^-2 * z * y^-1 * z^-1 * y, y^-1 * z * y^-2 * z * y^-3 * z * y^-2 * z * y^-1 * z^2 ] T97.135 : Triangle type {2,15,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-1 * y^4, y^15 ] T97.136 : Triangle type {2,15,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-1 * y * z^-2 * y^5 * z^-1 * y * z^-2 * y ] T97.137 : Triangle type {2,16,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * x * y^-1 * z * y^2 * z^-1 * x * z^2 ] T97.138 : Triangle type {2,16,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y^2 * z^-1, x * z^2 * y^-2 * z^-1 * y * z^-2, y * x * y^-4 * z * y^-2 * z^2 ] T97.139 : Triangle type {2,16,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, y^2 * x * y^-2 * z * y^-1 * z^-2, x * z^2 * y^-2 * z^-1 * y * z^-2 ] T97.140 : Triangle type {2,16,16} Group order 512 Chiral action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z * y^-1 * z^2, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y ] T97.141 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y * x * y^-2 * z^-1 * x * y^-10 * z^-1 * y, x * z^6 * y * x * z * y^-1 * z^-7 ] T97.142 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^-2 * x * z * y * x * z * y * z^-3 * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T97.143 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^2 * y * z^-4 * x * z^5 * y^-1 * z^-3, y^2 * z^-2 * y^7 * z^-1 * y^2 * z^-1 * y ] T97.144 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * y^-4 * z^-1 * y^3, x * z^2 * y * z^-2 * x * z^2 * y * z^-8 ] T97.145 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * x * z * y^-2 * z^5 ] T97.146 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z^2 * y^-5 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T97.147 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z * y * x * z * y^-2 * z^5 ] T97.148 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-6 * z^-1 * x * y^-1 * z^2, z * y * x * z * y^-2 * z^5 ] T97.149 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.150 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, y^3 * z^-1 * y^6 * z^-1 * y^3 * z^-2 ] T97.151 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-1 * z * y * x * z * y * x * y^-1 * z^-3 * x * y^-1 ] T97.152 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z, z^2 * y^-1 * z * y^-8 * z^2 * y^-1 * z ] T97.153 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.154 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z^-3 * x * y^-1 ] T97.155 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^2 * z^-1 * y^4 * z^-1 * y^3 * z^-1 * y^2 * z^-1 * y ] T97.156 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, (y * z^-3)^2, x * y^-4 * z^-1 * y^3, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T97.157 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.158 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, z^2 * y^-1 * z * y^-8 * z^2 * y^-1 * z ] T97.159 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T97.160 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T97.161 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, z^2 * y * z^-1 * y^2 * z^-1 * x * y^-2 * z * y^-1 * z^-1 * x ] T97.162 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * x * z * y * x * y^-1 * z^-4, y^-6 * z^-2 * y * x * z ] T97.163 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T97.164 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T97.165 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-4 * z^-1 * y^3, x * z^3 * y^-2 * z^-4 * y ] T97.166 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^2 * y^-2 * z^-1 * y * z^-2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, (y^-4 * z * y^-3)^2 ] T97.167 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, x * z^2 * y^-2 * z^-1 * y * z^-2, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T97.168 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, (y * z^-3)^2, y^-6 * z * y^-1 * z^-1 * x * z ] T97.169 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-3)^2, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2 ] T97.170 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y^-1 * z * y^-3 * z^-1 * x * z^2 * y^-1 ] T97.171 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, x * y^-5 * z^-2 * y^2 * z^-1 ] T97.172 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-3)^2, x * y^-5 * z^-2 * y^2 * z^-1 ] T97.173 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z^2 * y^-2 * z^-5, y * z^-2 * y * z^-1 * y * z^-1 * y^4 * z^-3 * y * z^-1 ] T97.174 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y^-5 * z^-1 * x * z * y^-2 ] T97.175 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * y^-5 * z^-2 * y^2 * z^-1, y * z^-2 * y^2 * z^-1 * y^8 * z^-1 * y ] T97.176 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2, x * z^2 * y^-2 * z^-1 * y * z^-2, (y^-3 * z^5)^2 ] T97.177 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-2 * y)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T97.178 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-2 * y)^2, (y * z^-1)^4 ] T97.179 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^-6 * z * y^-1 * z^-1 * x * z, x * y^-5 * z^-2 * y^2 * z^-1 ] T97.180 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1, y^-6 * z * y^-1 * z^-1 * x * z, x * y^-5 * z^-2 * y^2 * z^-1 ] T97.181 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^-6 * z * y^-1 * z^-1 * x * z ] T97.182 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-1 * z^2 * y^-3 * z^-1 * x * z * y^-1 * z ] T97.183 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.184 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y * x * y^-1 * z * y^2 * z^-1 * x * z^2, z * y^-3 * z * y^-11 ] T97.185 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y^2 * z^-2 * y * z^-1 * y^2)^2 ] T97.186 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-1 * z * y * x * z * y * x * y^-1 * z^-2 * y * x * z ] T97.187 : Triangle type {2,16,16} Group order 512 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^-1 * z^2 * y^-1 * z * y^-2 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T97.188 : Triangle type {2,16,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-10 * x * z * y * z^-4 * x * z^4 * y^-1 * z^-7 ] T97.189 : Triangle type {2,16,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, z^-10 * y^2 * x * z^2 * y^-1 * z^-15 ] T97.190 : Triangle type {2,16,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-1 * x * z^4 * y * z^-4 * x * z * y * z^-4 * x * z^4 * y^-1 * z^-7 ] T97.191 : Triangle type {2,16,112} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^4 * y^-3 * z^4 * y^-1, z^9 * y * x * z^4 * y^-1 * z^-13 * x ] T97.192 : Triangle type {2,20,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1 * y^3)^2, (y * z^-4)^2 ] T97.193 : Triangle type {2,20,20} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z * y^3 * x * y^-1 * z^-2 ] T97.194 : Triangle type {2,24,72} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-2 * y * z^-1, y^-1 * z^2 * y^-2 * z^4 * y^-1 * z * y^-1 * z * y^-11 ] T97.195 : Triangle type {2,24,72} Group order 432 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^2 * z^-1 * y^4 * z^-5 ] T97.196 : Triangle type {2,24,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-10 * z^-1 * y * x, z^-1 * x * z^7 * y * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 ] T97.197 : Triangle type {2,24,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^9 * y * z^-2 * x * z^6 ] T97.198 : Triangle type {2,24,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-10 * z^-1 * y * x, z^9 * y * x * y^-1 * z^-1 * x * z^2 * y^-1 * z^-3 * x ] T97.199 : Triangle type {2,24,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-11 * z^4 * y^-5 * z^4 ] T97.200 : Triangle type {2,28,28} Group order 448 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-3 * y, y^2 * z^-1 * y^12 * z^-1 * y^8 * z^-1 * y * z^-1 * y ] T97.201 : Triangle type {2,28,28} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^3 * z^-1 * y * z^-2 * y * z^-3 * y * z^-1 * y^5 * z^-2 * y * z^-1 * y * z^-1 * y * z^-3 ] T97.202 : Triangle type {2,36,36} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-23 * z^4 * y^-5 * z^4 ] T97.203 : Triangle type {2,51,102} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-51 ] T97.204 : Triangle type {2,52,52} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^36 * z^-1 * y^10 * z^-2 ] T97.205 : Triangle type {2,100,100} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-64 * y^35 ] T97.206 : Triangle type {2,195,390} Group order 390 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^130 * y^-64 ] T97.207 : Triangle type {2,196,196} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^65 * z^-130 * y ] T97.208 : Triangle type {2,388,388} Group order 388 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^64 * z^-129 * y ] T97.209 : Triangle type {3,3,6} Group order 1152 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * y * x^-1 * z^2 * y * z^-1 * x^-1, y * z^-2 * x^-1 * y * x^-1 * y * z^-2 * x^-1 * z, z * y * x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * x, y * x^-1 * y * x * z * y * x^-1 * y * x * y^-1 * x * y^-1 * x * z ] T97.210 : Triangle type {3,3,6} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, x * z * y * x * z * y * x * z * x^-1 * z * y * x * z * y * x * z * y * x * z * y * x^-1 * y * x * z * y ] T97.211 : Triangle type {3,3,6} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, x * z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y ] T97.212 : Triangle type {3,3,6} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * y * x^-1 * z^2 * y * z^-1 * x^-1, y * z^-2 * x^-1 * y * x^-1 * y * z^-2 * x^-1 * z, z * y * x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * x, x * z * y * x * z * x^-1 * z * y * x * z * y * x * z^-1 ] T97.213 : Triangle type {3,3,6} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * y * x^-1 * z^2 * y * z^-1 * x^-1, y * z^-2 * x^-1 * y * x^-1 * y * z^-2 * x^-1 * z, z * y * x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * x, (x * z * y)^4 ] T97.214 : Triangle type {3,3,6} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z, x * y^-1 * z^-1 * x^-1 * y * x^-1 * z * x^-1 * y^-1 * z^-1 * x * z^-1 * x^-1 * y^-1 ] T97.215 : Triangle type {3,3,12} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * y * z^-1 * x^-1 * y * x^-1 * y * x * y^-1 * x * z, z * y * x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * x ] T97.216 : Triangle type {3,3,12} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, z * y * x^-1 * z * y * x^-1 * y^-1 * x * z * y^-1 * x, y * x * y^-1 * z^2 * y * x * z * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * z ] T97.217 : Triangle type {3,3,12} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x, x * y^-1 * z^-2 * x^-1 * z^2 * x^-1 * z^2 * y * x * z^-2 ] T97.218 : Triangle type {3,3,12} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x * z * y * x^-1 * z^3 * y * x^-1, y * x * z * y^-1 * z^-1 * x^-1 * y * z^-3 * x^-1 ] T97.219 : Triangle type {3,3,12} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^3, (x * z * y^-1 * z^-1)^2, x * z * y * x^-1 * y * x^-1 * y^-1 * z^-4 ] T97.220 : Triangle type {3,3,15} Group order 720 Reflexible action Defining relators: [ x^3, x * y * z, y^3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z, y^-1 * z^-2 * x^-1 * y^-1 * x * z^2 * y * x, z^-2 * x^-1 * z * y * x^-1 * z * y * z^-3 ] T97.221 : Triangle type {3,4,4} Group order 1152 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * x * y^-1 * z^-1 * y * x * z * y * z^-1 * y, y * x^-1 * y^-1 * z^-1 * y * x^-1 * z * y * x * z^2 ] T97.222 : Triangle type {3,4,4} Group order 1152 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (y * z^-1)^4 ] T97.223 : Triangle type {3,4,6} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * x * z * y * x * y^-1 * z^-1 * y, (x^-1 * z^2 * y)^2 ] T97.224 : Triangle type {3,4,6} Group order 768 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, z * y * x * z * y^-1 * z^-1 * x^-1 * z * y^-1 * z^2 * y * x ] T97.225 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, x^-1 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 * z ] T97.226 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, x^-1 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-1 * x * z ] T97.227 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-2 * x * z^-2 ] T97.228 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, (x^-1 * z^2 * y)^2, y * z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x^-1 ] T97.229 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 ] T97.230 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, (x^-1 * z^2 * y)^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 ] T97.231 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, y * z^-1 * x^-1 * y^-1 * z^-2 * x^-1 * z * y^-1 * x * z * y * x * z^2 * y^-1 * z^-1 * x * z * y^-1 * x * z * y^-1 * x * z ] T97.232 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T97.233 : Triangle type {3,4,6} Group order 768 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T97.234 : Triangle type {3,4,12} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, y^-1 * z^-2 * x^-1 * y * x^-1 * y * z^-2 * x^-1 * z ] T97.235 : Triangle type {3,4,12} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z * y^-1 ] T97.236 : Triangle type {3,4,12} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * y^-1 * z * y^-1 * x * z^2 * y, (z^-1 * x^-1 * y^-1)^3 ] T97.237 : Triangle type {3,4,12} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, y * z^-1 * x * y^-1 * x * z * y^-1 * z^-1, (z^-1 * x^-1 * y^-1)^3 ] T97.238 : Triangle type {3,4,12} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, (z^-1 * x^-1 * y^-1)^3, y * z^-1 * y * z^-1 * x^-1 * y^2 * z^-2, z^-4 * x^-1 * z^3 * y^-1 ] T97.239 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T97.240 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1 ] T97.241 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^2 * y * z^-1 * x * z * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-1 * x * z * y * z^-1 * x * z^2 * y * z^-1 * x ] T97.242 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, (x * z^2 * y^-1 * z^-1)^2 ] T97.243 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, (x * z^2 * y^-1 * z^-1)^2 ] T97.244 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x * z^-1 ] T97.245 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2, y * z^-1 * y * z^-1 * x^-1 * z^4, (x * z^2 * y * z^-1)^2 ] T97.246 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T97.247 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z * y ] T97.248 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x * z * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 ] T97.249 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, z^-4 * x^-1 * y^-1 * z * y * z^-1, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T97.250 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x * z^-1 ] T97.251 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1, z^-12 ] T97.252 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, z^-12 ] T97.253 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y * z^-1 * y * z^-1 * x^-1 * z^4, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T97.254 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * x * z * y ] T97.255 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * y^-2 * x * z * y^-1 * z, z^-4 * x^-1 * z^3 * y^-1, y * z^-2 * x^-1 * y^-1 * x * z * y * z^-2 ] T97.256 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-4 * x^-1 * z^3 * y^-1 ] T97.257 : Triangle type {3,4,12} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, (z^-1 * x^-1 * y^-1)^3, z^-4 * x^-1 * z^3 * y^-1 ] T97.258 : Triangle type {3,6,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * y^-1 * z^-1 * x^-1 * y^2 * z^-1, (y * x^-1 * z)^3 ] T97.259 : Triangle type {3,6,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1 ] T97.260 : Triangle type {3,6,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T97.261 : Triangle type {3,6,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-1 * x^-1 * y^-1 * x * z^2 * y, z^-1 * x * y^-2 * x * y^-1 * z^-1 * y, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2 ] T97.262 : Triangle type {3,6,6} Group order 576 Chiral action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * y^-1 * z^-1 * y)^2, (x * z * y^-1 * z^-1)^2, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y^-1 * z * y^2 * x^-1 * z^2 * y^-1 * z ] T97.263 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, z^6, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T97.264 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z * y^-1 * z^-1 * y * x * z * y^-2, y^2 * x^-1 * y * x^-1 * y^-1 * x * z^2 ] T97.265 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, x^-1 * z * y^-2 * x * z * y^-1 * z, x^-1 * y^-1 * z * y^-1 * x * y^-1 * z^2, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T97.266 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z^6, z^-2 * y * x^-1 * z * y^-2 ] T97.267 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-2 * y * x^-1 * z * y^-2 ] T97.268 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * x * z * y^-1 * z^-1, z^-1 * x * z * y^-1 * x * y^-1 * z^-1 * y, x * z * y^2 * x^-1 * y^-1 * z^-1 * y^2 ] T97.269 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-2 ] T97.270 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * y * z^-2, (x * z * y)^4 ] T97.271 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T97.272 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^2 * z^-1 * y * x^-1 * z * y^-1 * z^2 ] T97.273 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * z * y^-2 * z^-1 ] T97.274 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T97.275 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6 ] T97.276 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, z^6, y * z^-2 * x^-1 * y^-2 * z ] T97.277 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.278 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, z^-1 * x * z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * z^-1 * y^2 * z^-2 * y ] T97.279 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * y^-1 * z^-1 * y)^2, (x * z * y^-1 * z^-1)^2, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, z^-2 * y^2 * x^-1 * z * y^3 ] T97.280 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * y^-1 * z^-1 * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T97.281 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * y^-1 * z^-1 * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T97.282 : Triangle type {3,6,6} Group order 576 Reflexible action Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.283 : Triangle type {3,7,7} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, y^-7, (x * z * y^-1 * z^-1)^2 ] T97.284 : Triangle type {3,7,7} Group order 504 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-7, z^-1 * y * z^-2 * y * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.285 : Triangle type {3,8,24} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T97.286 : Triangle type {3,8,24} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * y * x * y^-1 * x * z * y^-1 * z^-1, y^8 ] T97.287 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^8, z^-1 * y^3 * x^-1 * y^4 ] T97.288 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-2 ] T97.289 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-2 * z, z * y^-3 * x * z * y * x ] T97.290 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^2 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-1 * x^-1 * y^-2 * x * z * y^2, y^8 ] T97.291 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2 ] T97.292 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, (x * z * y)^2, y^8, z^-1 * y^3 * x^-1 * y^4 ] T97.293 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^8, z^-3 * y^2 * z^-3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T97.294 : Triangle type {3,8,24} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3, y^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T97.295 : Triangle type {3,9,9} Group order 432 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * y ] T97.296 : Triangle type {3,9,9} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-9, (x^-1 * y^-1 * z^-1)^4 ] T97.297 : Triangle type {3,9,117} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-2 * y * x^-1 * z^4, y^-9 ] T97.298 : Triangle type {3,9,117} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-4 * x^-1 * z * y^2 * z^-1, y^-9 ] T97.299 : Triangle type {3,9,117} Group order 351 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y * z^-1 * x * z^3 ] T97.300 : Triangle type {3,10,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, x^-1 * y^-3 * x * z^3, (y * z^-3)^2 ] T97.301 : Triangle type {3,10,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z^2, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1, y^2 * x * y^-1 * x * y^-1 * z^-1 * y ] T97.302 : Triangle type {3,10,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * y * x^-1 * y * x^-1 * z^3 * y, (y * z^-3 * y)^2, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T97.303 : Triangle type {3,10,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-1 * x^-1 * z^2 ] T97.304 : Triangle type {3,12,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.305 : Triangle type {3,12,12} Group order 384 Chiral action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, y^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z ] T97.306 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^2 * x * z^2 * y ] T97.307 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-2 * x^-1 * y^-1 * x * y^-3 ] T97.308 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * y^-1 * z * y, z * y * z^-1 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.309 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.310 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.311 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (y * z^-1)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, y^2 * x * y^-2 * x * y^-3 * z ] T97.312 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * y^-3 * x * z^3 ] T97.313 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, x^-1 * y^-3 * x * z^3, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T97.314 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-2 * x^-1 * y^-2 * z, (x * y^-1 * z^-1 * y)^2, (y * z^-1)^4, y^2 * x^-1 * y * x^-1 * y * z^-1 * x * z ] T97.315 : Triangle type {3,12,12} Group order 384 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (y * z^-1)^4, x * y^-1 * z^3 * y^-1 * z^-2 * y^3 ] T97.316 : Triangle type {3,15,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, y^-1 * z^-1 * y * x^-1 * y^2 * x, x^-1 * y * z^-1 * x^-1 * z * y * z^-1 ] T97.317 : Triangle type {3,15,15} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * z * y^-2, z^-2 * y * x^-1 * y^-1 * x * y^-1 ] T97.318 : Triangle type {3,21,21} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 * y^-1 ] T97.319 : Triangle type {3,24,104} Group order 312 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-3 * y^2 * z^-1 * y * z^-1 ] T97.320 : Triangle type {3,26,78} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y * z^-5 * y^11 * z^-2 * y^5 ] T97.321 : Triangle type {3,27,27} Group order 324 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-1 * z^2 * y^-2 * x * y^-1 * z * y^-1 * z ] T97.322 : Triangle type {3,27,27} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y^2 * z^-2 * y * z^-1 * y * z^-5 * y * z^-2 * y^3 * z^-1 * y^2 * z^-1 * y * z^-2 ] T97.323 : Triangle type {3,34,102} Group order 306 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-17 * y * z^-2 * y^6 * z^-1 * y * z^-1 * y^5 ] T97.324 : Triangle type {3,75,75} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, z^-4 * y * z^-1 * y * z^-5 * y * z^-2 * y^4 * z^-2 * y^4 ] T97.325 : Triangle type {3,98,294} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-79 * z * y^-10 * z * y^-6 * z ] T97.326 : Triangle type {3,99,99} Group order 297 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-13 * y * z^-2 * y^2 * z^-1 * y^10 * z^-2 * y ] T97.327 : Triangle type {3,99,99} Group order 297 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^8 * z^-1 * y^10 * z^-1 * y^78 * z^-1 ] T97.328 : Triangle type {3,291,291} Group order 291 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^7 * z^-1 * y^10 * z^-1 * y^78 ] T97.329 : Triangle type {4,4,5} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-2 * y)^2, (x * z^-1)^4, x^-1 * z * y * x^-2 * y^-1 * z^-2 * y ] T97.330 : Triangle type {4,4,5} Group order 640 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z * y * x^-1 * y^-1 * x * z * y * x, (x * y^-1)^4 ] T97.331 : Triangle type {4,4,5} Group order 640 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * z^-1 * y * z^-1 * x * z * y * z^-1 * y * z^-1 ] T97.332 : Triangle type {4,4,5} Group order 640 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1 ] T97.333 : Triangle type {4,4,5} Group order 640 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^2 * y * x^-1 * z * y^-1 * x, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T97.334 : Triangle type {4,4,5} Group order 640 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1)^4, (y * z^-1)^4, x^-1 * z * y * x^-2 * y^-1 * z^-2 * y, x^-1 * y^-1 * z^-1 * x^-2 * z * y * z^-1 * y ] T97.335 : Triangle type {4,4,5} Group order 640 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, z * y^-1 * z^-1 * x^-1 * z * y * x ] T97.336 : Triangle type {4,4,6} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, z^6, y * z^-1 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T97.337 : Triangle type {4,4,6} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, z^6, (x * y^-1)^4, (x * z^2 * y^-1)^2, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y ] T97.338 : Triangle type {4,4,6} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^6, z * x^-1 * z * x^-1 * y^-1 * z * y^-1, (x * y^-1)^4 ] T97.339 : Triangle type {4,4,6} Group order 576 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^6, (x * y^-1)^4 ] T97.340 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, z^-1 * x^-1 * y^-2 * x * z * y^2, z * y^-1 * z * y * x * z * x^-1 * z ] T97.341 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y^-2 * x * z * y^2 ] T97.342 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * x * z^-1 * y * x * z^3 ] T97.343 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * x * z^-1 * y * x * z^3, y^-1 * z^-2 * y * x * z^-2 * x^-1 ] T97.344 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, (x * y^-1)^4, z^-1 * x^-1 * y^-2 * x * z * y^2 ] T97.345 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y^-1 * z^-2 * y * x * z^-2 * x^-1, y * z^-1 * x * z^-1 * y * z^-1 * x * z ] T97.346 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * y^-1)^4, z^-1 * x^-1 * y^-2 * x * z * y^2, y^-1 * z^-2 * y * x * z^-2 * x^-1, (y * z^-1)^4 ] T97.347 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-1 * x^-1 * y^-2 * x * z * y^2, y * z^-1 * x * z^-1 * x^-1 * z * y^-1 * z, z^8, y^-1 * z^-1 * y * x^-2 * z^2 * y * x^-1 ] T97.348 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-2 * y ] T97.349 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^8, z^-4 * x^-1 * z^3 * y^-1, x^-1 * y * x^-1 * y * x^2 * y^-1 * z * y^-1 * z^-1 ] T97.350 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * y^-1)^4, z^-1 * x * z^-1 * y * x * z * y * z^-1, y^-1 * z^-2 * y * x * z^2 * x^-1 ] T97.351 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-1 * x * z^-1 * y * x * z * y * z^-1 ] T97.352 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, y^-2 * z^-2 * x^-1 * z^2 * y^-1 * z ] T97.353 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y, z^8 ] T97.354 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, (x * z^-1)^4, (y * z^-1)^4 ] T97.355 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z * y * z^-1 * y * x * z^-2 * x^-1, x^-1 * z^2 * y * x^-1 * z * y^-1 * z, (y * z^-1)^4 ] T97.356 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z * y * z^-1 * y * x * z^-2 * x^-1, x^-1 * z^2 * y * x^-1 * z * y^-1 * z, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T97.357 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^-1 * y^-1 * z^-1, (x * z^-1)^4, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T97.358 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 ] T97.359 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-2 * y * x^2 * z^2 * y^-1, z * y * z^-1 * y * x^-1 * z^2 * x^-1, z^8 ] T97.360 : Triangle type {4,4,8} Group order 512 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * z * y, (y * z^-1)^4, z^8 ] T97.361 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, z^8, x^-1 * y * x^-1 * y * x^2 * z * y * z^-1 * y ] T97.362 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, (x * y^-1)^4, (x * z^-1)^4 ] T97.363 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1)^4, x * z * x^-1 * y^-1 * z * y * x * z * y * x * z^-1 * y ] T97.364 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, z^8, x^-1 * y * x^-1 * y * x^2 * y^-1 * z * y^-1 * z^-1 ] T97.365 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1)^4, (x * z * x^-1 * y^-1 * z * y)^2 ] T97.366 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, x * z^-1 * x^-1 * y^-1 * z^-1 * y * x * z * x^-1 * y^-1 * z * y ] T97.367 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, (x * z^-1 * x^-1 * y^-1 * z^-1 * y)^2 ] T97.368 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T97.369 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, (y * z^-1)^4, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T97.370 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T97.371 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, z^-2 * y * x^-1 * z * y^2, (x * y^-1)^4, (x * z^-1)^4 ] T97.372 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^8, z^-4 * x^-1 * z^3 * y^-1, x^-1 * z * x^-1 * y * x^2 * y^-1 * x * z^-1 * x^-1 ] T97.373 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, (x * z^-1)^4, z^8 ] T97.374 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2 ] T97.375 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, z^8 ] T97.376 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z^-2 * y * x * z^2 * x^-1, z * y^-1 * z * y * x * z * x^-1 * z, (x * z^-1)^4, z^8 ] T97.377 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T97.378 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-2 * y * x * z^2 * x^-1, (x * z^-1)^4, y * z^-1 * x * z^-1 * x^-1 * z * y^-1 * z, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, x * z * y * x^-2 * z^2 * y^2 ] T97.379 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * y * x^-1 * z * y^2, y * x * z^-1 * y * x * z^3, z * y^-1 * z^-1 * y * x * z^-1 * x^-1 * z, (x * z^-1)^4 ] T97.380 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x * z^-1 * y * x * z^3, z * y^-1 * z^-1 * y * x * z^-1 * x^-1 * z, y^-1 * z^-2 * y * x * z^-2 * x^-1, (x * z^-1)^4 ] T97.381 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y^-1 * z^-2 * y * x * z^-2 * x^-1, (x * z^-1)^4, (y * z^-1)^4 ] T97.382 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, z^-3 * y * x * z * y * x, z * y^-1 * z * y * x * z * x^-1 * z, (x * z^-1)^4 ] T97.383 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, (y * z^-1)^4 ] T97.384 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, (x * z * y)^2, (x * z^-1)^4, (y * z^-1)^4 ] T97.385 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * x * z^-1 * y * x * z^3, z * y^-1 * z^-1 * y * x * z^-1 * x^-1 * z, (x * z^-1)^4 ] T97.386 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, (x * z^-1)^4, (y * z^-1)^4 ] T97.387 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-2 * y * x * z^2 * x^-1, (x * z^-1)^4, y * z^-1 * x * z^-1 * x^-1 * z * y^-1 * z, z^8, y^-1 * z^-1 * y * x^-2 * z^2 * y * x^-1 ] T97.388 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, (x * z * y)^2, (x * y^-1)^4 ] T97.389 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * y * x^-1 * z * y^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, (x * y^-1)^4 ] T97.390 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^-2 * y * x^-1 * z * y^2, (x * y^-1)^4 ] T97.391 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, (x * y^-1)^4, z^-3 * y * x * z * y * x ] T97.392 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z * y)^2, (x * z^-1)^4, (y * z^-1)^4 ] T97.393 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y^-1 * z^-2 * y * x * z^-2 * x^-1, (x * z^-1)^4, z^8, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.394 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, (x * z * y)^2, (x * z^-1)^4, z^8, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.395 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z^-1)^4, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 ] T97.396 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z * y)^2, (x * z^-1)^4, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 ] T97.397 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z^-1)^4, (y * z^-1)^4 ] T97.398 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^8 ] T97.399 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.400 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, (x * z^-1)^4, z^8, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.401 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, z^-2 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1, y * z^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-3 ] T97.402 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * y * x^-1 * z * y^2, y * x * z^-1 * y * x * z^3, z * y^-1 * z^-1 * y * x * z^-1 * x^-1 * z, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T97.403 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (y * z^-1)^4, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1 ] T97.404 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2, z^-1 * x * z^-2 * x^-1 * z * y * z^-1 * x ] T97.405 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * y^-2 * x * z * y^2, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T97.406 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z * y)^2, (x * y^-1)^4 ] T97.407 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * y^-1)^4, y^-1 * z^-2 * y * x * z^2 * x^-1 ] T97.408 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, (x * y^-1)^4, y * x * z^-1 * y * x * z^3 ] T97.409 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * y^-1)^4, y * x * z^-1 * y * x * z^3, z * y^-1 * z^-1 * y * x * z^-1 * x^-1 * z, y^-1 * z^-2 * y * x * z^-2 * x^-1 ] T97.410 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * z^-1 * y * x * z * y * z^-1, x^-1 * y^-1 * z^-1 * y * x * z^-3, y^-1 * z^-2 * y * x * z^2 * x^-1 ] T97.411 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-2 * y * z^-1 * x^2 * z^2 * y * z^-1 ] T97.412 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^8 ] T97.413 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z^-2 * y * x * z^2 * x^-1, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T97.414 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4, z^8, z^-2 * x * z^-1 * y * x * z^-3 * y ] T97.415 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * z^-2 * y * x * z^2 * x^-1, z^8, z^-2 * y * z^-1 * x^2 * z^2 * y * z^-1 ] T97.416 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^8 ] T97.417 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z * y * z^-1 * y * x^-1 * z^2 * x^-1, z^-1 * x * z * y^2 * z^-2 * x, z^8 ] T97.418 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^8 ] T97.419 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z * y * x^-1 * y^-1 * z^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^8 ] T97.420 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2, z^8 ] T97.421 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, (x * z^-1)^4, z^8, z^-2 * x * z^-1 * x^-1 * z * y * x * z^-1 ] T97.422 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z^-2 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1, x^-1 * z^3 * y * x * z^2 * y^-1 * z^-1 ] T97.423 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^8, x^-1 * z^3 * y * x * z^2 * y^-1 * z^-1 ] T97.424 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^2 * y ] T97.425 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z^-2 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T97.426 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y^-2 * z^-1 * x^-1 * z * y * x * y^-1 * z * y^-1 * z^-1 * x ] T97.427 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, (y * z^-1)^4, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T97.428 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^2 * z * y * z^-1, (y * z^-1)^4 ] T97.429 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T97.430 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-2 * y ] T97.431 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1)^4, (y * z^-1)^4 ] T97.432 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1)^4, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.433 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^2 * z * y * z^-1, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.434 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-1)^4, (y * z^-1)^4 ] T97.435 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z * y * z^-1 * y * x * z^-2 * x, x^-1 * z^2 * y * x * z * y^-1 * z, z^8, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.436 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^8 ] T97.437 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-1)^4, z^8, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2 ] T97.438 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z * y * z^-1 * y * x * z^-2 * x, x^-1 * z^2 * y * x * z * y^-1 * z, (y * z^-1)^4 ] T97.439 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^8, z^-1 * y * z^-1 * y * x^-1 * z^2 * y * z^-1 ] T97.440 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * z * y ] T97.441 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, z * y^-2 * z^-1 * x^-1 * z * y * x * y^-1 * z^-1 * x * y^-1 * z ] T97.442 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, (y * z^-1)^4, z^8, z * y * z^-2 * x^2 * z^3 * y^-1 ] T97.443 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, z^8, z^-1 * x * z^2 * y * x^-1 * z * y^-1 * z^-2 ] T97.444 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, (x * z^-1)^4, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2 ] T97.445 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x * z^-1)^4, (y * z^-1)^4, z^8, z^-1 * x^-1 * y * x^-2 * z^2 * y^2 ] T97.446 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x * z * y * x * z^-1 * x^2 * z * y * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 ] T97.447 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^2 * z * y * x * z^-2 ] T97.448 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2, z^-2 * x^-1 * y * x^2 * z * x^-1 * z * y ] T97.449 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2, z^-1 * x * z^-2 * x^-1 * z * y^-1 * z^-1 * x ] T97.450 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, x^-1 * z * x^-1 * z * x^-1 * z * y^-1 * z^2, z * y * x^-1 * y * x^2 * z^3 * x^-1 ] T97.451 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T97.452 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-3)^2, z^8, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1 ] T97.453 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y ] T97.454 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-3)^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T97.455 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1 ] T97.456 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y^-1 ] T97.457 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y ] T97.458 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y^-1, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y^-1 ] T97.459 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y ] T97.460 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * z * x^-1 * z * x^-1 * z * y^-1 * z^2 ] T97.461 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1 ] T97.462 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z * x^-1 * z * y * x^-1 * z * x^-1 * z^2 ] T97.463 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * z^-1 ] T97.464 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^2 * y * x^-2 * z^3 * x^-1, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^2 * z * y * x * z^2 ] T97.465 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-3)^2, z^8, z^-2 * x^-1 * y * x^2 * z * y^-1 * z^-1 * x ] T97.466 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, z^8, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y, z * y * x^-1 * y * x^2 * z^3 * x^-1 ] T97.467 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, z^8, z * y * x^-1 * y * x^2 * z^3 * x^-1 ] T97.468 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^-2 * y * x^-1 * z * y^2, (x * z^-1)^4, (x * z^-3)^2, z^8 ] T97.469 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y^-1 ] T97.470 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, z^8, z^-1 * x^-1 * z^2 * y^-1 * x * z^3 * y^-1 ] T97.471 : Triangle type {4,4,8} Group order 512 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x * z * y * x * z^-1 * x^2 * z * y * z^-1 * x * z^-1 * x^2 * y^-1 * x * z^-1 * x * z^-1 ] T97.472 : Triangle type {4,4,10} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y^-1 * z^-2 * x^2 * z^2 * y^-1, y * x^-1 * z * y^-1 * x * z^-3, (x * z * y^-1 * z^-1)^2 ] T97.473 : Triangle type {4,4,10} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, (y * z^-2)^2, z * x^-1 * y * x^2 * z * y * x^-1 ] T97.474 : Triangle type {4,4,10} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * y * x^-1 * z * y^-1 * x, z * x^-1 * z * x^-1 * y^-1 * z * y^-1 ] T97.475 : Triangle type {4,4,10} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, x^-1 * y * z^-2 * x^-1 * y^-1 * x^-1 * y * z^-1 * x * z * y, (x * z^-2 * x * z^-1)^2 ] T97.476 : Triangle type {4,4,10} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, x^-1 * y * z^-2 * x^-1 * y^-1 * x^-1 * y * z^-1 * x * z * y, (x * z^-2 * x * z^-1)^2 ] T97.477 : Triangle type {4,4,14} Group order 448 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1, z^8 * y^-1 * x^-1 * z^5 ] T97.478 : Triangle type {4,4,26} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-4 * x^-1 * z^5 ] T97.479 : Triangle type {4,4,26} Group order 416 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^16 * y * z^-7 * x * z^2 ] T97.480 : Triangle type {4,4,50} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-2 * y * z^-5 * x * z^-6 ] T97.481 : Triangle type {4,4,50} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-38 * x^-1 * z * y^-1 * z^-10 ] T97.482 : Triangle type {4,4,98} Group order 392 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^82 * y * x^-1 * y * x^-1 * z^14 ] T97.483 : Triangle type {4,4,194} Group order 388 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^84 * y * x^-1 * z^12 ] T97.484 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x * z * y^-1, y * x^-1 * y * x^-1 * z * y * z^-1 ] T97.485 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x * z^-1 * x^-1 * y^-1 * x * z^-2 * y ] T97.486 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * z * y, (z^-1 * y)^3, y^2 * x^-2 * y^-1 * z * x^-1 ] T97.487 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T97.488 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z * x^-1 * z * y^-2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.489 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.490 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^3 * x^-1 * z^2 * y^-1, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T97.491 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z * x^-1 * z * y^-2, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T97.492 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T97.493 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.494 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^2 * x^-1 * y^-1 * z * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T97.495 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, y^-1 * z^2 * x^-1 * y^-1 * z * y^-1 ] T97.496 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^2 * x^-1 * y^-1 * x * z * y^-1 * z ] T97.497 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-1 * y, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.498 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T97.499 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-1 * y, z^-2 * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T97.500 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T97.501 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.502 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1 ] T97.503 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z * y^-1 * z * x^-1 * z * y^-2, y * x^-1 * y * x^2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T97.504 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * x^-1 * z^2 * y * x * y^-2 * z^-2 ] T97.505 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * x^-1 * z^2 * y * x * y^-1 * z * y * z^-1 ] T97.506 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, y * z^-2 * x^-1 * z^3, y^-1 * z^2 * x^-1 * y^-1 * z * y^-1 ] T97.507 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, (y * z^-2)^2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.508 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (y * z^-2)^2, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T97.509 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T97.510 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T97.511 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^2 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.512 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T97.513 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y * z^-1 * x^-1 * z * y^-2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T97.514 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 ] T97.515 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T97.516 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, x^-1 * y^-1 * z^-1 * x^-1 * y^2 * z^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T97.517 : Triangle type {4,6,12} Group order 384 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, y * z^-1 * y * x^-1 * y * x * z, y^-1 * z * y * x^2 * z^2 * x^-1 ] T97.518 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2, z^3 * x^-1 * z^2 * y^-1 ] T97.519 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T97.520 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, x^-1 * y^2 * x^2 * z * x^-1 * z ] T97.521 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.522 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2 ] T97.523 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T97.524 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y * x^-1 * z^2 * x^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T97.525 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y^2 * x^-1 * z * y^3, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-3 ] T97.526 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T97.527 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1, x^-1 * y^-1 * z^-1 * x^2 * z * y^-1 * z, x * z^-1 * x^-1 * y^-1 * x * z^-2 * y ] T97.528 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x^-1 * z^3, y * x * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * z ] T97.529 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, z^-3 * x^-1 * z^2 * y^-1, x^-1 * y^2 * x^2 * z * x^-1 * z ] T97.530 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, (x * z * y)^2, z^-3 * x^-1 * z^2 * y^-1 ] T97.531 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, (x * z * y)^2, z^3 * x^-1 * z^2 * y^-1 ] T97.532 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, z^3 * x^-1 * z^2 * y^-1, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1 ] T97.533 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^-3 * x^-1 * z^2 * y^-1 ] T97.534 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, z^-3 * x^-1 * z^2 * y^-1, x^-1 * y^2 * x^2 * z * x^-1 * z ] T97.535 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1, y * z^-1 * x^-1 * y^-1 * x * y^-2 * z^-1 ] T97.536 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.537 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, y^-1 * z * y^-1 * z * y^-3 * z^-1 * x^-1 * y^-2 * z^-1 * y * x ] T97.538 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y * z^-1 * y, y * z^-2 * x^-1 * z^3, y^-1 * z * y^-1 * z * y^-3 * z^-1 * x^-1 * y^-2 * z^-1 * y * x ] T97.539 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, (x * z * y^-2)^2, x^-1 * y * x^-1 * y * x^-1 * y * z^-3 ] T97.540 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-2 * x^-1 * z^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.541 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, y * z^-2 * x^-1 * z^3, z * y^2 * x^-2 * z^2 * y * x^-1 ] T97.542 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.543 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * y^-2 * z^-2 ] T97.544 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * y^-1 * z * y * z^-1 ] T97.545 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * y^-2 * z^-2 ] T97.546 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * y^-1 * z * y * z^-1 ] T97.547 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, x^-1 * y^2 * x^2 * z * x^-1 * z, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T97.548 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.549 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.550 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-2 * x^-1 * z^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, y * z^-1 * x^-1 * y^-1 * x * y^-1 * z * y ] T97.551 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, y * z^-2 * x^-1 * z^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.552 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z^3 ] T97.553 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T97.554 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.555 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^-3 * x^-1 * y * z^-2, y * x * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * z ] T97.556 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * x * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * z ] T97.557 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, y^2 * x^-2 * y^-1 * z * x^-1 ] T97.558 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z^2 * x^-1 * y^-1 * x * z * y^-1 * z ] T97.559 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z ] T97.560 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * z^3, y^-1 * z * y * x^2 * z^2 * x^-1 ] T97.561 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3, y^-1 * z * y * x^2 * z^2 * x^-1 ] T97.562 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z, y * z^-2 * x^-1 * z^3 ] T97.563 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^2 * z^2 * x^-1, z^-3 * y * x^-1 * z * y^-1 * z^-1 ] T97.564 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, z^-3 * y * x^-1 * z * y^-1 * z^-1 ] T97.565 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z ] T97.566 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (z^-1 * x)^3, (y * z^-2)^2 ] T97.567 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z, x * z^-2 * x^-1 * z * y * z^-1 ] T97.568 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y^-1 * z * y * x^2 * z^2 * x^-1 ] T97.569 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z ] T97.570 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1 ] T97.571 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * y * x^2 * z^2 * x^-1 ] T97.572 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T97.573 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1 ] T97.574 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3 ] T97.575 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-1 * x * y^-1 * z^-4 * x^-1 * y^-1 * z^-3, z * y^-1 * z^2 * y^-1 * z^-3 * x^-1 * z^-3 * x^-1 * z ] T97.576 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y^2 * x * z^3, y * x * z * y * x^-1 * z * y * x * y^-1 * z^-1 * x * z ] T97.577 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y * x^-1 * y^2 * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * z^2 * y^2 ] T97.578 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (z^-1 * y)^3, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y^2 * x * z^2 * y^2 ] T97.579 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T97.580 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^-1 * z^2 * x^-1 * z * y^-1 * z ] T97.581 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T97.582 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, y^-1 * z^2 * x^-1 * z * y^-1 * z ] T97.583 : Triangle type {4,6,12} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * y * x * z^-2 * x^-1 * y^-1 * x * z * x^-1 * z * y^-1 * z^-1 ] T97.584 : Triangle type {4,6,20} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, (y * z^-2)^2, z^-3 * x * z^2 * y * x * y^-1 * z^-2 * x^-1 * y^-1 ] T97.585 : Triangle type {4,6,84} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-8 * x * z^4 * y^-1 * z^-15 ] T97.586 : Triangle type {4,8,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z * y^-1 * z^-1 * x^2 * z^2 * y^-1 ] T97.587 : Triangle type {4,8,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, (x^-1 * z * y)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, y * z^-1 * y * x^2 * z^3 ] T97.588 : Triangle type {4,8,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z * y^-1 * z^-1 * x^2 * z^2 * y^-1 ] T97.589 : Triangle type {4,8,40} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, y * z^-1 * y * x^2 * z^3, y^8 ] T97.590 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-6 * x^-1 * z * y * x * z^3 * y * z^-1 * x^-1 * z^2 * y * z^-4 ] T97.591 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 * y * x^-1 * z * y * x^-1 * y * z^-5 * x * z^3 ] T97.592 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^7 * y * z^-4 * x * z * y^-1 * z^-3 * x^-1 * z^3 ] T97.593 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-8 * x^-1 * z^4 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-2 * x * z * y ] T97.594 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-6 * x^-1 * z * y * x * z^2 * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-5 ] T97.595 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-6 * x^-1 * z * y * x * z^3 * y * z^-1 * x^-1 * z * y^-1 * z^-5 ] T97.596 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-6 * x^-1 * z * y * x * z^2 * y^-1 * z^-2 * x^-1 * z^2 * y * z^-4 ] T97.597 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^25 * y * z^-7 * x * z^7 ] T97.598 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^4 * y * z^-1 * x^-1 * z^8 * y * z^-5 * x ] T97.599 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^-11 * x^-1 * z^4 * y * z^-4 ] T97.600 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 * y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-2 * x * z^3 ] T97.601 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^9 * y * z^-3 * x^-1 * z * y * z^-5 * x ] T97.602 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-4 * x * z * y * x * y^-1 * z^-7 * x * z^4 ] T97.603 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 * y * x^-1 * z * y * x^-1 * y * z^-5 * x^-1 * z^3 ] T97.604 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-4 * x * z * y * x * y^-1 * z^-7 * x^-1 * z^4 ] T97.605 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^26 * y * x^-1 * y * x * z^12 ] T97.606 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^6 * y * z^-1 * x * z^5 * y^-1 * z^-6 * x ] T97.607 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^-11 * x * z^3 * y^-1 * z^-5 ] T97.608 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^7 * y^-1 * z^-1 * x * y^-1 * z^-2 * x^-1 * z * y^-1 * z^-1 * x^-1 * z^5 ] T97.609 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^12 * y^-1 * z^-2 * x * z^5 ] T97.610 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-4 * x * z^3 * y * z^-5 * x^-1 * z^5 ] T97.611 : Triangle type {4,8,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^9 * y * z^-3 * x^-1 * z * y * z^-5 * x^-1 ] T97.612 : Triangle type {4,10,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T97.613 : Triangle type {4,10,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x * z^-1 * y, x^-1 * z * y * x * z * y, y * x^-1 * y^-1 * z * y^2 * x * y^-1 * z * y ] T97.614 : Triangle type {4,10,20} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1, y^10 ] T97.615 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * y^-2 * z, y^3 * z^-1 * y^5 * z^-1 * y^3 * z^-2 * y * z^-2 ] T97.616 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^3 * z^-1 * y^2 * z^-1 * y^5 * z^-6 ] T97.617 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1, y^-5 * x^-1 * z * y^-1 * z^2 ] T97.618 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1, y^-5 * z * y^-2 * z ] T97.619 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^-1 * z^2 * y^-1, y^-5 * x * z * y^-1 * z^2 ] T97.620 : Triangle type {4,18,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^3 * z^-2 * y * z^-4 * y * z^-2 * y^5 ] T97.621 : Triangle type {4,20,70} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1, y^7 * z^-1 * y * z^-1 ] T97.622 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^-1 * z^3 * y^-4 * x * y^-2 * z^2, y^-6 * z * x^-1 * y^-5 ] T97.623 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-1 * z^3 * y^-3 * z * x^-1 * z * y^-3, y^-6 * z * x^-1 * y^-5 ] T97.624 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * z^-1 * y^3 * x^-1 * z^-1 * y^2 * z^-14 ] T97.625 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-2 * y^3 * z^-1 * y^4 * z^-13 ] T97.626 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^3 * y^-7 * z * y^-1 ] T97.627 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^3 * y^-6 * z^3 ] T97.628 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T97.629 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x^-1 * z * y^3 * x * y^-1 * z^-3 ] T97.630 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-2 * z * y^4 * x^-1 * y^-5, x^-1 * z^3 * y * x^-1 * z * y * x^-1 * y * x * y^-3 * z^-4 ] T97.631 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^-3 * z^-1 * y^2 * x^-1 * y^-2 * z^-1 * x * y^-3, z^5 * y * x^-1 * y * x^-1 * z^5 ] T97.632 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T97.633 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x^-1 * z * y^3 * x * z * y * z^-2 ] T97.634 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, y * z^-2 * x^-1 * z^3, y^2 * z^-1 * y^2 * z^-3 ] T97.635 : Triangle type {4,24,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, y^-1 * z * y * x^-1 * y^-3 ] T97.636 : Triangle type {4,34,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-8 * y^2 * z^-2 * y^8 * z^-2 * y^11 ] T97.637 : Triangle type {4,66,132} Group order 264 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-35 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T97.638 : Triangle type {4,130,260} Group order 260 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^33 * z^-1 * y^5 * z^-1 * y^12 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T97.639 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y^3 * x^2 * y^-1 * z^2, y * x^-1 * y^-2 * x * z^3 ] T97.640 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, z * y^-1 * z^-1 * x * z^2, z^-1 * y * x^-2 * z * y^-2 ] T97.641 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, (x * z * y)^2, z * y * x^-2 * y * x^-1 * z, y * x * z^-1 * x^-1 * y * x * z^-1, z * x^-1 * y * x^2 * y^-1 * x * y^-1 ] T97.642 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-2 * y^2 * z^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y^-1 ] T97.643 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, (y * z^-1 * y)^2, z * y * x^-2 * y * z^-1 * x ] T97.644 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, y^2 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x ] T97.645 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, z * y * z^-1 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y * z^-2 ] T97.646 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, (x * z * y)^2, z^-1 * y * x^-2 * y^-1 * x * z^-1, x * z^-1 * x^-2 * z * y^-2 ] T97.647 : Triangle type {5,10,10} Group order 320 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T97.648 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, y^6, z^6, y * z^-1 * x^-2 * y^-1 * z * x^-1, x * z^-1 * y * x^-1 * z * y^2, z^2 * y * x^-1 * z * y^-1 * x, x^-1 * z * x^-1 * y^-1 * x * z * y * z^-1 ] T97.649 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, z * y^-2 * x * y^-1 * z, y^6, y^-1 * z^-1 * x^-2 * y^2 * x^-1 ] T97.650 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^6, z^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2 ] T97.651 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y, z * x^-1 * y^-1 * x^2 * y^-2 * z ] T97.652 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, z^-1 * x * z^-1 * x^2 * y^-1 * x * y^-1 ] T97.653 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, z * y^-1 * z^-1 * x^2 * y^-1 * x * y^-1 ] T97.654 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, y^6, y^-1 * z^-1 * x^-2 * y^2 * x^-1 ] T97.655 : Triangle type {6,6,6} Group order 384 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * z * y^-1 * x * y^-1 * z, z^-1 * x^-1 * y * x^2 * z * x^-1 * y^-1, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1 ] T97.656 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, x^-1 * z * x^-1 * z * y * x * z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T97.657 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.658 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * z^-1 * x^-2 * y^-1 * z * x^-1, x * z^-1 * y * x^-1 * z * y^2, z^2 * y * x^-1 * z * y^-1 * x, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.659 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * z^-1 * x^-2 * y^-1 * z * x^-1, x * z^-1 * y * x^-1 * z * y^2, z^2 * y * x^-1 * z * y^-1 * x, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T97.660 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, z^6, y * x^-3 * z * x^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.661 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.662 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T97.663 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x * z * y)^2, z^6, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.664 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y^-1 * z^-1 * x^2 * y^-2 * z ] T97.665 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z ] T97.666 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, z^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T97.667 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, y^6, (x * z * y)^2, z^6, y * x^-3 * z * x^-2, z^-1 * y * z^-1 * x^2 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z ] T97.668 : Triangle type {6,6,6} Group order 384 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y^6, y * x^-3 * z * x^-2, (y * z^-1)^4 ] T97.669 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z^-1 * y, z^-1 * y * x^-1 * y * x^-1 * y^-2 * x * y^-1 ] T97.670 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-4 * x^-1 * z^3 * y^-1 ] T97.671 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T97.672 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z^-2 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-2 ] T97.673 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * z * y^-1 * z^-1 ] T97.674 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T97.675 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2 ] T97.676 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, y * x^-3 * z * x^-2 ] T97.677 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^2 * z^-1 * x^2 ] T97.678 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * z * y^-1 * z^-1 ] T97.679 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^2 * y * x^2 * z^3, z^-1 * x^-1 * z * y^-1 * z^-1 * x * z^2 * y * z^-1 ] T97.680 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^2 * y * x^-1 * z^3, (x * z^2 * y^-1 * z^-1)^2 ] T97.681 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T97.682 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T97.683 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, z^4 * y * x^-1 * z * y * x^-1 * z^5 ] T97.684 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^4 * y^-1 * z^-2 * x * z^5 ] T97.685 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (y * z^-2)^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^-1 * x * z * y * x^-1 * y^-1 * z^-2 ] T97.686 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, (y * z^-2)^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z * y^-1 * x * y^-1 * x * z^3 ] T97.687 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^-2 * z * x^-1 * y, z * y^2 * x^-1 * z * y^-1 * z, z^-2 * y * x^-1 * z * y^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z * y^-1 * x * y^-1 * x * z^3 ] T97.688 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^-2 * z * x^-1 * y, z * y^2 * x^-1 * z * y^-1 * z, z^-2 * y * x^-1 * z * y^2, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^-2 * x * y^-1 * x * z^2 * y ] T97.689 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^8, z^4 * y^-1 * z^-2 * x^-1 * z^5 ] T97.690 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, z^4 * y * x^-1 * z * y * x^-1 * z^5 ] T97.691 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, x^6, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T97.692 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T97.693 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, (x^-1 * z * y)^2, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1, z * y * x^-2 * y * x^-1 * y^-1, y^8 ] T97.694 : Triangle type {6,8,24} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z * y^-1, (x^-1 * z * y)^2 ] T97.695 : Triangle type {6,9,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, z * y^-1 * z^3 * y * z^-2 * x * z^2 * y * x^-1 ] T97.696 : Triangle type {6,9,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, x^-1 * y^-1 * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T97.697 : Triangle type {6,10,45} Group order 270 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y * x * z^-1 * x^-1 * y * z^-2 ] T97.698 : Triangle type {6,10,45} Group order 270 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y * z^-2 * y^2 * z^-1 * y * z^-2, z^2 * y^-1 * z^-2 * x * z^4 ] T97.699 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * z * x^-1, (x * z * y)^2, z^2 * y^-1 * x^2 * z^3 ] T97.700 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, x * z^-1 * x^-2 * z * y^-1 * z^-1, x * z^-2 * x^-1 * z * x^-1 * y^-1, z^3 * x^-1 * z^2 * y^-1 ] T97.701 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^-3 * z^2 * y^-2 * z * y^-1 * z^3 ] T97.702 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y * x^-3 * z * x^-2, y * z^-2 * x^-1 * y * z^-2 ] T97.703 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * z^-1 * x * z * y^-1, x * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z ] T97.704 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1 ] T97.705 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * y^-1 * z * y^-1 ] T97.706 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-1 * z^2 * y^-1 * z * x^-1 * z * x * y^-1 * z * y^-2 ] T97.707 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, z^3 * y^-2 * z * y^-3 * z^2 * y^-1 ] T97.708 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y^3 * z^-2, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T97.709 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * x^2 * z^2 * y^-1 ] T97.710 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z * y^-2 * z^2 * y^-1 * z * x^-1 * y^-3 * z * y^-1 ] T97.711 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * x^-3 * z * x^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-2 * x^-1 * y * z^-2 ] T97.712 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-2 * z * y^-1 ] T97.713 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, (y * z^-1 * y)^2, (x^-1 * z * y)^2 ] T97.714 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^-1 * z^3 * y^-3 * z * x^-2 * y^-1 * z * y^-1 * z ] T97.715 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, (y * z^-1 * y)^2, (y * z^-2)^2 ] T97.716 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * z * x^-2, z^2 * y^-1 * z * y^-2 * z^3 * y^-1 * z^2 ] T97.717 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-1 * y^-1 * x^2 * z * y * x, z^-1 * y * z^-1 * x^2 * z^-2 * y ] T97.718 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, (y * z^-1)^6 ] T97.719 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, (y * z^-1 * y)^2, (x^-1 * z * y)^2, z * y * x^-2 * y * x^-1 * y^-1, x^-1 * z * x^-2 * z * y * z^-1 ] T97.720 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, y * x^-3 * z * x^-2, y^-1 * z^-1 * x^-2 * y^-1 * z^-1 * x, z * y^-1 * z * y^-2 * z^3 * y^-3 * z ] T97.721 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^-2 * z^2 * y^-1 * z^4 * y^-1 * z^2 ] T97.722 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T97.723 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, x^-1 * y * x^-2 * y^-2 * z, z * y^-2 * x^2 * y^-1 * z * y^-1 ] T97.724 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y * z^-1 * y * x^-1 * z^2 * y, z^-1 * x * z^-1 * x^-1 * z * x^-1 * y^-1, z^-1 * y^4 * z^-3 ] T97.725 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T97.726 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x * y^-2 * x * z * y^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T97.727 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.728 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.729 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, z * y * z^-1 * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.730 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.731 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * z * x^-2, y^-1 * z * y * x^2 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.732 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * x^-2 * y^-2 * x, z^-2 * y * x^-1 * z * y^-2, z * x^-1 * y^-1 * x^2 * z * x^-1 * y^-1 ] T97.733 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-2)^2, (y * x^-1 * z)^3 ] T97.734 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, z^-3 * x^-1 * z^2 * y, z * y^3 * x * z * y * x ] T97.735 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, z^-1 * y^2 * x^-1 * y^3, y * x^-1 * z * x^-1 * z * y^3 * x^-1 * y^-3 * z * y^2 ] T97.736 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, z^-1 * y^2 * x^-1 * y^-3, (y * x^-1 * z)^3 ] T97.737 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, z^-2 * y * x^-1 * z * y^-2, y^-3 * z^-1 * x * z^-1 * y * x * y^-4 * z^-1 * x * y^-1 ] T97.738 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, z^-1 * y^2 * x^-1 * y^3, y^-12 ] T97.739 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, (y * z^-1)^4 ] T97.740 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^3 * x^-1 * y^-1 * z * y, z * y * z^-1 * x^-1 * z^3, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T97.741 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, x * z * x^-2 * y^-1 * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T97.742 : Triangle type {6,12,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, z^-2 * y * x^-1 * z * y^-2, y^-12 ] T97.743 : Triangle type {6,12,44} Group order 264 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^5 * y * z^-1 * x * z^3 * y^-1 * z^-1 * x^-1 * z^10 ] T97.744 : Triangle type {6,40,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-7 * z * y^-2 * z^6 * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-8 * z * y^-1 * z * y^-1 * z ] T97.745 : Triangle type {6,40,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^4 * z^-3 * y^5 * x^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y ] T97.746 : Triangle type {6,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y * z^-1 * y^4 * z^-4 ] T97.747 : Triangle type {6,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y * z^-1 * y^7 * z^-1 ] T97.748 : Triangle type {6,60,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-4 * y * z^-2 * y^5 * x^-1 * y * z^-1 * y * z^-2 * y * z^-2 ] T97.749 : Triangle type {6,117,234} Group order 234 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^9 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-6 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T97.750 : Triangle type {6,117,234} Group order 234 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^11 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 * z^-6 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T97.751 : Triangle type {8,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1, x^8 ] T97.752 : Triangle type {8,8,12} Group order 288 Chiral action Defining relators: [ x * y * z, x^-1 * z * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1, x^8 ] T97.753 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T97.754 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z^-1 * y)^2, (x * z * y)^2, y^-1 * x * z * y^-1 * x * z^3 ] T97.755 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^-2 * x^-3 * y * z^-3 ] T97.756 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * x^-3 * y * z^-3 ] T97.757 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^2 * x^-2 * z * y^-1 * x, z^-3 * x^-1 * z^2 * y^-1, x^8 ] T97.758 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^2 * x^-2 * z * y^-1 * x, x^8, z * y^-1 * z^-1 * x^2 * z * y^-1 * z ] T97.759 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^2 * x^-2 * z * y^-1 * x, z^3 * x^-1 * z^2 * y^-1, x^8 ] T97.760 : Triangle type {8,8,12} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z * x^-3 * y^-3, z^2 * x^-2 * z * y^-1 * x, x^8, z^2 * y^-1 * x^2 * z^2 * y^-1 ] T97.761 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.762 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z * y^2 * x * z * x^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T97.763 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T97.764 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * y^-1 * z^-2 ] T97.765 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, (x * z * y)^2, y^2 * x^-2 * y^-1 * z * x^-1 ] T97.766 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, z * y^-2 * x * z * x^-1, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y * z^-1 * y ] T97.767 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T97.768 : Triangle type {8,16,16} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * y * x^-1 * y^-2 * z, y * z^-2 * x^-1 * z * y^2 ] T97.769 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x^8, z^-1 * y^4 * z^-3 ] T97.770 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^9 * z^-4 * y^3 ] T97.771 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * x^-2 * z * y^-1 * x, x^8, z^-2 * y^3 * z^-2 * y ] T97.772 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, z^-1 * y^4 * z^-3 ] T97.773 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, x^8, z^-2 * y^3 * z^-2 * y ] T97.774 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, z^-1 * y^4 * z^-3, y * x^-4 * z * x^-3 ] T97.775 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, (y * z^-1)^4 ] T97.776 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * y * x^-1 * z * y^-2, (y * z^-1)^4 ] T97.777 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, (y * z^-1)^4 ] T97.778 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T97.779 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T97.780 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^3 * y^-1 ] T97.781 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, (y * z^-1)^4, z^-4 * x^-1 * z^3 * y^-1 ] T97.782 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * y^-1 * x^2 * z * y^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, y^4 * x^-1 * y^-2 * z^-1 * y, z * y^-1 * z^-2 * x^-1 * z^4 ] T97.783 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^8, y^4 * x^-1 * y^-2 * z^-1 * y, z^2 * y^-1 * x * y^-1 * x * z^4 ] T97.784 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^8, z * y * z^-1 * x^-1 * y^-1 * x * z^4, x * z * y^4 * x^-1 * y^-1 * z^-1 * y ] T97.785 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, y^2 * z^-1 * y^2 * z^-3 ] T97.786 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T97.787 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-2 * y^3 * z^-3 * y * z^-1 * y^2 * z^-1 ] T97.788 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-1 * y^4 * z^-3 ] T97.789 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * z^2 * y, z^-2 * x^-2 * z * y^-1 * x, z^-1 * y^4 * z^-3 ] T97.790 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, (x^-1 * z * y)^2, z^-1 * x^-3 * z^2 * y, y^2 * z^-1 * y^2 * z^-3 ] T97.791 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, z^-1 * y^4 * z^-3 ] T97.792 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * x^-2 * z * y^-1 * x, x^8, y * z^-1 * y * z^-1 * x^-1 * y * z^-3 ] T97.793 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, y * x^-3 * y^-1 * z * y, y^2 * z^-1 * y^2 * z^-3 ] T97.794 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, x^8, z^-1 * y^4 * z^-3 ] T97.795 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, x^-1 * z * x^-2 * z * y * z^-1, y^2 * z^-1 * y^2 * z^-3 ] T97.796 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * z * x^-2 * z * y * z^-1, z^-1 * y^4 * z^-3 ] T97.797 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * x^-2 * z * y^-1 * x, x^8, (y * z^-1)^4 ] T97.798 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y^4 * z^-3 ] T97.799 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, z^-1 * y^4 * z^-3 ] T97.800 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, x^8, (y * z^-1)^4 ] T97.801 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^8, y^4 * x^-1 * y^2 * z^-1 * y ] T97.802 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x^8, y^4 * x^-1 * y^2 * z^-1 * y ] T97.803 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * x^-4 * z * x^-3, y^-4 * x^2 * z * y^-1 * z * y^-1 ] T97.804 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, x^8, z * y^-1 * z^2 * x^-1 * z^4 ] T97.805 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, y^4 * x^-1 * y^2 * z^-1 * y ] T97.806 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-3 * y^4 * z^-3 * y * z^-1 * y^2 * z^-1 ] T97.807 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T97.808 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, (y * z^-2 * y)^2 ] T97.809 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, y * z^-2 * x^-1 * y^-2 * z, z^-1 * y^4 * z^-3 ] T97.810 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, x^8, (y * z^-1)^4 ] T97.811 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y)^2, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T97.812 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.813 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x^8, z^-1 * y^4 * z^-3 ] T97.814 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y)^2, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.815 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, z^-1 * y^4 * z^-3 ] T97.816 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * y^2 * z^-1 * y^2 * z^-1 * y * z^-3 * y^2 * z^-1 ] T97.817 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^4 * z^-3 ] T97.818 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, y * x^-3 * y^-1 * z * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.819 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, x^8, y * z^-1 * y * z^-1 * x^-1 * y * z^-3 ] T97.820 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * y * x^-1 * z * y^-2, z^-1 * y^4 * z^-3 ] T97.821 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * x^-2 * z * y^-1 * x, x^8, z^-2 * y^3 * z^-2 * y ] T97.822 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z * y^2 * x^-1 * z * x^-1, z * y * x^-2 * y * x^-1 * y^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.823 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^3 * z^-2 * y ] T97.824 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^3 * z^-1 * y * z^-1 * y^3 * z^-5 * y ] T97.825 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y)^2, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y ] T97.826 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, z^-1 * x^-3 * z^2 * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T97.827 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^8, y * z^-1 * y * z^-1 * x^-1 * y * z^-3 ] T97.828 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * z^2 * y, z^-2 * x^-2 * z * y^-1 * x, z^-2 * y^3 * z^-2 * y ] T97.829 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, z^-2 * y^3 * z^-2 * y ] T97.830 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, x^8, z^-2 * y^3 * z^-2 * y ] T97.831 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y * z^-1 * y * z^-2 * y * z^-1 * y^2 * z^-2 * y * z^-1 * y^2 * z^-1 ] T97.832 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y^3 * z^-2 * y ] T97.833 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, y * z^-1 * y * z^-1 * x^-1 * y * z^-3 ] T97.834 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y)^2, y * x^-3 * y^-1 * z * y, z^-2 * y^3 * z^-2 * y ] T97.835 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-1 * z * y, z^-1 * y * x^-2 * y^-2 * x, z^-2 * y * x^-1 * z * y^-2, z^-2 * y^3 * z^-2 * y ] T97.836 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z * y^2 * x^-1 * z * x^-1, z * y * x^-2 * y * x^-1 * y^-1, y^2 * z^-1 * y^2 * z^-3 ] T97.837 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8, (y * z^-1)^4 ] T97.838 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * y * x^-1 * z * y^-2, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, z^-4 * x^-1 * z^3 * y^-1 ] T97.839 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^8, z^-1 * y * x * y^-1 * x * y^-2 * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T97.840 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^-4 * x^-1 * z^3 * y^-1 ] T97.841 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x^8, z^-4 * x^-1 * z^3 * y^-1 ] T97.842 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x^-1 * z * y)^2, (y * z^-1)^4 ] T97.843 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, (y * z^-1)^4 ] T97.844 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T97.845 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, (x^-1 * z * y)^2, (y * z^-1)^4 ] T97.846 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, (y * z^-1)^4 ] T97.847 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * z^-2 * x^-1 * y^-2 * z, x^8, y^-1 * z^-1 * x * y^-1 * x * y^-2 * z ] T97.848 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z * y^-2, x^8 ] T97.849 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, (y * z^-1)^4 ] T97.850 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^8, (y * z^-1)^4 ] T97.851 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, (y * z^-1)^4 ] T97.852 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T97.853 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^8, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T97.854 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x^-1 * z * y)^2, z^2 * y^2 * x^-1 * z^2 * y^-1 * z ] T97.855 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, (x^-1 * z * y)^2, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T97.856 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^-2 ] T97.857 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T97.858 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^8, z^-1 * y * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 * z^-1 ] T97.859 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, y * x^-3 * y^-2 * z^-1, y^5 * z^-1 * y * z^-1 ] T97.860 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, x^8, y * x^-4 * z * x^-3, y^-1 * z^3 * x^-1 * z^2 * y^-2 ] T97.861 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, z^-2 * x^-2 * z * y^-1 * x, x^-1 * z * x^-2 * y^-1 * z^-2, (y * z^-2 * y)^2 ] T97.862 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, (x * z * y)^2, y * x^-3 * y^-2 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, x^-1 * z * x^-2 * y^-1 * z^-2, y^5 * z^-1 * y * z^-1 ] T97.863 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, z^-1 * x^-3 * z * y^-1 * z^-1, z^-1 * y^4 * z^-3 ] T97.864 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^8, y * x^-4 * z * x^-3, y^-1 * z * y^-2 * x^2 * y^-1 * z * y^-2 ] T97.865 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * y^-2 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, y^3 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T97.866 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^-5 * x^-1 * y^-1 * x^-1 * z * y * z^-4 * x^-1 * z^2 * y * z^-1 ] T97.867 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^4 * y^-1 * z^-2 * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z^5 ] T97.868 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^-10 * x^-1 * z^2 * y * z^-3 ] T97.869 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^2 * y^-1 * z^-5 * x^-1 * y * z^-2 * x * z^5 ] T97.870 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * y^3 * z^-2 * y, z^2 * y * z^-1 * x^-1 * z^4 ] T97.871 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^2 * y * z^-1 * x^-1 * z^4 ] T97.872 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x^-1 * z * x^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.873 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * y^3 * z^-2 * y, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.874 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * y * x^-1 * z * y^-2, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.875 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, (x * z^-2)^2, y^4 * x^-1 * y^-1 * z * y^2, z^-2 * x^-1 * z * y * x * z * y * z^-2 ] T97.876 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^8, z^-1 * y^3 * x^-1 * y^-4, z * y * x^-1 * z * y * x * z^4 ] T97.877 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^8, z^-1 * y^3 * x^-1 * y^-4, z^-2 * x^-1 * z * y * x * z * y * z^-2 ] T97.878 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, (x * z^-2)^2, y^4 * x^-1 * y^-1 * z * y^2, z * y * x^-1 * z * y * x * z^4 ] T97.879 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * y * x^-1 * z * y^-2, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, z^2 * y * z^-1 * x^-1 * z^4 ] T97.880 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x^8, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.881 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, x^8, z^2 * y * z^-1 * x^-1 * z^4 ] T97.882 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^8, z^-1 * y^3 * x^-1 * y^-4, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.883 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, (x * z^-2)^2, y^4 * x^-1 * y^-1 * z * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T97.884 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^8, z^-1 * y^3 * x^-1 * y^-4, z^-4 * x^-1 * z^2 * y * z^-1 ] T97.885 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^4 * x^-1 * y^-1 * z * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T97.886 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T97.887 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T97.888 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * y * x^-1 * z * y^-2, x^8, y^-1 * z^-1 * x * y^-1 * x * z * y^-2 ] T97.889 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2, x^8 ] T97.890 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * x^-2 * y^-2 * x, x^8 ] T97.891 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2, y * x^-3 * y^2 * z^-1 ] T97.892 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * y * z^-1 * x, y^3 * x^-1 * z^3 ] T97.893 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-2)^2, (x * z^-2)^2, y * x^-3 * y^2 * z^-1, z * x^-3 * z * y^-1 * z, y^3 * x^-1 * z^3 ] T97.894 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x * z * y)^2, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * y * z^-1 * x, x^8 ] T97.895 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y)^2, x^-1 * y * x^-2 * y * z^-1 * y, z^-1 * y * x^-2 * y^-2 * x, x^-1 * z * x^-2 * y^-1 * z^2 ] T97.896 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * y * x^-2 * y * z^-1 * y, z^-1 * y * x^-2 * y^-2 * x, x^-1 * z * x^-2 * y^-1 * z^2, y^3 * x^-1 * z^3 ] T97.897 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * z * y)^2, y * x^-3 * y^2 * z^-1, z * x^-3 * z * y^-1 * z, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1 ] T97.898 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2 ] T97.899 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, y * x^-3 * y^2 * z^-1, z * x^-3 * z * y^-1 * z, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1 ] T97.900 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x * y^-2)^2, (x * z * y)^2, (x * z^-2)^2 ] T97.901 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y * x^-3 * y^2 * z^-1 ] T97.902 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, (x^-1 * z * y)^2, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-2 * y * z^-1 * x ] T97.903 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x * y^-2)^2, (x * z * y)^2, (x * z^-2)^2, y * x^-3 * y^2 * z^-1, z * x^-3 * z * y^-1 * z ] T97.904 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, y^3 * x^-1 * z^3 ] T97.905 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, (x * z * y)^2, x^8 ] T97.906 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, (x^-1 * z * y)^2, x^-1 * y * x^-2 * y * z^-1 * y, z^-1 * y * x^-2 * y^-2 * x ] T97.907 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, (x^-1 * z * y)^2 ] T97.908 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T97.909 : Triangle type {8,16,16} Group order 256 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, x^-1 * y * x^-2 * y * z^-1 * y, z^-1 * y * x^-2 * y^-2 * x, x^-1 * z * x^-2 * y^-1 * z^2 ] T97.910 : Triangle type {8,24,30} Group order 240 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^3 * x^-1 * z * y^-1 * z, x^8 ] T97.911 : Triangle type {8,24,30} Group order 240 Chiral action Defining relators: [ x * y * z, z^-2 * x^2 * y^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y * z^-1 * y ] T97.912 : Triangle type {8,24,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z^-1 * x * z^8 * y ] T97.913 : Triangle type {8,24,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x^8, z^-4 * x^-1 * z * y^-1 * z^-4 ] T97.914 : Triangle type {8,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^21 * y^-5 * z ] T97.915 : Triangle type {8,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^4 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T97.916 : Triangle type {8,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^21 * y^-4 * z * y^-1 ] T97.917 : Triangle type {8,112,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T97.918 : Triangle type {9,18,78} Group order 234 Chiral action Defining relators: [ x * y * z, z^-2 * x^2 * y^-1 * z^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x^-1 * z * y * z^-1 ] T97.919 : Triangle type {9,18,78} Group order 234 Chiral action Defining relators: [ x * y * z, z^2 * y^-1 * x * z^-1 * x, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * z^-1 * x^2 * z^-2 * y ] T97.920 : Triangle type {10,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * x^-1 * z^3, x^10 ] T97.921 : Triangle type {10,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y, y * z^-1 * y * z^-1 * y * z^-1 * y * x^-1 * y * z^-1 * y * z^-2 ] T97.922 : Triangle type {10,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^10, y^2 * z^-4 * x^3 * y * z^-1 * y * z^-2 * y ] T97.923 : Triangle type {10,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x^2 * z * x^-1, (x * y^-2)^2, (z^-1 * y)^3, y * z^-1 * y * x^-1 * y^-1 * z^2 ] T97.924 : Triangle type {10,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x * y^-1 * x)^2, y * x * z^-1 * x^-2 * y^-1 * x * z * x^-1 ] T97.925 : Triangle type {10,44,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^7 * x^-3 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T97.926 : Triangle type {12,12,30} Group order 240 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * x^-1 * z^3, y * z^-1 * y * x^2 * z^3 ] T97.927 : Triangle type {12,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, z^-1 * x^-1 * y * x^-1 * z * y^-1 * z^-1, z^3 * x^-1 * z^2 * y^-1 ] T97.928 : Triangle type {12,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, y * x^-1 * y * x^-1 * z^3 ] T97.929 : Triangle type {12,12,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z^-3 * x^-1 * z * y * x^-1 * z^3 * y * z^-1 ] T97.930 : Triangle type {12,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-3 * y^-1 * x^2, x * z^-1 * x * z^-1 * x * z^-3, x^-2 * y * x^-2 * y^4 ] T97.931 : Triangle type {12,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^-3 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-5 ] T97.932 : Triangle type {12,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 ] T97.933 : Triangle type {12,72,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-1 * y^2 * x^-2 * y^4, x^-1 * z^2 * x^-2 * z^4 ] T97.934 : Triangle type {12,72,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y^2 * z^-1 * y, x^-12 ] T97.935 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, z^-1 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 ] T97.936 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y^-3 * x^2 * y^-2 * z, x^-1 * z * x^-4 * z^5 ] T97.937 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, z^-6 * y * z^-1 * y * x * z^-1 * y * z^-2 * y^2 * z^-2 * y ] T97.938 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^2 * x^-1 * y * z^-1 * y, x^-2 * y * x^-9 * z ] T97.939 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, z^-4 * y * z^-1 * y^3 * x * z^-1 * y * z^-2 * y^2 * z^-2 * y ] T97.940 : Triangle type {12,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^5 * x^-4 * y * z^-5 * y * z^-1 * y * z^-1 * y^3 ] T97.941 : Triangle type {14,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * x^-1 * y^3 * z^-1, x^2 * z^-3 * y * z^-1 * x^4 * z^-1 * x * z^-2 ] T97.942 : Triangle type {14,16,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * y^-1 * z^5 * y^-1 * z^5, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.943 : Triangle type {14,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, x * y^-2 * x * y^-1 * z^-1, (x * z * y)^2, y^-2 * z * x^-1 * z^3 ] T97.944 : Triangle type {14,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * z * y^-1, y^2 * x^2 * z^2, (x * y^-4)^2 ] T97.945 : Triangle type {14,28,28} Group order 224 Chiral action Defining relators: [ x * y * z, (y * z^-1)^2, z * y * x^2 * z^2, x^-14 ] T97.946 : Triangle type {14,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, z^-1 * x^4 * z^-3, (y * z^-1 * y^2)^2 ] T97.947 : Triangle type {14,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^-4 * x^2 * y^-4 ] T97.948 : Triangle type {14,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^10 * z^-1 * x^2 * y^-1 * x ] T97.949 : Triangle type {14,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^5 * y^-3, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.950 : Triangle type {14,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.951 : Triangle type {14,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-6, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.952 : Triangle type {14,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-2 * z^4, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.953 : Triangle type {14,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-1 * z^5 * y^-1 * x^2 * y^-4, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T97.954 : Triangle type {15,15,15} Group order 240 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, (x * z * y)^2, z^-1 * y * x^-2 * y^-1 * z * y^-1, y^3 * x^-2 * y * x^-1 * y^2 ] T97.955 : Triangle type {15,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y^2 * x * y^-2, (x * z * y)^2, y^-1 * x^5 * y^-4 ] T97.956 : Triangle type {15,15,15} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, y * z^-1 * x^-1 * y^-1 * x * z * x^-1 * z, y^2 * x^-3 * y^4 ] T97.957 : Triangle type {15,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-1 * z^5 * y^-1 * z^5, x^4 * y^-5 * x * z^-5 * x^5 ] T97.958 : Triangle type {15,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3 * y^-7, x^4 * y^-5 * x * z^-5 * x^5 ] T97.959 : Triangle type {15,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-6, x^4 * y^-5 * x * z^-5 * x^5 ] T97.960 : Triangle type {16,16,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^-2 * x^-1 * z^3 * y^-1 * z^-4 * x * z * y * z^-2 ] T97.961 : Triangle type {16,16,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-2 * x^-1 ] T97.962 : Triangle type {16,16,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^-2 * x * z^3 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-3 ] T97.963 : Triangle type {16,16,56} Group order 224 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^4 * x^-1 * z^3 * y^-1, z^-2 * x * z * y^-1 * z^-8 * x * z * y^-1 ] T97.964 : Triangle type {16,104,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-1 * z^5, y^-6 * z * y^-3 * x^5 * y^-1 * x * y^-1 * x * y^-1 ] T97.965 : Triangle type {16,104,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2 * y^-8, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T97.966 : Triangle type {16,104,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^8 * x^-1 * z^5, y^-5 * z^3 * y^-2 * x^5 * y^-3 ] T97.967 : Triangle type {16,104,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-5 * z, x^4 * y^-4 * x^2 * z^-4 * x^6 ] T97.968 : Triangle type {18,24,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * z * y, y^3 * z^-1 * y^5 * z^-2 * y ] T97.969 : Triangle type {18,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^3 * y^-2 * x^2 * y^-1 * x^5 * y^-2 * x * y^-3 * x ] T97.970 : Triangle type {18,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y^3, z^3 * y^-1 * z * y^-1 * z * y^-1 * z^4 ] T97.971 : Triangle type {18,24,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-2 * z^4, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-3 ] T97.972 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^5 * z^-1 * x * z^-1 * x ] T97.973 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^2 * z^-1 * x * z^-2 * x * z^-5 * y ] T97.974 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, (y * x^-1 * y^5)^2 ] T97.975 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x * z^-1 * x^3 * z^-1 * x * z^-1, y^-3 * x^2 * y^-3 ] T97.976 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^2 * y^-2 * x^2 * y^-1 * x^6 * z^-1 * x * y^-1 * z^-1 * x^3 * y^-1 ] T97.977 : Triangle type {18,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * y^3, z^-2 * x^4 * z^-4 ] T97.978 : Triangle type {18,36,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-4 * y * x^-1 * z, z^-1 * y^2 * z^-1 * y^3 * z^-2 * y * z^-2 ] T97.979 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-5 * z, x^5 * y^-4 * x^2 * z^-4 * x^7 ] T97.980 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x^2 * z^-3, y^-3 * x * y^-1 * x * y^-4 ] T97.981 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x * z^-1 * x * y^-1 * z^-1 * x^7 * z^-2 * x^4 ] T97.982 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, z^-1 * y^2 * x^-1 * y^-3, x^7 * z^-1 * x^7 * y^-5 * x ] T97.983 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * x^3 * y^-2 * x, z^-4 * x^2 * z^-4 ] T97.984 : Triangle type {18,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * x^4 * y^-3, z^-3 * x * z^-1 * x * z^-4 ] T97.985 : Triangle type {21,30,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-2 * z^4, x * y^-1 * x * y^-6 * x^5 * y^-3 ] T97.986 : Triangle type {24,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y * x^-3 * z * y * x^-1 ] T97.987 : Triangle type {24,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-4 * y * x * z^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-2 * x^3 * z^-1 * y * z^-1 ] T97.988 : Triangle type {24,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y * x, y * x^3 * z^2, z^6 * x^-1 * z * x^-1 * z^4 ] T97.989 : Triangle type {24,24,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, z^-1 * y^2 * x * z^-1 * x, y * x^-3 * y * z^-1 * x^-1 ] T97.990 : Triangle type {24,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-4 * x * z^4, y * z^-6 * x^2 * z^-3 * x * z^-1 ] T97.991 : Triangle type {24,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * x * z ] T97.992 : Triangle type {24,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x * y^-1 * x * y^-1 * z^-1 * x ] T97.993 : Triangle type {24,24,36} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-5 * x * z * y^-1 * z^-2 ] T97.994 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-2 * z^3 * y^-1 * z * y^-3 * z^3 * y^-2 * x * y^-1 ] T97.995 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, x^2 * y^-2 * z * y^-7 * z * y^-2 * x^2 * y^-3 ] T97.996 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^-1 * y * x^-2 * y^2 * x^-8 * y * x^-1 ] T97.997 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * x^2 * z^-4, x^-1 * y * x^-6 * y * x^-1 * y^2 ] T97.998 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^6 * z^-3, x^-1 * y^3 * x^-6 * y^3 * z^-1 * y ] T97.999 : Triangle type {26,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-11 * z * x^-2 * y^2 * x^-7 * z * x^-4 ] T97.1000 : Triangle type {30,35,42} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-4 * z^2, y^-10 * x^5 * y^-1 * x * y^-3 ] T97.1001 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-26 * z^2 * x^-6 * y^2 * x^-6 ] T97.1002 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^5, z^12 * y^-4 * z^4 ] T97.1003 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * z^5)^2, y^-6 * z^5 * y^-1 * x^5 * y^-1 * x * y^-1 * x * y^-1 ] T97.1004 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z * y^-3 * x^5 * y^-2, z^9 * y^-1 * z^5 ] T97.1005 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-4 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T97.1006 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^5 * x^-6, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^5 * y^-3 ] T97.1007 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-4, x^-8 * z^4 * x^-7 * z * x^-2 ] T97.1008 : Triangle type {40,100,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^3 * x^-1 * z^8 * x^-1 * z * x^-1 * z^5 * x^-1 * y^-1 * z^5 * x^-1 * z * x^-1 * z ] T97.1009 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^9 * z^-2 * y^3 * x^-4 * y^10 ] T97.1010 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^5 * x^-1 * z^5, x^3 * y^-4 * x^9 ] T97.1011 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-6, x^4 * y^-4 * x^2 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T97.1012 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^3 * x^-9 * z^8 * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 * x^-1 * z * x^-1 * z ] T97.1013 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^-4 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T97.1014 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-36 * y * x^-8 * z * x^-5 ] T97.1015 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-4 * z^2, y^-5 * z * y^-3 * x^5 * y^-3 ] T97.1016 : Triangle type {50,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^7, z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T97.1017 : Triangle type {51,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^15 * x^-1 * y^2 * x^-1 * y^2 * x^-1 * y^5 ] T97.1018 : Triangle type {51,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, y^-4 * z * y^-1 * z, x^-5 * y * x^-1 * z * y ] T97.1019 : Triangle type {51,51,51} Group order 204 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z * y^-2 * x * y^-1 * z, x^-3 * z^2 * x^-1 * z * x^-2 * z * x^-1 ] T97.1020 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-2, x^8 * y^-6 * x^2 ] T97.1021 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-3 * z * y^-7 * z^3 * y^-7 ] T97.1022 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-30 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T97.1023 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^11 * x^-14 * y^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T97.1024 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * y^2 * z^-4, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T97.1025 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-24 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 * x * z^-2 ] T97.1026 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, (y^-5 * x * y^-1)^2, z^-10 * y * z^-4 ] T97.1027 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y * x^-2 ] T97.1028 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x * z^-4 * x^5 * z^-1, y^-9 * z^2 * y^-4 ] T97.1029 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-2 * y^8, z * x^-6 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T97.1030 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-4 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-2 ] T97.1031 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x * z^-4 * x^2 * z^-4, y^-13 * x * y^-1 * x * y^-1 ] T97.1032 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-3 * z^2 * x^-3, y^-6 * x * y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T97.1033 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^2 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T97.1034 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1 * x * z^-4 * x * y * z^-4, y^-2 * x^6 * y^-7 ] T97.1035 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-6 * x^5 * y^-6 * x * y^-1 * x * y^-1 * x * y^-1 ] T97.1036 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-46 * y * x^-1 * y * x^-9 * y * x^-8 ] T97.1037 : Triangle type {66,99,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-5 * y * z^-9 * y * z^-5 * y * x * z^-5 * y * z^-1 * y ] T97.1038 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^15 * y^-1 * x^12 * y^-1 * x^70, y * z^-1 ] T97.1039 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^4 * z^-1 * x^4 * y^-5 * x^3 ] T97.1040 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^5 * z^-3 * x^6 * y^-1 * x ] T97.1041 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-1 * y * z^-5 * y^4 * z^-1 * y, x^2 * y^-1 * x^6 * y^-5 * x^3 ] T97.1042 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-52 * x^2 * y^-12 ] T97.1043 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-4 * y^6, x^6 * z^-3 * x^6 * y^-1 * x^2 ] T97.1044 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-1 * x^4 * y^-5 * x, z^-11 * y^5 * z^-2 ] T97.1045 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4 * z * y^-1, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T97.1046 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y * z^-1 * y * z^-1 * y * z^-5 * y^3 * z^-3 ] T97.1047 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^3 * x^-6 * z^4 * x^-1 * z^7 ] T97.1048 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^7 * z^-3 * x^8 * z^-1 * x ] T97.1049 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^15 * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T97.1050 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * z^-2 * y^3 * x^-5 * y^2, z^-3 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T97.1051 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^5 * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x^3 ] T97.1052 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^5 * z^-1 * x^4 * y^-6 * x * y^-1 * x^2 ] T97.1053 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^8 ] T97.1054 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^29 * x^-1 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y ] T97.1055 : Triangle type {98,196,196} Group order 196 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^-3 * x * z^-8 * y * z^-5 * y^3 * z^-6 ] T97.1056 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x^-2 * y^-1, y^75 * x^-1 * y^22, x * z^-1 ] T97.1057 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-4, z^-4 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T97.1058 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^4 * x^-5 * z * x^-2, y^-1 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-2 ] T97.1059 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^2 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T97.1060 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, z^2 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T97.1061 : Triangle type {195,195,195} Group order 195 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^-4 * y * z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-5 ] Genus 98 T98.1 : Triangle type {2,4,198} Group order 792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-198 ] T98.2 : Triangle type {2,4,392} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-50 * x * y^-1 * z^-145 ] T98.3 : Triangle type {2,6,6} Group order 1164 Chiral action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, x * z * y^-1 * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 * x * y^-1 * z^-2 * y * z^-2 * y * z^-2 * y * z^-1 ] T98.4 : Triangle type {2,6,100} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-62 * x * z^17 * y * x * z * y * x * y^-1 * z^-17 ] T98.5 : Triangle type {2,6,294} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-59 * x * z^13 * y * z^-1 * x * z^7 * y * z^-6 * x * z * y^-1 * z^-8 ] T98.6 : Triangle type {2,8,8} Group order 776 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T98.7 : Triangle type {2,8,132} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-41 * x * z^5 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * y^-1 * z^-11 ] T98.8 : Triangle type {2,10,245} Group order 490 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^33 * y * z^-8 * x * z * y^-1 * z^-3 * x * z^2 ] T98.9 : Triangle type {2,12,80} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-7 * x * z * y * x * z^3 * y * x * z^4 * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-16 ] T98.10 : Triangle type {2,16,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^3 * x * y^-1 * z * y * x * z * y * x * y^-4 * z^-1 * x * y^-1 * z^-1 * y, z^17 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^4 ] T98.11 : Triangle type {2,20,110} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-8 * z^4 * y^-3 * z^4 * y^-1, z^11 * y * z^-4 * x * z^4 * y^-1 * z^-1 * x ] T98.12 : Triangle type {2,28,32} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z * y * x * z^5 * y * x * y^-3 * z^-1 * x * y^-1 * z^-1 * x ] T98.13 : Triangle type {2,30,210} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-17 * z^4 * y^-5 * z^4 ] T98.14 : Triangle type {2,42,70} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * z * y * x * z^2 * y^-1 * z^-3, y * z^-1 * y^9 * z^-1 * y^2 ] T98.15 : Triangle type {2,58,203} Group order 406 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-4 * x * z^4 * y^-1 * z^-2, y^-16 * z^4 * y^-6 * z^3 ] T98.16 : Triangle type {2,68,102} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, y^-21 * z^4 * y^-6 * z^2 * y^-1 ] T98.17 : Triangle type {2,100,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^-13 * y^12 * z^-4 * y^18 * z^-3 ] T98.18 : Triangle type {2,197,394} Group order 394 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^131 * y^-64 * z ] T98.19 : Triangle type {2,198,198} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^66 * z^-132 ] T98.20 : Triangle type {2,392,392} Group order 392 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^65 * z^-131 ] T98.21 : Triangle type {3,6,6} Group order 582 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z * y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-2 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z ] T98.22 : Triangle type {3,6,6} Group order 582 Chiral action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z^-1 * x^-1 * z * y * x * y^-1 * x * y^-1 * z^-1 * y * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * y ] T98.23 : Triangle type {3,14,56} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y * x * z^2 * y, z * y^-1 * z * y^-1 * z^5 * y^-1 * z^4 ] T98.24 : Triangle type {3,39,52} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z^3 * y^-6 * z * y^-1 ] T98.25 : Triangle type {3,100,100} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^78 * y^-14 * z^6 * y^-1 ] T98.26 : Triangle type {3,294,294} Group order 294 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-79 * z * y^-18 ] T98.27 : Triangle type {4,4,99} Group order 396 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^83 * y^-1 * x^-1 * z^15 ] T98.28 : Triangle type {4,4,196} Group order 392 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^82 * y * x^-1 * z^15 ] T98.29 : Triangle type {4,6,168} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-8 * x * z^4 * y^-1 * z^-1 * x * z * y * z^-3 * x^-1 * z * y^-1 * z^-7 ] T98.30 : Triangle type {4,8,21} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^8 * y * x * z^7 * y^-1 * z^-4 * x ] T98.31 : Triangle type {4,20,140} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x * z^3 * y^-1 * z^-2 * x^-1 * z * y * z^-3 * x^-1, y^7 * z^-1 * y * z^-1 ] T98.32 : Triangle type {4,34,136} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 * z^-2 * y^7 * z^-2 * y^12 ] T98.33 : Triangle type {4,132,132} Group order 264 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-33 * z^3 * y^-1 * z * y^-12 * z * y^-7 * z^2 * y^-5 * z ] T98.34 : Triangle type {5,245,245} Group order 245 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-16 * z * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T98.35 : Triangle type {5,245,245} Group order 245 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^-18 * z^3 * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-9 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T98.36 : Triangle type {6,6,50} Group order 300 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^34 * y * x * z^15 ] T98.37 : Triangle type {6,6,147} Group order 294 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^28 * y^-1 * z^-5 * x * y^-1 * z^-4 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T98.38 : Triangle type {6,12,66} Group order 264 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y * z^-5 * x^-1 * z^5 * y^-1 * x * z^5 * y * z^-1 * x * z^2 ] T98.39 : Triangle type {6,18,126} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, y * z^-2 * x * z * y^-1 * z^-4 * x^-1 * z^5 ] T98.40 : Triangle type {6,18,126} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z^-3 * x * z * y^-1 * z^-1 * x * z^7 * y^-1 ] T98.41 : Triangle type {6,60,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^3 * y^-1, z^-2 * y * z^-2 * y * z^-4 ] T98.42 : Triangle type {6,80,80} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y^2 * z^-2 * y^2 * z^-2 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 ] T98.43 : Triangle type {8,8,66} Group order 264 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-19 * x * y^-1 * x * y^-1 * z^-12 ] T98.44 : Triangle type {8,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, x^8, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T98.45 : Triangle type {8,29,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^3 ] T98.46 : Triangle type {8,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^8, z^-1 * y^11 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^6 ] T98.47 : Triangle type {8,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^2 * z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T98.48 : Triangle type {8,224,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^-3 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T98.49 : Triangle type {10,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x * y^-1 * x * z^2 * y^-1, x^10 ] T98.50 : Triangle type {10,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, (z^-1 * x)^3, x^-1 * z^2 * y * x * z^2 * y ] T98.51 : Triangle type {10,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, (x * z * y^-1 * z^-1)^2 ] T98.52 : Triangle type {10,15,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3, (x^-1 * z^2 * y)^2 ] T98.53 : Triangle type {10,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^10, z^2 * y^-1 * z^-3 * x^-1 * z^6 ] T98.54 : Triangle type {10,110,110} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-4 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 ] T98.55 : Triangle type {10,110,110} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^2 * y^-7 ] T98.56 : Triangle type {12,12,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-2 * y * x^-8 * y, z^-9 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T98.57 : Triangle type {12,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-4 * y * x * y^2 * z^-1 * y * z^-4 * y^4 ] T98.58 : Triangle type {14,32,32} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^5 * z * y^-1 * z * x^-4 * y * z^-1 * y * x^2, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 ] T98.59 : Triangle type {15,16,16} Group order 240 Chiral action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, y * x^-3 * z^2 * y, y^-4 * z * y^-5 * z * y^-2 * z * y^-1 * z ] T98.60 : Triangle type {15,16,16} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-15, y^5 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y ] T98.61 : Triangle type {15,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-5 * z, x^4 * y^-5 * x * z^-5 * x^5 ] T98.62 : Triangle type {15,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-5 * y * z^-5 * y * z^-1 * y^3, z^4 * x^-1 * z^5 * x^-1 * z^5 ] T98.63 : Triangle type {16,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T98.64 : Triangle type {20,20,55} Group order 220 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, y^-3 * x^2 * y^-3, z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x * z^4 * y ] T98.65 : Triangle type {20,20,55} Group order 220 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * z^3 * x^-2 * z * y^-1 * z^2, y^-1 * z^-1 * x^-1 * z^4 * y * z^-1 * x * z^3 ] T98.66 : Triangle type {21,70,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, z^-2 * y^4 * z^-4 ] T98.67 : Triangle type {21,70,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, z^-4 * y^2 * z^-4 ] T98.68 : Triangle type {21,70,70} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T98.69 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-4 * x^3 * y^-1 * x * y^-1 * x * z * y^-1 * x^2 * y^-2 ] T98.70 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.71 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^-2 * x * z^-1 * x * z^-3 ] T98.72 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, z^-4 * x^2 * z^-4 ] T98.73 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2, z^-1 * x^5 * z^-2 * x * z^-1 ] T98.74 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, y^-1 * z^3 * x^-1 * z * x^-1 * z^3 * x^-1 * z^4 ] T98.75 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * z^3, y^-4 * x^2 * y^-4 ] T98.76 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-4 * x^-1 * z^3 * y^-1, z^-1 * x * z^-1 * x^3 * z^-4 ] T98.77 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (y * z^-3)^2, x^-5 * z^3 * y ] T98.78 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, x^6 * y^-4 ] T98.79 : Triangle type {26,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x * z^-3 * x^6 * y^-2 * x^2 * z^-1 * x ] T98.80 : Triangle type {27,27,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z * x^-3 * z^3, x^-1 * y * x^-2 * z * x^-1 * y ] T98.81 : Triangle type {27,27,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z, z * y^-1 * z * x^-1 * z * x^-1 * y^-1 * z^4 ] T98.82 : Triangle type {27,27,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z * x^-1, z^-1 * x^-3 * y^-1 * x^2, y^-4 * x * z * y^-1 * z ] T98.83 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.84 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y * x^-5 * y^6 * x^-1, z^9 * x^-1 * z^5 ] T98.85 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^5 * y^-6, x^7 * z^-5 * x * z^-1 * x * z^-1 * x ] T98.86 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^5 * x^-4 * z^2, y^4 * x^-5 * y^3 * z^-2 * y^5 ] T98.87 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-4 * z^2, y^5 * x^-4 * y^6 * x^-1 * y^3 ] T98.88 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-16 * y^3 * x^-4 * z^3 * x^-6 ] T98.89 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-5 * z, x^-3 * y * x^-5 * y^6 * x^-3 ] T98.90 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-1 * z^5, x^-2 * y * x^-5 * y^6 * x^-2 ] T98.91 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^4 * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y ] T98.92 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-5 * z, y^3 * x^-5 * y * z^-5 * y * z^-1 * y^3 ] T98.93 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-4 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * z * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T98.94 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-3 ] T98.95 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^3 * y^-2, z^-3 * x^6 * z^-5 * x * z^-6 ] T98.96 : Triangle type {29,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-6 * z, z^2 * x^-4 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T98.97 : Triangle type {30,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x * z^3 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T98.98 : Triangle type {30,30,105} Group order 210 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, y * z^-1 * x * z^-1 * x * z^-5 * y * x^2 * z^-5 ] T98.99 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-5 * z, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^5 * y^-1 * x * y^-3 ] T98.100 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y * x^-5 * y^5 * x^-2, z^3 * y^-1 * z * y^-1 * z^5 * y^-6 * z ] T98.101 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^2 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^12 ] T98.102 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^4 * y^-1 * x^5 * y^-1 * x * y^-1, x * y^-1 * x^5 * z^-5 * x * z^-1 * x * z^-1 * x ] T98.103 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, z^14 * x^-7 * z * x^-1 * z * x^-1 * y * x^-10 * z * x^-1 * z * x^-1 * z ] T98.104 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^2 * y^-8, x^2 * y^-1 * x^5 * z^-5 * x * z^-1 * x * z^-1 * x^2 ] T98.105 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-8 * z^3 * y^-2 * x^5 * y^-1 * x * y^-1 * x * y^-3 ] T98.106 : Triangle type {34,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-5 * z, x^5 * y^-5 * x^5 * y^-1 * x^4 ] T98.107 : Triangle type {35,42,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-1 * z^-1, y^-1 * z * y^-1 * x^2 * z * y^-1 * z ] T98.108 : Triangle type {35,42,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^4 * z^-2, x^6 * y^-1 * z^-1 ] T98.109 : Triangle type {35,42,42} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-1 * z^-1, y^-1 * z * x^-1 * y^-1 * x * z * y^-1 * z ] T98.110 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x * y^-11, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z ] T98.111 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^4 * x^-6, y^-4 * z * y^-1 * z^5 * y^-1 * x^4 * y^-4 ] T98.112 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-3 * x^5 * y^-1, z^-2 * x^6 * z^-5 * x * z^-5 ] T98.113 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-29 * y * x^-1 * y * x^-1 * y * x^-8 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T98.114 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * z^-1 * x, z^-5 * y^2 * z^-5 * y * z^-1 * y * z^-1 * y * z^-3 ] T98.115 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^14 * x^-8 * y^10 ] T98.116 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * y^-1 * z^5, x^4 * y^-5 * x^4 * z^-1 * x^4 ] T98.117 : Triangle type {50,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-2 * y^2 * x^-9 * z^3 * x^-4 * z^3 * x^-6 ] T98.118 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x^2 * z^-3, y^-4 * x^2 * y^-2 * z * y^-1 ] T98.119 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, z^-1 * x^-3 * y^-1 * x^2, x * z * y^-1 * z * y^-9 ] T98.120 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y * z^-1 * y * z^-1 * y * z^-3, x^6 * y^-4 ] T98.121 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, y * x^-1 * y^3 * x^-6 * y * x^-1 * y * z^-1 * y ] T98.122 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z * x^-3 * z^3, y^-1 * z^2 * y^-1 * z * y^-6 * z ] T98.123 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, y * x^-4 * y * x^-1 * y^2, y^-1 * z * y^-1 * z * x^-1 * z^4 ] T98.124 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^-7 * z * y * x^-9 ] T98.125 : Triangle type {51,68,68} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^2 * z^-1 * x * z^-1 * x * z^-1 * x * y^-1 * x * y^-1 * x^7 * y^-1 * x ] T98.126 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^6 * z^-3 * y^2 * x^-4 * y^5 ] T98.127 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 ] T98.128 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^4 * y^-7, z^-4 * x * z^-4 * x^2 * z^-4 ] T98.129 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^3 * z^-3, y^-6 * x * y^-6 * x * y^-2 ] T98.130 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^99, y * z^-1 ] T98.131 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * z^-4 * x^4 * z^-2, y^5 * z^-1 * y^4 * x^-6 * y^4 ] T98.132 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^3 * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 * x ] T98.133 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * z^-4 * y^6, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-3 ] T98.134 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^17 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-1 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T98.135 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-42 * x^3 * z^-6 ] T98.136 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^6 * z^-1 * x^4 * y^-6 * x * y^-1 * x^3 ] T98.137 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T98.138 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-9 * y * z^-4, y^4 * z^-2 * y^3 * x^-5 * y^3 ] T98.139 : Triangle type {99,198,198} Group order 198 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-17 * z^2 * x^-15 ] T98.140 : Triangle type {100,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-6 * z * y * x^-1 * z * x^-9 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T98.141 : Triangle type {100,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, x^-1 * z * x^-1 * z^2 * x^-4 * z^5 ] T98.142 : Triangle type {100,100,100} Group order 200 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^3 * z^-1 * x, y^2 * z^-3 * y^2 * x^-1 * y * x^-1 * y^3 * z^-1 * y * z^-1 * y^3 * z^-1 ] T98.143 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x^-2 * y^-1, y^75 * x^-1 * y^23, x * z^-1 ] T98.144 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-53 * x * y^-12 ] T98.145 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^30 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.146 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^15 * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-5 * x * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.147 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^5 * y^-1 * x * y^-2 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.148 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-1 * x * y^-2 ] T98.149 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^2 * x^-1 * y * x^-1 * y * x^-1 * y^6 * x^-6 * y * x^-1 * y * x^-1 * y^3 ] T98.150 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-2 * x * y^-1 * x * y^-1 * x^6 * y^-6 * x * y^-1 * x * y^-2 ] T98.151 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x^2 * y^-1 * x * y^-1 * x^6 * y^-6 * x^4 ] T98.152 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-6 * x * z^-4, x^-2 * y * x^-1 * y^6 * x^-9 ] T98.153 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-4 * x * y * z^-4, y^-1 * x * y^-1 * x^6 * y^-8 ] T98.154 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-4 * x * y * z^-4, x^-3 * y^5 * x^-8 ] T98.155 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4 * x * y * z^-4, x^5 * z^-3 * x^2 * y^-5 * x^3 ] T98.156 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * z^-3 * x^2 * y^-5 * x^2, y^5 * z^-5 * y^7 ] T98.157 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-6, y^-2 * z * y^-6 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T98.158 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^6 * z^-3 ] T98.159 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * z^-3 * x^7, y^-7 * z^5 * y^-1 * z * y^-1 * z^2 ] T98.160 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-5 * y^6, x^-2 * y * x^-1 * y^6 * x^-1 * z^4 * x^-6 ] T98.161 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-2 * x * z^-3 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^3 * z^-6 ] T98.162 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-3 * x^7, y^-2 * z * y^-7 * z^3 * y^-6 ] T98.163 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * z^-1 * y * z^-5 * y^4 * z^-2, x^4 * z^-2 * x^3 * y^-6 * x^2 ] T98.164 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-4 * x^5 * z^-1, y^-6 * x * y^-1 * z^5 * y^-5 ] T98.165 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * y^-4 * x, y^2 * z^-1 * y * z^-1 * y * z^-5 * y^2 * z^-4 ] T98.166 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y * z^-4 * y^4 * z^-1 * y, x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T98.167 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y^5 * x^-1 * y^4, z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^2 * z^-4 ] T98.168 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-1 * z^3 * x^-1 * z^4 * x^-1 * z * x^-7 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T98.169 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-31 * y * x^2 * z^-7 ] T98.170 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^6 * x^-2 * z^3 * x^-4, y * z^-1 * y * z^-1 * y * z^-5 * y^6 ] T98.171 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-4 * x^7 * z^-1 * x * z^-1 ] T98.172 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * z^3 * x^-5 * z^2 * x^-8 ] T98.173 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^4 * z^-1 * y^13 * x^-2 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y ] T98.174 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x * z^-4 * x^3 * z^-3, y^7 * z^-4 * y * x^-6 * y * x^-1 * y^3 ] T98.175 : Triangle type {197,197,197} Group order 197 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y^5 * x^-7, z^-2 * x * z^-1 * x * z^-1 * x * z^-4 * x * y * z^-4 ] Genus 99 T99.1 : Triangle type {2,3,12} Group order 2352 Chiral action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y * z^-1 * x * z * y * x * z^2 * y * x * z^2 * y * z^-2 * x * z^2 * y * z^-1 * y * z^-1 * x * z^2 * y * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x * z ] T99.2 : Triangle type {2,3,12} Group order 2352 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y^-1 * z^-2 * x * z * y^-1 * z^2 * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x * z * y * x * z * y * x * z * y * x * z^2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x * z ] T99.3 : Triangle type {2,3,14} Group order 2058 Reflexible action Defining relators: [ x^2, y^3, x * y * z, z^2 * y * x * z * y * x * z * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^7 * y * z^-1 * x^2 * y^-1 * z^-1 * x * z^6 ] T99.4 : Triangle type {2,4,8} Group order 1568 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * y * x * y^-1 * z * y * x * z * y^-1 * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y * z^-1 * x * z^2 * y * z^-1 * y ] T99.5 : Triangle type {2,4,8} Group order 1568 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y * x * z * y^-1 * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y * x * z * y * z^-1 * y * z^-1 * x ] T99.6 : Triangle type {2,4,12} Group order 1176 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, z * y * z^-1 * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x ] T99.7 : Triangle type {2,4,102} Group order 816 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-83 * x * z^10 * y * z^-1 * x * y^-1 * z^-6 ] T99.8 : Triangle type {2,4,200} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-200 ] T99.9 : Triangle type {2,4,200} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-82 * x * z^7 * y * z^-2 * x * y^-1 * z^-7 ] T99.10 : Triangle type {2,4,396} Group order 792 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-51 * x * y^-1 * z^-146 ] T99.11 : Triangle type {2,6,52} Group order 624 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-8 * x * z^6 * y * x * y * z^-7 * x * z * y^-1 * z^-1 ] T99.12 : Triangle type {2,7,14} Group order 686 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T99.13 : Triangle type {2,8,8} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y * z^-1 * y * x * y^-1 * z^2 * y * x * z * y^2 * z^-1 * x * y^-1 * z^-2 * y^2 * z^-1 * x * z ] T99.14 : Triangle type {2,8,8} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y^-1 * z * y^2 * x * y^-1 * z^3 * y^-1 * z^3, x * z * y^3 * x * z * y * x * y^-3 * z^-1 ] T99.15 : Triangle type {2,8,8} Group order 784 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * z^-1 * y * x * y^-1 * z^2 * y * x * z * y^2 * z^-1 * x * y^-1 * z^-2 * y^2 * z^-1 * y * z^-1 * x ] T99.16 : Triangle type {2,8,12} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-4, z^2 * y^-4 * z^-2 * y * x * y^-1 ] T99.17 : Triangle type {2,8,12} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T99.18 : Triangle type {2,8,12} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, z^3 * y^-3 * z^-1 * y * x * y^-2 ] T99.19 : Triangle type {2,8,12} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, y * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, (y^3 * z^-1)^3 ] T99.20 : Triangle type {2,8,68} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^45 * y * x * z * y * z^-1 * x * y^-1 * z^-3 * x * z^15 ] T99.21 : Triangle type {2,8,68} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-31 * x * z^20 * y * x * y^-1 * z^-9 * x * z^2 * y^-1 * z^-3 ] T99.22 : Triangle type {2,8,264} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-28 * x * z^21 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-7 ] T99.23 : Triangle type {2,8,264} Group order 528 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-28 * x * z^21 * y * x * y^-1 * z^-9 * x * z^2 * y^-1 * z^-3 ] T99.24 : Triangle type {2,12,12} Group order 588 Chiral action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * z * y^3 * x * z^3 ] T99.25 : Triangle type {2,12,12} Group order 588 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-2 * z^-1 * y ] T99.26 : Triangle type {2,12,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, y^12, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-2 * x * z * y^-1 * z^-3 ] T99.27 : Triangle type {2,12,120} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-4 * x * z^22 * y^-1 * z^-7 * x * z^2 * y^-1 * z^-3 ] T99.28 : Triangle type {2,14,35} Group order 490 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-4 * y^5 * z^-4, z^-3 * x * z^8 * y * x * z^5 * y^-1 * z^-17 ] T99.29 : Triangle type {2,14,231} Group order 462 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-4 * y^5 * z^-4, z^-2 * x * z^8 * y * x * z^4 * y^-1 * z^-17 ] T99.30 : Triangle type {2,15,40} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^4 * y^2 * x * z^3 ] T99.31 : Triangle type {2,20,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-4 * z^-1 * x * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-6, z^14 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z ] T99.32 : Triangle type {2,20,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^6 * y * z^-5 * x, y * x * y^-1 * z * y * x * z * y^8 * x * z * y^6 ] T99.33 : Triangle type {2,20,220} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-8 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^9 * y * z^-4 * x * z * y^-1 * z^-5 ] T99.34 : Triangle type {2,27,108} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, z * y^-7 * z^3 * y^-12 * z * y^-1 * z * y^-1 ] T99.35 : Triangle type {2,38,209} Group order 418 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-6 * z^4 * y^-2 * z^6 ] T99.36 : Triangle type {2,46,207} Group order 414 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^6 * y * z^-4 * x * z^2 * y^-1 * z^-4, y^-10 * z^4 * y^-4 * z^5 ] T99.37 : Triangle type {2,52,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y * z^-13 * y^12 * z^-4 * y^21 * z^-1 ] T99.38 : Triangle type {2,52,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y * z^-18 * y^10 * z^-5 * y * z^-15 * y^2 ] T99.39 : Triangle type {2,68,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-31 * y^13 * z^-2 * y^21 * z^-1 ] T99.40 : Triangle type {2,102,102} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-97 * z * y^-1 * z ] T99.41 : Triangle type {2,134,201} Group order 402 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-30 * y^13 * z^-2 * y^20 * z^-1 ] T99.42 : Triangle type {2,199,398} Group order 398 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^132 * y^-66 ] T99.43 : Triangle type {2,200,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-64 * y^33 * z^-2 ] T99.44 : Triangle type {2,200,200} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^67 * z^-132 * y ] T99.45 : Triangle type {2,396,396} Group order 396 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^66 * z^-131 * y ] T99.46 : Triangle type {3,3,6} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-2 * x^-1 * z * y * x * z * y^-1 * z^-1 * x * z ] T99.47 : Triangle type {3,3,6} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z * y * x * z)^3, x * y^-1 * z^-1 * x * z^2 * y^2 * z^-1 * x * z * y^-1 * z^-1 ] T99.48 : Triangle type {3,3,6} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * x^-1 * z * x^-1 * y^-1 ] T99.49 : Triangle type {3,3,6} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z * x^-1 * z^2 * x^-1 * y^-1 * x * z^2 * y * x * z, x * z * x^-1 * z * x^-1 * y^-1 * z^-1 * y * x * y^-1 * x * y^-1 * x * y^-1 ] T99.50 : Triangle type {3,3,6} Group order 1176 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z * x^-1 * z^2 * x^-1 * y^-1 * x * z^2 * y * x * z, x^-1 * z * y * x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z * y * z^-1 ] T99.51 : Triangle type {3,3,6} Group order 1176 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z^-1 * x * z^-1 * x * z^-1 * x^-1 * y * x * z * y * x^-1 * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x^-1 ] T99.52 : Triangle type {3,3,7} Group order 1029 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^3 * y^-1 * x^-1 * z^3, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T99.53 : Triangle type {3,3,52} Group order 624 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^5 * y^-1 * z^-3 * x^-1 * y^-1 * z^-1 * x^-1 * z^5 ] T99.54 : Triangle type {3,3,199} Group order 597 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * x * z * y * z^-3 * x * z * y * z^-7 ] T99.55 : Triangle type {3,4,8} Group order 672 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z^2 * y * x * z * y^-1 ] T99.56 : Triangle type {3,4,8} Group order 672 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T99.57 : Triangle type {3,4,12} Group order 588 Chiral action Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (y * x^-1 * z)^3, z^-1 * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 ] T99.58 : Triangle type {3,4,12} Group order 588 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y^-1 * z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-1 * x * z * y * z^-1 * x * z * y^-1 * x * z * y * z^-1 ] T99.59 : Triangle type {3,4,12} Group order 588 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * x^-1 * z * y * x * z * y^-1 * z^-1 * x^-1 ] T99.60 : Triangle type {3,14,84} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z * y^-2 * z * y^-1 * z^2 * x^-1 * y^-2 * z^3 ] T99.61 : Triangle type {3,16,48} Group order 336 Chiral action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1, z^3 * y^-1 * z^2 * y^-1 * z * y^-4 * z^3 * y^-1 ] T99.62 : Triangle type {3,21,28} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^-4 * x^-1 * z^3 ] T99.63 : Triangle type {3,39,78} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-2 * y * z^-1 * y^4 * z^-2 * y ] T99.64 : Triangle type {3,52,52} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^8 * z^-1 * y * z^-1 * y * z^-2 * y^4 * z^-3 * y^5 ] T99.65 : Triangle type {3,100,300} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-80 * z * y^-10 * z * y^-7 * z ] T99.66 : Triangle type {3,297,297} Group order 297 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^8 * z^-1 * y^10 * z^-1 * y^79 ] T99.67 : Triangle type {4,4,4} Group order 784 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y * z^-1 * x^-1 * y * x^-1 * z * y * z^-1 * x^-1 ] T99.68 : Triangle type {4,4,4} Group order 784 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x^-1 * y * z^-1 * y * x^-1 * y^-1 * x * z^2 ] T99.69 : Triangle type {4,4,4} Group order 784 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1 * z * y^-2 * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y * x * z ] T99.70 : Triangle type {4,4,4} Group order 784 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * z^-1 * x * z^-1 * x^2 * z^2 * x^-1 * z * x^-1 * y^-1 * z^-1 ] T99.71 : Triangle type {4,4,6} Group order 588 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * x * z * y^-1 * x * z^2 * y^-1 ] T99.72 : Triangle type {4,4,6} Group order 588 Chiral action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y^-1 * z^-2 * x^2 * z^2 * y^-1 ] T99.73 : Triangle type {4,4,6} Group order 588 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, x * z^-2 * y * x * z^-1 * y * z^-1 ] T99.74 : Triangle type {4,4,6} Group order 588 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^2 * y^-1 * z * y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x * z * x^-1 ] T99.75 : Triangle type {4,4,51} Group order 408 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-40 * x^-1 * y * x^-1 * y * x * z * y * z^-7 ] T99.76 : Triangle type {4,4,100} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^4 * x^-1 * y^-1 * z^3 ] T99.77 : Triangle type {4,4,100} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T99.78 : Triangle type {4,4,100} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-39 * x * y^-1 * z^-10 ] T99.79 : Triangle type {4,4,100} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-39 * x * z * y * z^-9 ] T99.80 : Triangle type {4,4,100} Group order 400 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^84 * y^-1 * x^-1 * z^15 ] T99.81 : Triangle type {4,4,198} Group order 396 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^83 * y^-1 * x * z^15 ] T99.82 : Triangle type {4,8,8} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T99.83 : Triangle type {4,8,8} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, x^-1 * y^-1 * z * y^-1 * x * z * y^-1 * z ] T99.84 : Triangle type {4,8,8} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y * z^-1 ] T99.85 : Triangle type {4,8,8} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x^-1 * y^-2 * z^-1 * y * z^-1 ] T99.86 : Triangle type {4,8,8} Group order 392 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, (x * z * x^-1 * y^-1)^2, y^-1 * x * y^-2 * x * z^3 ] T99.87 : Triangle type {4,8,80} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^8 * y^-1 * z^-4 * x^-1 * y^-1 * z^-3 * x^-1 * z^3 ] T99.88 : Triangle type {4,8,80} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y^2 * x^-1 * y * z^-2, y^2 * z^-1 * x^-1 * z^2 * y ] T99.89 : Triangle type {4,8,80} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * z^2 ] T99.90 : Triangle type {4,8,80} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^25 * y * z^-7 * x^-1 * z^7 ] T99.91 : Triangle type {4,8,80} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^26 * y * x^-1 * y * x^-1 * z^12 ] T99.92 : Triangle type {4,12,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, y * z^-2 * y * x^-1 * y^-1 * z^-3 ] T99.93 : Triangle type {4,12,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1, y^-1 * z^3 * y^-3 * x * y^-1 * z * y^-1 * z * y^-1 ] T99.94 : Triangle type {4,12,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-2 * z * x^-1 * y^-3, z^-2 * y^2 * x^-1 * y^-1 * z^-1 * y^2, y^2 * z^-1 * y * x^-1 * z^4, z^-3 * y * x^-1 * y^-1 * z^2 * y^-1 ] T99.95 : Triangle type {4,12,12} Group order 336 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * x^-1 * z * y * x * z^2 * y, y^-1 * z^2 * y^-3 * z^4 * y^-2 ] T99.96 : Triangle type {4,12,26} Group order 312 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y * x^-1 * z * y^2 * x * z * y * z^-2 ] T99.97 : Triangle type {4,12,26} Group order 312 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^4 * y^-1 * z^-5 * x^-1 * z^6 * y * z^-6 * x * z^3 ] T99.98 : Triangle type {4,12,75} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z^-1 * y * z^-1 * x^-2 * z^2 * y * z^-1 ] T99.99 : Triangle type {4,12,75} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^10 * y^-1 * z^-1 * x * z * y * z^-3 * x^-1 * z^8 ] T99.100 : Triangle type {4,16,144} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^3 * y * z^-3 * x * z^3 * y * z^-1 * x^-1 * z^2 * y * z^-2 * x^-1 * z ] T99.101 : Triangle type {4,16,144} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^3 * y * z^-3 * x * z^3 * y * z^-1 * x^-1 * z^2 * y * z^-2 * x * z ] T99.102 : Triangle type {4,18,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * y^5 * x^-1 * y * z^-4 * y^3 * z^-1 ] T99.103 : Triangle type {4,18,72} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^3 * y^-1, y^-3 * z^7 * y^-1 * z * y^-1 * z^3 * y^-1 * z ] T99.104 : Triangle type {4,28,70} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 * z * y^-2 * z ] T99.105 : Triangle type {4,28,70} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-1 * z^-2 * x^-1 * y * z^-2 * x * z, y^-4 * z^2 * y^-3 * z^3 * y^-1 * z ] T99.106 : Triangle type {4,67,268} Group order 268 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-36 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T99.107 : Triangle type {4,68,68} Group order 272 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-33 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-12 * z * y^-1 ] T99.108 : Triangle type {4,68,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-40 * z * y^-1 * z * y^-2 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T99.109 : Triangle type {4,68,68} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-8 * y^2 * z^-2 * y^5 * z^-1 * y * z^-3 * y^11 ] T99.110 : Triangle type {4,264,264} Group order 264 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, z * y^-31 * z * y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T99.111 : Triangle type {4,264,264} Group order 264 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-34 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T99.112 : Triangle type {6,6,26} Group order 312 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T99.113 : Triangle type {6,6,26} Group order 312 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^4 * x^-1 * z * y^-1 * z^2 ] T99.114 : Triangle type {6,6,26} Group order 312 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z * y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-3 * x * z * y * x^-1 ] T99.115 : Triangle type {6,7,42} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^3 * x^2 * y^-1 * z^2, y^-7 ] T99.116 : Triangle type {6,7,42} Group order 294 Chiral action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z * x^-1 * y^-1 * x^2 * z^-1 * y * x^-1, y^-7 ] T99.117 : Triangle type {6,7,42} Group order 294 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-7 ] T99.118 : Triangle type {6,8,8} Group order 336 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, z * x^-1 * y^-1 * x * z * x^-1 ] T99.119 : Triangle type {6,12,132} Group order 264 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y * z^-5 * x^-1 * z^5 * y^-1 * z^-1 * x^-1 * z^8 ] T99.120 : Triangle type {6,80,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-10 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-8 * z * y^-1 * z * y^-1 * z ] T99.121 : Triangle type {6,120,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-3 * y * z^-3 * y^5 * x^-1 * y * z^-1 * y * z^-2 * y * z^-2 ] T99.122 : Triangle type {6,120,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, z * y^-5 * z^2 * y^-2 * z^6 * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-8 * z * y^-1 * z * y^-1 * z ] T99.123 : Triangle type {7,7,7} Group order 343 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, x^-7, y^-7 ] T99.124 : Triangle type {7,34,238} Group order 238 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y^13 * z^-1 * y * z^-1 * y * z^-1 * y ] T99.125 : Triangle type {7,35,35} Group order 245 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-1 * z * y^-2 * z^6 * y^-13 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T99.126 : Triangle type {7,231,231} Group order 231 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-4 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-2 ] T99.127 : Triangle type {7,231,231} Group order 231 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-2 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-1 * z ] T99.128 : Triangle type {7,231,231} Group order 231 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-2 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^3 ] T99.129 : Triangle type {8,8,34} Group order 272 Chiral action Defining relators: [ x * y * z, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * x^-1 * z^3, x^8, (x * y^-1 * x^2)^2 ] T99.130 : Triangle type {8,8,34} Group order 272 Chiral action Defining relators: [ x * y * z, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1, x^8, (x * y^-1 * x^2)^2 ] T99.131 : Triangle type {8,8,34} Group order 272 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, y^-1 * z^-3 * x^-1 * z^4 ] T99.132 : Triangle type {8,8,34} Group order 272 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, x^8, z^2 * y^-1 * z * y^-1 * x * z^-1 * x * z^2 ] T99.133 : Triangle type {8,8,34} Group order 272 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-10 * x^-1 * z^2 * y^-1 * z^-1 * x * z^4 * y^-1 * z^-6 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T99.134 : Triangle type {8,8,34} Group order 272 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^34 ] T99.135 : Triangle type {8,8,132} Group order 264 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-10 * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 * x * z^5 * y * z^-1 ] T99.136 : Triangle type {8,8,132} Group order 264 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-10 * x^-1 * z * y * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-4 * x * y * z^-4 * x^-1 * z * y ] T99.137 : Triangle type {8,20,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, z^-1 * y^5 * z^-2 * y * z^-1 ] T99.138 : Triangle type {8,20,120} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, z^-1 * y^5 * z^-2 * y * z^-1 ] T99.139 : Triangle type {8,24,60} Group order 240 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, x^8 ] T99.140 : Triangle type {8,24,60} Group order 240 Chiral action Defining relators: [ x * y * z, z^-2 * x^2 * y^-2, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T99.141 : Triangle type {8,24,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, x^8, z^-3 * x^-1 * z * y * x^-1 * z * y * z^-3 ] T99.142 : Triangle type {8,24,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^8, z^-1 * x * z^5 * y * z^-3 ] T99.143 : Triangle type {8,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-3 * z * y^-1 * z^-1, z^-1 * y * x^-2 * y^2 * z^-1 ] T99.144 : Triangle type {8,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1 ] T99.145 : Triangle type {8,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, x^8, z^-3 * y * z^-1 * y * z^-4 ] T99.146 : Triangle type {8,30,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^8, z * y^3 * x^-1 * y^-1 * z * x^-1, y^2 * z^-1 * y^3 * z^-1 * y * z^-2 ] T99.147 : Triangle type {9,12,36} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^2 * y * x^2 * z^3, z^-2 * x^-1 * y^-1 * x * z^2 * y, x^-9 ] T99.148 : Triangle type {9,12,36} Group order 252 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * x^-3 * y^3, x^-1 * z * x^-2 * z * y^-1 * z, z^2 * y * x^-1 * z^3, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T99.149 : Triangle type {9,75,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^6 * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^2 ] T99.150 : Triangle type {9,75,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^3 ] T99.151 : Triangle type {10,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1, y^-3 * x^2 * y^-3 ] T99.152 : Triangle type {10,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, (z^-1 * x)^3, z^-3 * x^-1 * z^2 * y^-1 ] T99.153 : Triangle type {10,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-3 * x^-1 * z^2 * y^-1, x^10 ] T99.154 : Triangle type {10,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, y^-1 * x^4 * y^-3 ] T99.155 : Triangle type {10,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1, (x * y^-1 * z^-1 * y)^2 ] T99.156 : Triangle type {10,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3, (y * z^-1)^4 ] T99.157 : Triangle type {10,23,230} Group order 230 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 ] T99.158 : Triangle type {10,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, y^-9 * z * y^-1 * z * y^-1 * z * y^-3 * z^2 * y^-1 * x * y^-1 * z^2 * y^-1 ] T99.159 : Triangle type {10,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^-4 * z * x^-1 * y, y^-2 * z * y^-3 * z * y^-2 * z^2 * y^-1 ] T99.160 : Triangle type {10,24,24} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^10, y * z^-3 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y ] T99.161 : Triangle type {10,24,24} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^9 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 ] T99.162 : Triangle type {10,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-2 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T99.163 : Triangle type {10,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^-3 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-3 ] T99.164 : Triangle type {11,11,23} Group order 253 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^2 * z * y, z * y^2 * x * z^-1 * x, z^2 * y * x * z^2, x^-1 * y * x^-7 * y^2 ] T99.165 : Triangle type {11,11,23} Group order 253 Chiral action Defining relators: [ x * y * z, y * z^-1 * x^2 * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^2, x^-11 ] T99.166 : Triangle type {11,11,23} Group order 253 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^2 * z^2, y * z^-1 * x^2 * z^-1 * y, x^-1 * y * x^-6 * y^2 * x^-1 ] T99.167 : Triangle type {11,11,23} Group order 253 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, y^2 * x^3 * z^-2 * y, x^-11 ] T99.168 : Triangle type {11,11,23} Group order 253 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, z^-1 * x^-3 * y^-2 * x, x^-11 ] T99.169 : Triangle type {12,12,60} Group order 240 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * z * x^-2 * y * z^-2, z^-2 * y * x^2 * z^-2 * y ] T99.170 : Triangle type {12,12,60} Group order 240 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^-1 * x^4 * y^-3, x * z^-1 * x^3 * z^-3 ] T99.171 : Triangle type {12,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z * y * z^-1 * x^-1 * z * y * x^-1 * z^5 ] T99.172 : Triangle type {12,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, z^-2 * x^3 * z^-2 * x, z^-3 * x^-1 * z * y * x^-1 * z^4 * y^-1 ] T99.173 : Triangle type {12,12,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, x^-1 * z^4 * y * z^-2 * x^-1 * z^3 * y * x * z^2 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T99.174 : Triangle type {12,19,228} Group order 228 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, z^-3 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T99.175 : Triangle type {12,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-12, z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T99.176 : Triangle type {12,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^-2 * z^7 * y^-4 * z^3 * y^-1 * z^2 * y^-1 ] T99.177 : Triangle type {12,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-12, y^7 * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y * z^-2 ] T99.178 : Triangle type {12,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^6 * x^-1 * y * z^-5 * y * z^-1 * y^4 ] T99.179 : Triangle type {12,216,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-12, y^7 * z^-5 * y * z^-1 * y * z^-1 * y^2 ] T99.180 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y^2)^2, (x * z^-1)^4 ] T99.181 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^3 * z^-2 * x, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T99.182 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * x^-1 * z * x^-1 * y^-1 * z * x^-1, y^-4 * x^2 * y^-4 ] T99.183 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4, y^-4 * x^2 * y^-4 ] T99.184 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, (y * z^-3)^2, z^-4 * x^-1 * y * z^-3 ] T99.185 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * x^4 * y^-3, z^-2 * y * z^-1 * y * z^-3 ] T99.186 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-4 * x^-1 * z^3 * y^-1, z^-4 * x^2 * z^-4 ] T99.187 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-4 * x^2 * z^-4 ] T99.188 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1, x^11 * y^-1 * x * z^-1 * x ] T99.189 : Triangle type {14,28,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, x^-2 * y * x^-2 * z * x^-9 ] T99.190 : Triangle type {15,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z * y^-1 * x^2 * z^2, (y^-1 * x)^3 ] T99.191 : Triangle type {15,15,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, (z^-1 * x)^3, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T99.192 : Triangle type {18,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-2 * z * x^-1 * z^3, y^-2 * x^4 * y^-4 ] T99.193 : Triangle type {18,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^-3 * x^2 * z^-3, y^-2 * x * y^-1 * x * z * y^-2 ] T99.194 : Triangle type {18,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x * y^-1 * z^-2 * x^5 * y^-1 * x ] T99.195 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-7, z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z^2 ] T99.196 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-3 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x ] T99.197 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^2 * y^-8, x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-4 ] T99.198 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3 * y^-2 * x^5 * y^-2, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^4 ] T99.199 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-4 * y^3 * z^-1 * y^4, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^4 ] T99.200 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-11, z^-2 * x^5 * z^-5 * x * z^-1 * x * z^-3 ] T99.201 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * y^-1 * z^5, y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y ] T99.202 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4 * z^2, x^-2 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-2 ] T99.203 : Triangle type {19,209,209} Group order 209 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-1 * z^5, y^-4 * z^2 * y^-3 * x^5 * y^-1 * x * y^-1 ] T99.204 : Triangle type {20,20,110} Group order 220 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * z^3 * x^-2 * z * y^-1 * z^2, z^6 * y * x^-1 * z^4 ] T99.205 : Triangle type {20,20,110} Group order 220 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^6 * y^-2, z^-1 * x^-1 * z * y * z^-3 * x^-1 * z^2 * y^-1 * z^-2 ] T99.206 : Triangle type {21,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x^3 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^4 ] T99.207 : Triangle type {21,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-2 * z^4, y^-8 * x^5 * y^-1 * x * y^-1 ] T99.208 : Triangle type {21,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-5 * y^3 * z^-2 * y^3, z^3 * x^-1 * z * x^-1 * z^5 * x^-6 * z ] T99.209 : Triangle type {21,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * y * z^-4, x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-3 ] T99.210 : Triangle type {21,70,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * z^5)^2, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-2 ] T99.211 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-5 * y^7, z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-6 * z ] T99.212 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^-5 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 ] T99.213 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-2 * z^4, x^-2 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-2 ] T99.214 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x * y^-6 * x^5 * y^-2, x^7 * z^-5 * x * z^-4 ] T99.215 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-4, x^-2 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 ] T99.216 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^5 * x^-2 * z^4, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x ] T99.217 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^2, x^-4 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-3 ] T99.218 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-9 * z * x^-8 * y * x^-5 ] T99.219 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-4 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-4 ] T99.220 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-1 * z^5, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x^4 ] T99.221 : Triangle type {23,207,207} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-1 * y * x^-5 * y^6 * x^-1 * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-4 * z^2 ] T99.222 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^2 * x^-2 * y * z^-2 * y * z^-1 * y * x^-3 * y^4 ] T99.223 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, x^2 * y^-4 * x^4 * y^-4 * z * y^-1 * x^2 * y^-2 * x ] T99.224 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, x^-1 * y * x^-2 * y^2 * x^-9 * y ] T99.225 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-4 * x^2 * z^-4, x^-1 * y * x^-7 * y^3 ] T99.226 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^5 * z^-1 * x * z^-2, x^-1 * y^2 * z^-5 * x^-1 * y^3 * z^-1 * y ] T99.227 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^9 * z^-1 * x * z^-1 * x * y^-1 * x^8 * z^-1 * x * y^-1 * x * y^-1 * x^2 ] T99.228 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z, y^-3 * z * y^-1 * z^5 * y^-6 ] T99.229 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-3 * z^3, y^-7 * z^4 * y^-1 * x^5 * y^-1 * x * y^-3 ] T99.230 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z^5 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T99.231 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, y^-7 * z^2 * y^-3 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T99.232 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y * x^-5 * y^7, z^4 * y^-1 * z^5 * y^-1 * z^5 ] T99.233 : Triangle type {26,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-2 * z * x^-11 * y^4 * x^-3 * z^3 * x^-6 ] T99.234 : Triangle type {27,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, x * y^-2 * x * z * y^-1, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T99.235 : Triangle type {27,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z * y^-2 * x * y^-1 * z, z^-1 * x^-3 * y^-1 * x^2, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T99.236 : Triangle type {27,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, z^10 * y^-7 * z * y^-1 ] T99.237 : Triangle type {27,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, z^-5 * x^3 * z^-7 ] T99.238 : Triangle type {27,27,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-2 * y * x * z^-1 * y ] T99.239 : Triangle type {30,35,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-6, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-7 ] T99.240 : Triangle type {30,35,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^4 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T99.241 : Triangle type {30,35,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^5 * y^-1, z^2 * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T99.242 : Triangle type {30,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^4 * y^-1 * x^3 * y^-1 * x * y^-1 * x * y^-1 * x * z^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T99.243 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * y^-1, z^-1 * x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-2 ] T99.244 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^7 * x^-5 * y^6 * x^-1 * y * x^-1 * y^4 ] T99.245 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-6 * x^7, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T99.246 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^7 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T99.247 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-6, x^3 * y^-2 * x^4 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T99.248 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^13 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T99.249 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T99.250 : Triangle type {34,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-11 * y^2 * x^-8 * z * x^-8 * z * x^-5 ] T99.251 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-5 * x^4 * z^-1 * x^2, z^10 * y^-1 * z^5 ] T99.252 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y * x^-12 * y^8 * z^-1 * y^10 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.253 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^-5 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T99.254 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, x^3 * y^-4 * x^9 ] T99.255 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-4 * z^2, x^2 * y^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x ] T99.256 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-4 * z^2, y^3 * x^-5 * y^3 * z^-2 * y^4 ] T99.257 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^2 * y^-3, z^-2 * x^7 * z^-5 * x * z^-1 * x * z^-4 ] T99.258 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y ] T99.259 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^4 * x^-6, y^8 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T99.260 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-7, x^4 * y^-4 * x^2 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T99.261 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^5 * x^-1 * y * z^-3 * y^3 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T99.262 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-5 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T99.263 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-30 * y * x^-1 * y * x^-1 * y * x^-8 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T99.264 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^21 * x^-1 * z^6 * x^-1 * z ] T99.265 : Triangle type {51,68,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-5 * z, x^5 * y^-5 * x^4 * z^-1 * x^5 ] T99.266 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^2 * x^-2 * y * z^-3 * y^2 * x^-2 * y * x^-1 * y^3 ] T99.267 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, x^2 * y^-2 * z * y^-8 * z * y^-1 * x^2 * y^-3 ] T99.268 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^-1 * y * x^-2 * y^2 * x^-8 * y * x^-1 ] T99.269 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x * z^-1 * x * z^-4, x^-1 * y * x^-6 * y * x^-1 * y^2 ] T99.270 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^5 * z^-1 * x * z^-2, x^-1 * y^2 * z^-5 * y^5 ] T99.271 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^9 * z^-1 * x * z^-1 * x * y^-1 * x^9 * y^-1 * x^4 ] T99.272 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-3 * z * y^-9 * z^2 * y^-6 * z^2 * y^-1 * x * y^-4 ] T99.273 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-3 * z^3, y^-3 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 ] T99.274 : Triangle type {52,52,52} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-4 ] T99.275 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-31 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^4 * x^-1 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.276 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-5 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.277 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-3 ] T99.278 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^7 * x^-1 * z^5, y * x^-1 * y * x^-5 * y^6 * x^-1 * y ] T99.279 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^6, z^10 * x^-1 * z^5 ] T99.280 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y^3, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6 * z^2 ] T99.281 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-7, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-6 * z ] T99.282 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7, x^5 * y^-2 * x^4 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x^3 ] T99.283 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-6, x^-6 * z^3 * x^-9 ] T99.284 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^26 * y^-1 * x^-2 * z^6 ] T99.285 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * y^-1, z^12 * x^-6 * z^3 ] T99.286 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^9 * x^-3 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T99.287 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-3 * z^3, y^4 * x^-4 * y * z^-5 * y^5 ] T99.288 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^3 * x^-7, y^6 * x^-1 * y * z^-5 * y * z^-1 * y^4 ] T99.289 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * z^4, x^-4 * y * x^-1 * y * x^-1 * y * x^-7 * y^3 * x^-6 ] T99.290 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^4 * z^-2 * y^10 * x^-4 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T99.291 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x * y^-4, z^12 * x^-4 * z^3 ] T99.292 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, y^2 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T99.293 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T99.294 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-8, x^-6 * z^4 * x^-5 * y * x^-2 ] T99.295 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, y^3 * z^-7 * y^4 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T99.296 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-4 * z^2, x^-5 * z^4 * x^-5 * y * x^-1 ] T99.297 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-6, y^-3 * z * y^-1 * z^5 * y^-1 * x^2 * y^-4 ] T99.298 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^5 * y^-1 * z^5, y^3 * x^-5 * y^3 * z^-2 * y^4 ] T99.299 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * x^-1 * z^4, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T99.300 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-67 ] T99.301 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^26 * x^-3 * y^3 * z^-1 * y^9 ] T99.302 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9 * y^3 * x^-1, y^7 * z^-5 * y * z^-1 * y * z^-1 * y^2 ] T99.303 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * x^4 * y^-2, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T99.304 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5, x^-2 * y * x^-8 * y^2 * x^-1 ] T99.305 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-11 * y * x^-8 * z * x^-6 * y^3 * x^-6 ] T99.306 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^2 ] T99.307 : Triangle type {67,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-3 * z^3, x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 ] T99.308 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 ] T99.309 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, y^-1 * z^3 * x^-4 * z * x^-1 * z^3 ] T99.310 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^5 * y^-1 * z^-2, y^7 * z^-1 * y * z^-1 ] T99.311 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^6 * y^-2, y^-1 * z^2 * y^-2 * x^-1 * z^4 ] T99.312 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z * y^-2 * x^-1 * z^3, x^-1 * z * y * x^-1 * y * x^-6 ] T99.313 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y^2 * x^-8 * y^2 ] T99.314 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z^-1 * x^2 * z^-1 * x^10 * y^-1 * x^4 * y^-1 * x ] T99.315 : Triangle type {68,68,102} Group order 204 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-14 * y * z^-2 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-6 * x * z^-6 ] T99.316 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^16 * y^-1 * x^12 * y^-1 * x^71, y * z^-1 ] T99.317 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^6 * y^-4 * x^12 ] T99.318 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^6 * y^-4 * x^2 * z^-5 * x * z^-1 * x^6 ] T99.319 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^9 * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.320 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3 * y^-7, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z ] T99.321 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * z^-2 * x^3, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T99.322 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z * x^-12 * z^8 * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 * x^-1 * z * x^-1 * z ] T99.323 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x * y^-8 ] T99.324 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^5 * x^-1 * z^5, y^3 * x^-4 * y^6 * x^-1 * y ] T99.325 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-4 * y^6 * x^-1 * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z ] T99.326 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, y^3 * x^-4 * y^6 * x^-1 * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T99.327 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^61 * x^-1 * z^5 ] T99.328 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^8 * y^-1 * z^5, y^3 * x^-4 * y^6 * x^-1 * y ] T99.329 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^2 * x^-8, z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T99.330 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^5 * x^-5 * z, y^4 * x^-5 * y^3 * z^-2 * y^5 ] T99.331 : Triangle type {100,200,200} Group order 200 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-36 * y * x^-8 * y * x^-5 ] T99.332 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x^-2 * y^-1, y^76 * x^-1 * y^23, x * z^-1 ] T99.333 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^53 * x^-2 * y^12 ] T99.334 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-29 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^4 * x^-1 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.335 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^19 * x^-1 * y * x^-1 * y^11 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.336 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y * x^-5 * y^5 * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.337 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-1 * y^6 * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.338 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^7 * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.339 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, y^-11 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T99.340 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^2 ] T99.341 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^5, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x ] T99.342 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^6 * x^-1 * z^5, y^4 * x^-4 * y^6 * x^-1 * y^2 ] T99.343 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^7 * x^-1 * z^5, x^-2 * y * x^-5 * y^6 * x^-2 ] T99.344 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^8 * x^-1 * z^5, x^3 * y^-5 * x^4 * z^-1 * x^3 ] T99.345 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y * x^-8 * y^2 * x^-1, z^9 * x^-1 * z^5 ] T99.346 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-5 * x^4 * z^-1 * x^2, z^10 * x^-1 * z^5 ] T99.347 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-5 * y^6, z^11 * x^-1 * z^5 ] T99.348 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-5 * z, x * y^-1 * x * y^-6 * x^8 ] T99.349 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^-4 * z * x^-1 * z * x^-1 * z^5 * x^-9 ] T99.350 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-6 * x * z^-22 ] T99.351 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-8 ] T99.352 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^4 * y^-2, z^-2 * x^5 * z^-5 * x * z^-1 * x * z^-3 ] T99.353 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-4 * z^2, x^2 * y^-1 * x * y^-6 * x^5 * y^-1 * x^3 ] T99.354 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-5 * z, y^-4 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^5 * y^-5 ] T99.355 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^2 * y^-8, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^4 ] T99.356 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9 * y^2, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T99.357 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-3 * z^3, x^-8 * y^5 * x^-3 ] T99.358 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-8 * z * x^-10 * z * x^-3 ] T99.359 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^3 ] T99.360 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y^3, z^-4 * y^3 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T99.361 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^3 * x^-7, y^4 * x^-4 * y * z^-5 * y * z^-1 * y * z^-1 * y^2 ] T99.362 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^26 * x^-2 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T99.363 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y * x^-1 * y^6 * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T99.364 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y * z^-1 * y^2 * z^-4 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T99.365 : Triangle type {199,199,199} Group order 199 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^5 * y^-1 * z^5, y^-5 * z^3 * y^-2 * x^5 * y^-3 ] Genus 100 T100.1 : Triangle type {2,3,72} Group order 1296 Reflexible action Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1, z^-1 * x * z^2 * y * z^-1 * x * z^6 * y * z^-1 * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-7 ] T100.2 : Triangle type {2,4,10} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5, z^10 ] T100.3 : Triangle type {2,4,10} Group order 1320 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^10, z^3 * y * z^-2 * x * z * y * z^-2 * x * z^2 * y^-1 * z^-1 * x ] T100.4 : Triangle type {2,4,15} Group order 1080 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^5, x * z^4 * y^-1 * z^-5, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * x * z^3 * y^-1 * z^3 * y^-1 * z^2 ] T100.5 : Triangle type {2,4,22} Group order 968 Reflexible action Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-22 ] T100.6 : Triangle type {2,4,202} Group order 808 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-202 ] T100.7 : Triangle type {2,4,400} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-52 * x * y^-1 * z^-147 ] T100.8 : Triangle type {2,6,36} Group order 648 Chiral action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^4 * y * z^-3 * x * z * y^-1 * z^-2 ] T100.9 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, (y * z^-1 * y * z^-1 * y)^2, x * z * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T100.10 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-21 * x * z^8 * y * z^-6 ] T100.11 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, (y * z^-1 * y * z^-1 * y)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 * x ] T100.12 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-20 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T100.13 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-19 * x * z^3 * y * z^-7 * x * z^4 * y^-1 * z^-1 ] T100.14 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^6, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T100.15 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^6, x * z * y * z^-3 * x * y^-1 * x * z * y^-1 * z^-4 ] T100.16 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T100.17 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-12 * x * z^11 * y^-1 * z^-2 * x * z * y^-1 * z^-3 * x * y^-1 * z^-4 ] T100.18 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^5 * y^-1 * z^-2 ] T100.19 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * x, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T100.20 : Triangle type {2,6,36} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^2 * x * y^-1 * z * y^2 * x * y^-2 * z^-1 * y * x, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T100.21 : Triangle type {2,6,102} Group order 612 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-20 * x * z^7 * y^-1 * z^-6 ] T100.22 : Triangle type {2,6,102} Group order 612 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^76 * y * z^-1 * x * z^5 * y * z^-1 * x * y * z^-7 * x * z^2 * y^-1 * z^-3 * x * z^3 ] T100.23 : Triangle type {2,6,102} Group order 612 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^82 * y * x * y * x * y^-1 * z^-6 * x * z^11 ] T100.24 : Triangle type {2,6,300} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^59 * y * x * z^14 * y * z^-1 * x * z^7 * y * z^-7 * x * z^2 * y^-1 * z^-3 * x * z^3 ] T100.25 : Triangle type {2,7,16} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, (z * y^-1 * z)^3, x * z * y * x * y^-2 * z^-1 * x * y^-1 * z^-1 * y ] T100.26 : Triangle type {2,7,16} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^-7, z * y * z^-1 * x * y^-1 * z^-2 * x, z^-1 * y * x * y^-3 * z^-1 * y * z^-3 ] T100.27 : Triangle type {2,8,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, (y * z^-2 * y^2)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T100.28 : Triangle type {2,8,10} Group order 720 Reflexible action Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (z^-1 * y)^5 ] T100.29 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^4, y^-9, (z * y^-1 * z)^3 ] T100.30 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, y^-9, (y * z^-2 * y * z^-1)^2 ] T100.31 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, z^12 ] T100.32 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^12 ] T100.33 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, x * z * y * x * y^-1 * z^-2 * y * z^-1, z^12 ] T100.34 : Triangle type {2,9,12} Group order 648 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^12 ] T100.35 : Triangle type {2,9,45} Group order 540 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z^4 * y^-1 * z^-5, x * z * y * z^-2 * y * x * y * z^-2 * y * z^-2 ] T100.36 : Triangle type {2,10,52} Group order 520 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^28 * y * x * z * y * x * y * z^-8 * x * y^-1 * z^-3 * x * z^8 ] T100.37 : Triangle type {2,12,42} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-1 * x * z^25 * y * z^-1 * x * z^4 * y^-1 * z^-9 ] T100.38 : Triangle type {2,12,42} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^15 * y * x * z^3 * y * x * z * y^-1 * z^-9 * x * y^-1 * z^-3 * x * z^7 ] T100.39 : Triangle type {2,12,42} Group order 504 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^12, (y * z^-1 * y^4)^2, z^-7 * x * z^3 * y^-1 * z^-3 ] T100.40 : Triangle type {2,12,240} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^12, z^-1 * x * z^24 * y * z^-1 * x * z^4 * y^-1 * z^-8 ] T100.41 : Triangle type {2,18,27} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * x * z * y * z^-1 * y^2 * z^-5 ] T100.42 : Triangle type {2,18,27} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-4, z^3 * y^-2 * z * y^-1 * z * y^-1 ] T100.43 : Triangle type {2,18,27} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, z * y^-4 * z * y^-2 * z ] T100.44 : Triangle type {2,18,27} Group order 486 Chiral action Defining relators: [ x^2, x * y * z, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-1 * z * y^-3 * z^4 ] T100.45 : Triangle type {2,18,27} Group order 486 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^5 * y^-3 * z^5, z^-1 * x * z^13 * y * z^-5 * x * z^4 * y^-1 * z^-2 ] T100.46 : Triangle type {2,18,225} Group order 450 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-6 * z^4 * y^-3 * z^4 * y^-1, z^-1 * x * z^12 * y * z^-4 * x * z^4 * y^-1 * z^-2 ] T100.47 : Triangle type {2,22,22} Group order 484 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-5 * z^-1 * x * z * y * x * z * y^2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-7, z^11 * y * x * z * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^3 ] T100.48 : Triangle type {2,22,22} Group order 484 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-1 * z^4 * y^-1 * z^4 * y^-4 * z * y^-6 * z, y^2 * x * y^-3 * z^-1 * y^2 * x * y^-5 * z * y^5 * x * y^-1 * z * y ] T100.49 : Triangle type {2,22,220} Group order 440 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^8 * y * z^-4 * x * z * y^-1 * z^-5, y^-9 * z^4 * y^-5 * z^4 ] T100.50 : Triangle type {2,36,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-2 * z^4 * y^-4 * z^5 ] T100.51 : Triangle type {2,36,72} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, x * y^-6 * z^-1 * y^5, z^2 * y^-1 * z * y^-4 * z * y^-1 * z * y^-2 * z^2 * y^-2 * z ] T100.52 : Triangle type {2,42,210} Group order 420 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, z^-5 * y^10 * z^-4 * y^22 * z^-1 ] T100.53 : Triangle type {2,52,208} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-4 * x * z^3 * y^-1 * z^-3, y^-13 * z^4 * y^-4 * z^4 * y^-1 ] T100.54 : Triangle type {2,69,138} Group order 414 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-33 * y^2 * z^-1 * y^8 * z^-1 * y * z^-4 * y * z^-14 * y^2 * z^-1 ] T100.55 : Triangle type {2,82,205} Group order 410 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y * z^-1 * y^12 * z^-4 * y^23 ] T100.56 : Triangle type {2,102,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-65 * y^35 * z^-1 ] T100.57 : Triangle type {2,201,402} Group order 402 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^133 * y^-66 * z ] T100.58 : Triangle type {2,202,202} Group order 404 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^68 * z^-134 ] T100.59 : Triangle type {2,400,400} Group order 400 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^67 * z^-133 ] T100.60 : Triangle type {3,3,36} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * z^-1 * x^-1 * y * x * z^2 ] T100.61 : Triangle type {3,3,36} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^-4 * x^-1 * z * y^-1 * x^-1 * z^3 * y^-1 * z^-2 ] T100.62 : Triangle type {3,3,201} Group order 603 Chiral action Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x * z^2 * y^-1 * z^-3 * x^-1 * z^3 * y * z^-1 * x * z^2 * y * z^-1 ] T100.63 : Triangle type {3,4,9} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^4 * y^-1 * x^-1 * z^4, z^-2 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z^4 * y^-1 * z^-1 ] T100.64 : Triangle type {3,4,9} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y^-1 * z^2 * y^-2 * x^-1 * z * y^-1 * z^2 ] T100.65 : Triangle type {3,4,9} Group order 648 Reflexible action Defining relators: [ x^3, x * y * z, y^4, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^2, y^-1 * z^2 * y^-2 * x^-1 * z * y^-1 * z^2 ] T100.66 : Triangle type {3,5,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, z^6, z^-1 * y * x^-1 * y^-1 * x * z * y^2, z^-1 * x^-1 * z * y * x^-1 * z * y * z^-1 * y ] T100.67 : Triangle type {3,5,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, x^-1 * z * y^-1 * x * z^2, (z^-1 * y)^3, x^-1 * y^-1 * z^-1 * y * x^-1 * y * x^2 * y^-1 * z^-1 * y * x * z^-1 ] T100.68 : Triangle type {3,5,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, y^-5, (y * z^-2)^2, z^6, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T100.69 : Triangle type {3,5,6} Group order 660 Reflexible action Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^-5, z^6, (x^-1 * z * y^2)^2 ] T100.70 : Triangle type {3,6,24} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, x^-1 * z^2 * y^-1 * x * z^3 ] T100.71 : Triangle type {3,6,24} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, (x * z * y^-1 * z^-1)^2 ] T100.72 : Triangle type {3,6,24} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-4 * x^-1 * z^3 * y^-1 ] T100.73 : Triangle type {3,6,134} Group order 402 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-4 * y * x^-1 * z * y * z^-3 ] T100.74 : Triangle type {3,8,12} Group order 432 Reflexible action Defining relators: [ x^3, x * y * z, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-2 * y * x^-1 * z * y^-2, y * x^-1 * z * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T100.75 : Triangle type {3,10,60} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-4 * x^-1 * z^3 * y^-1, y^10 ] T100.76 : Triangle type {3,12,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^2, y * z^-1 * y * z^-1 * x^-1 * y * x^-1 * y * z^-1 * y * z^-1 * x^-1 ] T100.77 : Triangle type {3,12,30} Group order 360 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-3 * x^-1 * z^3, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T100.78 : Triangle type {3,27,54} Group order 324 Chiral action Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * z^-1 * x^-1 * z^4, z * y^-4 * x * z * y^-1 * z^2 ] T100.79 : Triangle type {3,27,54} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, y * z^-9 * y * z^-3 * y * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-3 ] T100.80 : Triangle type {3,36,36} Group order 324 Chiral action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y * z^-2 * x^-1 * y^-2 * z, y^-3 * z * y^-5 * z * y^-1 * z ] T100.81 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-2 * z * y, y^-2 * z^2 * y^-1 * z^2 * y^-3 * z * y^-1 ] T100.82 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, y * z^-3 * y * z^-1 * y * z^-2 * y^3 ] T100.83 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-18 * y^13 * z^-1 * y^2 * z^-1 ] T100.84 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, y^-1 * z * y^-3 * z * x^-1 * z * y^-1 * z^2 * y^-1 * z ] T100.85 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, (y * z^-3 * y * z^-1)^2 ] T100.86 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2, y^-2 * z^5 * y^-1 * z * y^-3 ] T100.87 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-19 * y * z^-2 * y^6 * z^-5 * y * z^-1 ] T100.88 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-17 * y * z^-2 * y^2 * z^-1 * y^6 * z^-1 * y * z^-1 * y^2 * z^-2 ] T100.89 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, y^-2 * z^2 * y^-1 * z * x^-1 * z * y^-2 * z * y^-2 ] T100.90 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^3 * z^-1 * y^4 * z^-1 * y * z^-1 * y ] T100.91 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-3 * z^2 * y^-1 ] T100.92 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * x^-1 * y^-1)^3, y^-3 * z * y^-1 * z * y^-4 * z * y^-1 ] T100.93 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * z * y * z^-1 ] T100.94 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y * z^-2 * y^4 * z^-4 * y ] T100.95 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, y^-1 * z^4 * y^-1 * z^2 * x^-1 * z^3 * y^-1 ] T100.96 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y * z^-17 * y * z^-1 * y * z^-1 * y^4 * z^-1 * y^3 * z^-2 * y * z^-1 * y^2 ] T100.97 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, (y * z^-1)^6 ] T100.98 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, y * z^-2 * x^-1 * z^3, y * z^-1 * y * z^-1 * y^7 * z^-1 ] T100.99 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * x^-1 * z)^3, y^-1 * z * y^-4 * z * y^-1 * z^4 ] T100.100 : Triangle type {3,36,36} Group order 324 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * x^-1 * z)^3, y^-1 * z * y^-4 * z * y^-2 * z^2 * y^-1 ] T100.101 : Triangle type {3,52,78} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * y^-2 * z^2 * y^-1 * z^2 * x^-1 * y^-1 * z^2 * y^-1 * z ] T100.102 : Triangle type {3,101,303} Group order 303 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^9 * z^-1 * y^10 * z^-1 * y^79 * z^-1 ] T100.103 : Triangle type {3,102,102} Group order 306 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-81 * z * y^-10 * z * y^-8 * z ] T100.104 : Triangle type {3,102,102} Group order 306 Reflexible action Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^79 * y^-14 * z^7 * y^-1 ] T100.105 : Triangle type {3,102,102} Group order 306 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-21 * y^5 * z^-1 * y * z^-1 * y^5 ] T100.106 : Triangle type {3,300,300} Group order 300 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^-80 * z * y^-10 * z * y^-8 ] T100.107 : Triangle type {4,4,11} Group order 484 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6 * y^-1 * x^3 * z^4 ] T100.108 : Triangle type {4,4,101} Group order 404 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-5 * y * x * z^-5 ] T100.109 : Triangle type {4,4,101} Group order 404 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^85 * y^-1 * x^-1 * z^15 ] T100.110 : Triangle type {4,4,200} Group order 400 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^84 * y^-1 * x * z^15 ] T100.111 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, y^6, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^2 * z^-1 * x^-1 * y^-1 * z^-2 ] T100.112 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, y * x * y^-2 * x * z * y^-1 * z, z^8, y * z^-2 * y * x^-1 * y^-1 * z^3 ] T100.113 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^8, x^-1 * z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 * z ] T100.114 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, x^-1 * z * y^-1 * x * z * y, y^6, z * y * z^-1 * x^-1 * y^-2 * z ] T100.115 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^6, z * y^-1 * z^-1 * x^-1 * z * y^-2 ] T100.116 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, x * z * y^-1 * x * y^-1 * z^-1, y^6, (y * z^-2)^2 ] T100.117 : Triangle type {4,6,8} Group order 432 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * z * y, y^6, z^-2 * y * x^2 * y^-1 * z^-2 ] T100.118 : Triangle type {4,6,8} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y^-1 * z^-2 * y * x^-1 * y^-1 * x * y^-1 * z^2 * y ] T100.119 : Triangle type {4,6,8} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-2 ] T100.120 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, z * y^2 * x^-1 * z * y^-1 * z, z^3 * y * x^-1 * y * x^-1 * z^5 ] T100.121 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z^-1 * x * z^2 * y * x * z^2 * y * z^-3 ] T100.122 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * z * y^-2, y * x^-1 * y * z^-6 * x^-1 * z^2 ] T100.123 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^9 * y * x * z^6 * y * x * z^13 ] T100.124 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^6 * y * x^-1 * z^2 * y * z^-4 * x^-1 * y^-1 * z^-11 * x * z ] T100.125 : Triangle type {4,6,30} Group order 360 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z * y^-1 * z^-4 * x^-1 * y * x * z^3, y * z^-1 * x * z * y * z^-2 * x^-1 * z^-3 * x^-1 * z ] T100.126 : Triangle type {4,9,36} Group order 324 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * y^2 * x * y^-1 * z^-1 * x^-1, y^4 * x^-1 * y^-1 * z^3, y^-9 ] T100.127 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^-1 * y * x^-1 * y * z^-1 * x^-1 ] T100.128 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T100.129 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, (x^-1 * z * y)^2, z^-1 * y^2 * x^-1 * y^-3, y^-9 ] T100.130 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-9 ] T100.131 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-1 * y * x^-1 * z^4, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, y^-9 ] T100.132 : Triangle type {4,9,36} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-3, z^2 * y^2 * x * z^3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T100.133 : Triangle type {4,10,32} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^10, z^-4 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-3 * x^-1 * y^-1 * z^-2 ] T100.134 : Triangle type {4,12,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * y * z^-1, z^4 * y^-1 * x * z^4 ] T100.135 : Triangle type {4,12,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * x * z ] T100.136 : Triangle type {4,12,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * y * z^-1 * y, y^-2 * z * x^-1 * y^-3, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T100.137 : Triangle type {4,12,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z * x^-1 * y^-3, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-2, y^-1 * z * y^-3 * x^-1 * y^-2 * z * y^-1 ] T100.138 : Triangle type {4,12,150} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^10 * y^-1 * z^-1 * x * z * y * z^-3 * x * z^8 ] T100.139 : Triangle type {4,18,144} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * x^-1 * z^4, y^-3 * z^7 * y^-1 * z * y^-3 * z^2 * y^-1 ] T100.140 : Triangle type {4,28,140} Group order 280 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y^-1 * z^-2 * x^-1 * y * z^-2 * x^-1 * z, y^-4 * z^3 * y^-1 * z * y^-2 * z^2 * y^-1 ] T100.141 : Triangle type {4,68,136} Group order 272 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 * z^-2 * y^8 * z^-2 * y^11 ] T100.142 : Triangle type {4,134,268} Group order 268 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-33 * z * y^-1 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-12 * z * y^-1 * z * y^-1 * z ] T100.143 : Triangle type {5,6,12} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T100.144 : Triangle type {5,6,12} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^6, (x * z * y)^2, (z^-1 * y)^3, y^-1 * z^-1 * x^-2 * y * x * y^-1 ] T100.145 : Triangle type {5,6,12} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, y^-1 * z^-1 * x^-2 * y * x * z, x * z^-1 * y * x^2 * y^-1 * x * y^-1 ] T100.146 : Triangle type {5,6,12} Group order 360 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * x)^3 ] T100.147 : Triangle type {5,6,30} Group order 330 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * x^2 * z * x^-1 * y ] T100.148 : Triangle type {5,6,30} Group order 330 Chiral action Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^6, x * z^-2 * x^-1 * z * x^-1 * y^-1 ] T100.149 : Triangle type {5,51,255} Group order 255 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^19 * z^-1 * y^3 * z^-1 * y * z^-1 * y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T100.150 : Triangle type {5,52,52} Group order 260 Chiral action Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^-1 * z * y^-34 * z * y^-1 * z * y^-9 * z^2 * y^-2 ] T100.151 : Triangle type {5,52,52} Group order 260 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z^-1 * y * z^-17 * y^3 * z^-1 * y^6 * z^-1 * y^6 * z^-1 * y * z^-1 * y^11 * z^-1 * y ] T100.152 : Triangle type {5,250,250} Group order 250 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, y^22 * z^-1 * y * z^-1 * y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T100.153 : Triangle type {5,250,250} Group order 250 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^17 * z^-1 * y^3 * z^-1 * y * z^-1 * y^13 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T100.154 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, y^-1 * z * y * x^-1 * y^-1 * z^2, y^-1 * z^-2 * x^-1 * z^3 ] T100.155 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, y^6, (y * z^-2)^2, x^-1 * z^2 * y * x^-1 * y^-1 * z^-2 ] T100.156 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, x^-1 * y * x^-2 * y^-2 * z, y^-2 * x * y^-1 * x * y^-1 * z^2, z * y * x * y^-1 * x * z^3 ] T100.157 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, x^6, y^6, z^-1 * y * x^-2 * y^-2 * x, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 ] T100.158 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^3 * x^-1 * z^2 * y^-1, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T100.159 : Triangle type {6,6,18} Group order 324 Chiral action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T100.160 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^-5 * x^-1 * z^2 * y^-1 * x * z * y * x * z * y * z^-6 ] T100.161 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-2 * x^-1 * z^5 * y * z^-2 * x * y^-1 * z^-7 ] T100.162 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^8 * y^-1 * x * z^4 * y * x^-1 * z^4 ] T100.163 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^3 * x^-1 * z^2 * y^-1, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T100.164 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^3 * x^-1 * z^2 * y^-1, z * y * x^-1 * y^-1 * x * z^3 ] T100.165 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, z^-3 * x^-1 * z^2 * y^-1 ] T100.166 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y^6, y * x^-3 * z * x^-2, z^-1 * y^2 * x^-1 * y^3 ] T100.167 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-1 * x * z^6 * y^-1 * z^-1 * x * z^4 * y^-1 * z^-4 ] T100.168 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-2 * y * x^-1 * y * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * y * z^-1 ] T100.169 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-2 ] T100.170 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, (y * x^-1 * z)^3 ] T100.171 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^2 * z^-3, (y * x^-1 * z)^3 ] T100.172 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * x * z^2 * y^-1 * x * z^2 * y * z^-2 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-3 ] T100.173 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^-3 * x * z * y^-1 * z^-3 * x * z * y * z^-1 * x^-1 * z^3 * y * z^-3 ] T100.174 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-1 * y * x^-1 * y * z^-3 ] T100.175 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, (z^-1 * x^-1 * y^-1)^3 ] T100.176 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, x^-1 * y * x^-2 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z * y * z^-1 * x^-1 * z^3 ] T100.177 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1 ] T100.178 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^-1 * x * z^6 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-1 * x^-1 * z * y * z^-4 ] T100.179 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, z * y^-1 * x^2 * z * y^-1, y^6, z^-3 * x^-1 * z * y * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-5 ] T100.180 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^6, y^6, z^5 * y^-1 * z^-5 * x^-1 * y * z^-2 * x * z^4 ] T100.181 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, z^-2 * x^-2 * y * z^-1 * x, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T100.182 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, z^-2 * x^-2 * y * z^-1 * x, x^-1 * y^2 * x^-1 * y * x * z^-1, (x^-1 * z^2 * y)^2 ] T100.183 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z * y^-1 * x * y^-1 * x * z^3 ] T100.184 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, y^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, (x * z * y^-1 * z^-1)^2 ] T100.185 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z * y^-1, (x * y^-2)^2, y^6, (x * z^2 * y)^2 ] T100.186 : Triangle type {6,6,18} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z * y^-1, (x * y^-2)^2, y^6, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T100.187 : Triangle type {6,6,51} Group order 306 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^-1 * x * z^3 * y^-1 * z^-2 * x * y * z^-4 * x^-1 * z^2 * y * x^-1 * y^-1 * z^-1 ] T100.188 : Triangle type {6,6,51} Group order 306 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-29 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z^4 * y * x^-1 * y * z^-5 * x^-1 * z * y ] T100.189 : Triangle type {6,6,51} Group order 306 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^35 * y * x * z^15 ] T100.190 : Triangle type {6,6,150} Group order 300 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^28 * y^-1 * z^-1 * x * z^3 * y^-1 * z^-1 * x * y^-1 * z^-4 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T100.191 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, (x^-1 * z * y)^2, (x * z * y)^2, (z^-1 * x)^3 ] T100.192 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, (y * z^-1 * y)^2, z^2 * y * x * z^-1 * x^-1, x^-1 * z * x^-2 * z * y^2 ] T100.193 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, (y * z^-1 * y)^2, y * x^-1 * y * x^-1 * z * x^-1 * z, (x^-2 * y)^3 ] T100.194 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^-9 ] T100.195 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y^3 * z^-2, y * z^-1 * y * x * y^-1 * z^-1 ] T100.196 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * z^-1 * y * x * y^-1 * z^-1 ] T100.197 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T100.198 : Triangle type {6,9,9} Group order 324 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, (y^-1 * x)^3 ] T100.199 : Triangle type {6,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, y * x^-1 * y * x^-1 * y * x^-1 * z^5 ] T100.200 : Triangle type {6,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^6, z^-1 * x * z * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-1 ] T100.201 : Triangle type {6,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z^3 ] T100.202 : Triangle type {6,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * y^2 * x * z^-1 * x, z^4 * y * x^-1 * y * x * y^-1 * z^-1 * x^-1 ] T100.203 : Triangle type {6,12,16} Group order 288 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z^-1 * y, z * y * x^-2 * y * x * y^-1, z * y * z^-2 * x^-1 * z^4 ] T100.204 : Triangle type {6,15,30} Group order 270 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z * y^-2 * z^2 * y^-1 * z^2 * y^-5 * z ] T100.205 : Triangle type {6,15,30} Group order 270 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, z^-4 * y * z^-2 * y * z^-6 * y ] T100.206 : Triangle type {6,15,30} Group order 270 Reflexible action Defining relators: [ x * y * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y * x^-2 * y^2 * z^-1, z^-2 * x^-2 * z * y^-1 * x ] T100.207 : Triangle type {6,15,30} Group order 270 Reflexible action Defining relators: [ x * y * z, x^6, z^-2 * y * x * z^-1 * y, z^-2 * x^-2 * z * y^-1 * x, x * z * x^-2 * y^-1 * z^-2 ] T100.208 : Triangle type {6,28,84} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y * z^-4 * y * x * z^-1 * y * z^-1 * y * z^-2 * y^2 ] T100.209 : Triangle type {6,41,246} Group order 246 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-11 * z^6 * y^-2 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T100.210 : Triangle type {6,42,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3 * y^-1 * z * x^-1 * y^-2 * z^3 ] T100.211 : Triangle type {6,42,42} Group order 252 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^14 * z^-1 * y * z^-1 * y^8 * z^-6 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^3 ] T100.212 : Triangle type {6,42,42} Group order 252 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^6, z * y^-1 * z * y^-4 * z^2 * y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 * z * y^-10 * z * y^-1 ] T100.213 : Triangle type {6,42,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^3 * z^-1 * y^2 * x^-1 * z^-1 * y * z^-1 * y * z^-2 * y^2 ] T100.214 : Triangle type {6,42,42} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^2 * z^-1 * y^4 * z^-2 * y^3 ] T100.215 : Triangle type {6,240,240} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-10 * z^6 * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-8 * z * y^-1 * z * y^-1 * z ] T100.216 : Triangle type {7,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^-7, y^-2 * x^3 * y^-1 * z^2 ] T100.217 : Triangle type {7,7,8} Group order 336 Reflexible action Defining relators: [ x * y * z, (z^-1 * x)^3, (z^-1 * y)^3, x^-7, x^-1 * y * x^-2 * z^3 ] T100.218 : Triangle type {8,30,60} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^20 * y^-9 ] T100.219 : Triangle type {8,58,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z * y^-2 ] T100.220 : Triangle type {9,26,234} Group order 234 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^12 * z^-6 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T100.221 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y * z^-1 * x^2 * z^-1 * x^-1, x^-9 ] T100.222 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z^-1 * x^-1 * z^2, x^-9 ] T100.223 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, z^-1 * y * x * z^-1, x^-9, x^-1 * y * x^-3 * y * x^-1 * y * x^-1 ] T100.224 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y * z^-1 * y^2 * z^-2, x^-4 * y^2 * z^-1, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T100.225 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-2, x * z^-1 * x^2 * z^-2 ] T100.226 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y * x^-3 * y * z^-1 * x^-1, z * x^-3 * y^-1 * z * x^-1, z^-1 * y * x^-2 * y^-1 * x * y^-1 ] T100.227 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^-1 * z^11 * y^-1 * z * y^-1 * z^3 * y^-9 ] T100.228 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-9, y^-5 * z * y^-1 * z^2 ] T100.229 : Triangle type {9,27,27} Group order 243 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-9, y^-5 * x * y^-1 * z * y^-2 ] T100.230 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-7 * y * z^-1 * y^6 * x^3 * z^-4 * y^3 * z^-1 * y * z^-1 * y * z^-1 ] T100.231 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-9, y^-6 * z^3 ] T100.232 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, z * y^-4 * x * z^2 * y^-1 * z ] T100.233 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * y^-1 * z^-1, y^-6 * z^3 ] T100.234 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y^3 * z^-4 ] T100.235 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^4 * z^-1 * y * z^-1 * y ] T100.236 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y^-1 * z^-1, y^-6 * z^3 ] T100.237 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * x * z^-1 * x * z * y^-1, z^-1 * y^4 * z^-1 * y * z^-1 * y ] T100.238 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^2 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 ] T100.239 : Triangle type {9,27,27} Group order 243 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x * z^-1 * x * z * y^-1, y^6 * z^-3 ] T100.240 : Triangle type {9,225,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, z^-4 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T100.241 : Triangle type {9,225,225} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9, y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-10 ] T100.242 : Triangle type {10,10,26} Group order 260 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^-11 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * z * y^-1 * z^-9 ] T100.243 : Triangle type {10,24,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y^4 * x^-1 * y^-1 * z^-1 * y^2, x^10 ] T100.244 : Triangle type {11,21,231} Group order 231 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6 * z^2 ] T100.245 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-7 * z^2 ] T100.246 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, z^-3 * y^2 * z^-3, x^-11 ] T100.247 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, (x * y^-1 * x^2)^2, x^-11 ] T100.248 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-11 ] T100.249 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-2 * x * z^-1 * x * z^-3, x^-11 ] T100.250 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^-11, y^-8 * z * y^-1 * z * y^-1 * z * x^3 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 ] T100.251 : Triangle type {11,22,22} Group order 242 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-11, (x^-2 * y * x^-3)^2 ] T100.252 : Triangle type {11,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^8 * z^-5 * y * z^-1 * y * z^-1 * y^3 ] T100.253 : Triangle type {11,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^8 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T100.254 : Triangle type {11,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^12 * y^-6 * z^2 ] T100.255 : Triangle type {11,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, y^6 * x^-3 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T100.256 : Triangle type {11,220,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-11, z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T100.257 : Triangle type {12,12,21} Group order 252 Chiral action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * x * z^2, y^2 * x^-2 * y * x^-3 * y^2 * x^-1 * y ] T100.258 : Triangle type {12,12,21} Group order 252 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, x^-1 * y * x^3 * z^-2 * y, (x^-3 * y)^3 ] T100.259 : Triangle type {12,12,21} Group order 252 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, z * y * x^2 * z^-1 * x^-1, z^-2 * y * x * z^-2, y * x^-2 * y^2 * x^-2 * y * x^-4 ] T100.260 : Triangle type {12,12,21} Group order 252 Chiral action Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^-1 * y * x^3 * z^2 * y, x^-3 * y * x^-4 * y^2 * x^-2 ] T100.261 : Triangle type {12,12,21} Group order 252 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^-1 * y * x^-1 * y * x^-4 * y * x^-1 * y * x^-1, z^-7 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * z * y^-1 * z^-8 ] T100.262 : Triangle type {12,12,21} Group order 252 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, y * z^-1 * x * z^3 * y^-1 * z^-2 * x * z^5 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 ] T100.263 : Triangle type {12,12,21} Group order 252 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-1 * x * z^3, y^2 * x^-6 * y^4 ] T100.264 : Triangle type {12,12,120} Group order 240 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^-1 * x * z^3 * y^-1 * z^-2 * x * z^5 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 ] T100.265 : Triangle type {12,20,24} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^2 * z^-2, x^-1 * y^-1 * z * x^-1 * z * y^2 * x^-1 * y^-2 * z * y^2 ] T100.266 : Triangle type {14,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^3 * z^-2 * x, y^5 * z^-1 * y * z^-1, z * y * z^-2 * x^-1 * z^4 ] T100.267 : Triangle type {14,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-4 * x^2 * y^-4, z * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T100.268 : Triangle type {14,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3, (y * z^-3)^2, z^3 * y * x^-1 * z^4 ] T100.269 : Triangle type {14,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-4 * x^-1 * z * y * z^-2 ] T100.270 : Triangle type {14,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-3 * z^5 ] T100.271 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x^3 * z^-4, y^-2 * z * y^-1 * z * y^-7 ] T100.272 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-1 * y^4 * x^-1 * y^2 * x^-12 ] T100.273 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^2 * y^-3, y * z^-3 * y * z^-1 * x^4 * z^-1 * x * z^-1 * x * z^-1 * y^2 * z^-1 ] T100.274 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3, y^3 * z^-1 * y * x^-5 * y^2 * z^-1 * y * z^-1 * y^2 ] T100.275 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * x^4 * y^-3, z^4 * y^-1 * z * y^-1 * z^5 ] T100.276 : Triangle type {18,54,108} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^3 * z^-2 * x^8 * y^-2 * x^2 * y^-2 * z^-2 * x ] T100.277 : Triangle type {18,72,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * z * y, y^2 * z^-1 * y^3 * x^-1 * y^3 * z^-3 ] T100.278 : Triangle type {18,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, y^3 * x^-5 * y^3 * z^-2 * y^4 ] T100.279 : Triangle type {18,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, y^3 * x^-1 * y^2 * x^-6 * y^3 * x^-1 ] T100.280 : Triangle type {18,72,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^-3 * y^-1 * x^2, z^-1 * y^4 * z^-3, y * x^-5 * y * x^-2 * y^2 ] T100.281 : Triangle type {20,22,220} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * y^-1 * z^5, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 ] T100.282 : Triangle type {21,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-10, z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x * z^-2 ] T100.283 : Triangle type {21,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y^2 * z^-4, x^2 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^3 ] T100.284 : Triangle type {21,210,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^7 * y^-5 * x * z^-5 * x^8 ] T100.285 : Triangle type {22,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x^-1 * z^6 * y * z^-3, y^2 * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y^2 ] T100.286 : Triangle type {22,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-3 * x^2 * y^-3, z^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * z^-2 ] T100.287 : Triangle type {22,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-3)^2, z^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * z^-2 ] T100.288 : Triangle type {22,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1, z^-1 * x * z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * z^-2 ] T100.289 : Triangle type {22,22,110} Group order 220 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z^3 * x^-1 * z * x^-1 * z * y^-1 * z^2, z^-2 * x^-1 * z^3 * y^-1 * x * z * y * z^-2 ] T100.290 : Triangle type {24,27,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-4 * z^2, x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 ] T100.291 : Triangle type {24,27,216} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^-3 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-6 ] T100.292 : Triangle type {24,36,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-5 * y * x^-1 * y^2, z^2 * y^-3 * z^4 ] T100.293 : Triangle type {24,36,72} Group order 216 Chiral action Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-2 * x^2 * z^-1 * x, y^6 * x^-1 * y * x^-1 * y^2 * z^-1 * y * z^-1 ] T100.294 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3, x^-1 * y^2 * x^-8 * y * x^-1 ] T100.295 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-3 * y * z^-4 * x^2 * z^-1 * x * z^-3 * x^2 ] T100.296 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x * y^-6 * x^5 * y^-2, z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-6 * z ] T100.297 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * x^5 * z^-1 * x * z^-1 * x, y^-2 * x^4 * y^-4 ] T100.298 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^8 * z^-1 * x^2 * y^-1 * x^6 * y^-1 * x * y^-2 * z^-1 * x^3 * y^-1 ] T100.299 : Triangle type {24,36,72} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^8 * y^-5 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T100.300 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-12 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T100.301 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^13 * x^-7 * z * x^-1 * z^2 ] T100.302 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-4 * z^2, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-4 ] T100.303 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^2 * y^-3, z^12 * y^-1 * x^-5 * z^3 ] T100.304 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-3 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T100.305 : Triangle type {26,208,208} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z, x * y^-1 * x * y^-6 * x^5 * y^-1 * x^2 ] T100.306 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1, x^2 * y^-1 * x^2 * y^-1 * x * z^-1 ] T100.307 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-3 * y^-1 * x^2, y^-1 * z * y^-1 * z * y^-2 * z * y^-1 * x * z * y^-1 ] T100.308 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-3 * y^-1 * x^2, x^-1 * y * x^-2 * z * y * z^-1, y^-1 * z * x^-2 * z^3 ] T100.309 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z * y^-1, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T100.310 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^-4 * z^2 * y ] T100.311 : Triangle type {27,36,54} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y * x * z^2, x * z * y^-1 * x^2 * y^-1 * x^4 * y^-2 ] T100.312 : Triangle type {30,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * y^-1 * z^5 * y^-1 * z^5, x^-2 * y * x^-5 * y^6 * x^-2 ] T100.313 : Triangle type {30,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-5 * z^2 * x^-10 * z^2 * x^-5 * z^3 * x^-6 ] T100.314 : Triangle type {30,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T100.315 : Triangle type {35,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x * y^-11 * x * y^-1 * x * y^-1 * x * y^-1 * x^11 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T100.316 : Triangle type {35,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * y^-1, z^13 * x^-2 * z^5 ] T100.317 : Triangle type {35,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-6, y^4 * x^-4 * y^6 * x^-1 * y^2 ] T100.318 : Triangle type {35,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, x^3 * y^-5 * x^5 * y^-1 * x^2 ] T100.319 : Triangle type {35,42,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^7 * x^-4 * y^6 * x^-1 * y^5 ] T100.320 : Triangle type {36,36,36} Group order 216 Chiral action Defining relators: [ x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, x^-4 * y * x^-1 * z, y^3 * x^-1 * y * z^-1 * y ] T100.321 : Triangle type {36,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-4 * y * x * z^-1, z^-3 * x * z^-1 * x * z^-4 ] T100.322 : Triangle type {36,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x * z^-1 * x^7 * z^-1 ] T100.323 : Triangle type {36,36,36} Group order 216 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-1 * y * x^-6 * y^3 * z^-1 * y, x^-2 * z^2 * x^-4 * z^4 ] T100.324 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-8 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T100.325 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^5, y^-6 * z^2 * y^-3 * x^5 * y^-1 * x * y^-3 ] T100.326 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-5 * y^3 * z^-2 * y^3, z^10 * x^-1 * z^5 ] T100.327 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-4, z^-5 * y^5 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T100.328 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^17 * x^-1 * y^-2 * z^4 * x^-1 * z * x^-1 * z ] T100.329 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-6, y^8 * z^-5 * y * z^-1 * y * z^-1 * y^3 ] T100.330 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-5 * z, y^6 * x^-4 * y * z^-5 * y * z^-1 * y * z^-1 * y^4 ] T100.331 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^15 * y^-4 * z^6 ] T100.332 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z, z^18 * x^-4 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-12 * z * x^-1 * z * x^-1 * z ] T100.333 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^5 * y^-6, z^-1 * x^6 * z^-5 * x * z^-4 ] T100.334 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y^3 * z^-4, x^-4 * y * x^-1 * y * x^-7 * y^3 * x^-5 ] T100.335 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-5 * z, x^-3 * z * x^-1 * z^5 * x^-5 * y * x^-1 ] T100.336 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^5 * z^-4, x^-5 * z * x^-1 * z * x^-1 * z^5 * x^-4 * y^2 * x^-5 ] T100.337 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x^-7 * z^5 * x^-9 ] T100.338 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^5 * y^-1 * z^5, y^3 * x^-4 * y^6 * x^-1 * y ] T100.339 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-17 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * z * x^-6 ] T100.340 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T100.341 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^4 * z^-1 * x^2, z^5 * x^-1 * z^5 * x^-1 * z^5 ] T100.342 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-1 * z^5, x^-2 * y * x^-6 * y^4 * x^-2 ] T100.343 : Triangle type {41,205,205} Group order 205 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^5 * x^-6, y^4 * x^-4 * y * z^-5 * y^5 ] T100.344 : Triangle type {42,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-2 * x * z^3 * y^-1 * z^-4, y * z^-1 * y^4 * x^-3 * y * z^-3 * y ] T100.345 : Triangle type {42,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * z^3, y^-4 * x^2 * y^-4 ] T100.346 : Triangle type {42,42,105} Group order 210 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * x^-1 * z^3 * y^-1 * z * x^-1 * z * y^-1 * z^4 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T100.347 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-9 * z^2 * y^-6 * z^2 * y^-1 * x * y^-4 ] T100.348 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^4 * y^-2, z^5 * x^-1 * z^5 * x^-5 * z^2 ] T100.349 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-6, y^-4 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-6 ] T100.350 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^13 * x^-2 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y^11 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T100.351 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^8, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-2 * z^4 ] T100.352 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^3 ] T100.353 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^3 * y^-7, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 ] T100.354 : Triangle type {51,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-37 * z * x^-8 * y * x^-5 ] T100.355 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-2 * z * y^-3 * x * y^-1 * x * y^-1 * x * z * y^-2 * x * y^-1 ] T100.356 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T100.357 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6 * y^-2, z^-2 * x * z^-1 * x * z^-3 ] T100.358 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * x^-1 * z, z^-3 * y^3 * z^-3 * y ] T100.359 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^-4 * x^-1 * z^3 * y^-1, x^6 * z^-4 ] T100.360 : Triangle type {52,52,104} Group order 208 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-4 * x^-1 * z^3 * y^-1, z^-2 * x * z^-8 * x * z^-2 ] T100.361 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-11 * z * y^-12 * x^3 * y^-9 ] T100.362 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y * x^-5 * y^5 * x^-2, z^9 * y^-1 * z^5 ] T100.363 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T100.364 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-6, x * y^-1 * x^5 * z^-5 * x * z^-1 * x * z^-1 * x ] T100.365 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9 * y^3 * x^-1, y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 ] T100.366 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z, x^6 * y^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^2 ] T100.367 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^4 * y^-6, x^-6 * z^3 * x^-9 ] T100.368 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^3 * x^-7, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^5 * y^-3 ] T100.369 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^-7 * z * y^-3 * x^5 * y^-1 * x * y^-1 * x * y^-2 ] T100.370 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x * y^-4, z^4 * x^-1 * z * x^-1 * z^5 * x^-6 * z^2 ] T100.371 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^4 ] T100.372 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-3 * z^3, y^-5 * z * y^-3 * x^5 * y^-3 ] T100.373 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^33 * x^-1 * z^4 * x^-1 * z * x^-1 * z ] T100.374 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-48 * y * x^-1 * y * x^-1 * y * x^-16 ] T100.375 : Triangle type {68,102,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, z^-1 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T100.376 : Triangle type {69,69,69} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-11 * z^2 * y^-12 * x^5 * y^-8 ] T100.377 : Triangle type {69,69,69} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T100.378 : Triangle type {69,69,69} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^5 * x^-2 * z^4, y^5 * x^-4 * y^3 * z^-1 * y^6 ] T100.379 : Triangle type {69,69,69} Group order 207 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5, y^-1 * x * y^-6 * x^5 * y^-2 ] T100.380 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-25 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-8 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T100.381 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-14 * y * x^-1 * y * x^-1 * y * x^-10 * y * x^-5 ] T100.382 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-7 * z^3 * x^-7 ] T100.383 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^4 * z^-4, x * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T100.384 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-4 * z^2, x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^2 ] T100.385 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-4 * z^2, x^3 * y^-6 * x^8 ] T100.386 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-4 * z^2, x * y^-1 * x^5 * z^-5 * x * z^-1 * x * z^-1 * x ] T100.387 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-5 * x^4 * z^-1 * x^2, z^3 * y^-1 * z * y^-1 * z^5 * y^-6 * z ] T100.388 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-9 * y^2, z^-2 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-2 ] T100.389 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^4 * z^-1 * x, z^3 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z^2 ] T100.390 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-5 * y^3 * z^-2 * y^3, z^4 * x^-1 * z^5 * x^-1 * z^5 ] T100.391 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-4 * z^2, y^-4 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-2 ] T100.392 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-2 * x * z^-1 * x^6 * z^-13 ] T100.393 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-2 * z^4, y^-10 * x^5 * y^-1 * x * y^-3 ] T100.394 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-10, z^-2 * x^6 * z^-5 * x * z^-5 ] T100.395 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, z^-3 * y^2 * z^-4 * y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T100.396 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^8 * y^-1 * z^5, x^2 * y^-6 * x^5 * y^-2 ] T100.397 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-8, z^2 * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T100.398 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-2 * y^11 * z^-4 * y * z^-5 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T100.399 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^4 * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T100.400 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^4 * y^-2, z^2 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T100.401 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-2 * z^4, x * y^-1 * x * y^-6 * x^5 * y^-1 * x^2 ] T100.402 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-1 * y, x * z^-1 * x^7 * z^-5 * x * z^-1 * x * z^-1 * x^3 ] T100.403 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-25 * y^3 * z^-5 * y * z^-8 ] T100.404 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-4 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T100.405 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-1 * z^5, y^4 * x^-4 * y^6 * x^-1 * y^2 ] T100.406 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * x * y^-11, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-3 * z^3 ] T100.407 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^4 * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T100.408 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-6 * x^6, z^10 * y^-1 * z^5 ] T100.409 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^3 * y^-5 * x^2 * z^-3 * x^4, y^5 * x^-1 * y * z^-5 * y * z^-1 * y^3 ] T100.410 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^3 * z^-5 * x * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T100.411 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^19 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^5 * x^-1 * z * x^-1 * z ] T100.412 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^38 * x^-1 * y^12 ] T100.413 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T100.414 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-2 * z^4, x^3 * y^-4 * x^4 * z^-2 * x^4 ] T100.415 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-6, y^4 * x^-4 * y^2 * z^-3 * y^5 ] T100.416 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^8 * x^-2 * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T100.417 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z * y^-1 * z^5 * y^-1 * x^4 * y^-3, x^2 * y^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x ] T100.418 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^5 * y^-1 * z^10 * y^-1 * z^5 * y^-1 * z^6 * x^-1 * z ] T100.419 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^9 * x^-5 * y^6 * x^-1 * y * x^-1 * y^4 ] T100.420 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * z^-2 * x^3, z^2 * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T100.421 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-7 * x^4 * y * z^-5 * y * z^-1 * y * z^-6 ] T100.422 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * z^5)^2, x^4 * y^-4 * x^6 * y^-1 * x * y^-1 * x^2 ] T100.423 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T100.424 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z^2 * x^-8, y^7 * z^-5 * y * z^-1 * y * z^-1 * y^2 ] T100.425 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * z^5 * y^-6, z^3 * x^-1 * z * x^-1 * z^5 * x^-6 * z ] T100.426 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^7 * z^-3, x^5 * y^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T100.427 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^8 * x^-4 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-7 * z * x^-1 * z * x^-1 * z ] T100.428 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ x * y * z, y * x^-1 * y, z^61 * x^-2 * z^5 ] T100.429 : Triangle type {101,202,202} Group order 202 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^101, y * z^-1 ] T100.430 : Triangle type {102,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-28 * z * y^-12 * x^3 * y^-9 ] T100.431 : Triangle type {102,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^4 * y^-6, x^4 * y^-5 * x^2 * z^-3 * x^5 ] T100.432 : Triangle type {102,102,102} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, y^8 * z^-2, x^9 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x^2 ] T100.433 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x^-2 * y^-1, y^76 * x^-1 * y^24, x * z^-1 ] T100.434 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y^15 * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T100.435 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-2 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * z * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T100.436 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-3 * x^-1 * z^4, x^7 * y^-5 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x^3 ] T100.437 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-3 * z^3, x^5 * y^-4 * x^4 * z^-2 * x^6 ] T100.438 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-3 * z^3, x^4 * y^-5 * x^4 * z^-1 * x^4 ] T100.439 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-1 * z^5 * y^-3 * z^3, x^-4 * z^2 * x^-7 * y * x^-1 ] T100.440 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^2 * x^-8, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-3 * z^3 ] T100.441 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-10 * y, z^2 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z^2 ] T100.442 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, y^2 * x^-4 * y^3 * z^-1 * y^3, x^-3 * z * x^-1 * z * x^-1 * z^5 * x^-8 ] T100.443 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, z^-5 * y^6 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T100.444 : Triangle type {201,201,201} Group order 201 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-2 * z^4, y^5 * x^-1 * y * z^-5 * y * z^-1 * y^3 ] Genus 101 T101.1 : Triangle type {2,4,8} Group order 1600 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z^2 * y * z^-1 * y * x * z * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T101.2 : Triangle type {2,4,8} Group order 1600 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z^2 * y * z^-1 * y * x * z * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T101.3 : Triangle type {2,4,8} Group order 1600 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, (z^-1 * y)^5, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x, z^2 * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^2 * y^-1 ] T101.4 : Triangle type {2,4,8} Group order 1600 Chiral action Defining relators: [ x^2, x * y * z, y^4, z^8, y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-2 * x * z^2, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z ] T101.5 : Triangle type {2,4,8} Group order 1600 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, x * z * y * z^-2 * x * z^2 * y^2 * z^-2 * y * z^-3 ] T101.6 : Triangle type {2,4,8} Group order 1600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y * x * y^-1 * z^2 * y * x * z * y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * x * z * y * x * y^-1 * z^-1 * x ] T101.7 : Triangle type {2,4,8} Group order 1600 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y^-1 * z^2 * y * x * y^-1 * z^2 * y * x * z * y^-1 * z * y * z^-1 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T101.8 : Triangle type {2,4,12} Group order 1200 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^4, z^12, x * z * y * z^-1 * y * x * z * y^-2 * z^-1 * y * z^-2 * y, y^-1 * z * y * x * z^3 * y^-1 * z^2 * y^-1 * z^-1 * x * z, x * z * y^-1 * z^2 * y * x * y * x * z * y^-1 * z * y^-1 * z^-2 ] T101.9 : Triangle type {2,4,12} Group order 1200 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, y * x * y^-1 * z^2 * y^-1 * z * y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T101.10 : Triangle type {2,4,12} Group order 1200 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3 * y * z^-1)^2, z^12, z^2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z^-2 * x, x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^3 * y^-1 * z^-2 ] T101.11 : Triangle type {2,4,12} Group order 1200 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^12, y * x * y^-1 * z * y * x * z * y^-1 * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^2 ] T101.12 : Triangle type {2,4,20} Group order 1000 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-2 * x * z * y^-1 * z^-2 * x ] T101.13 : Triangle type {2,4,20} Group order 1000 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z^3 * y * z^-1 * x * z * y^-1 * z^-3, (y * z^-2)^4 ] T101.14 : Triangle type {2,4,20} Group order 1000 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T101.15 : Triangle type {2,4,20} Group order 1000 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T101.16 : Triangle type {2,4,24} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, y * z^-1 * y * z^-1 * x * y^-1 * z^-5 ] T101.17 : Triangle type {2,4,24} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x, y^-1 * z * y^-1 * z * y * z^-1 * y * z^-1 * x * z * y^-1 * z^2 ] T101.18 : Triangle type {2,4,24} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * z, z^-1 * x * z^8 * y * x * y * x * z^7 * y^-1 * z^-5 ] T101.19 : Triangle type {2,4,24} Group order 960 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T101.20 : Triangle type {2,4,24} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1 ] T101.21 : Triangle type {2,4,24} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^6, (y * z^-3 * y * z^-1)^2, y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * x * z^3 ] T101.22 : Triangle type {2,4,24} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y * z^-1 * y * x * z * y^2 * z^-1 * x * z^3 ] T101.23 : Triangle type {2,4,24} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T101.24 : Triangle type {2,4,44} Group order 880 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-20 * x * z^3 * y * z^-7 * x * y^-1 * z^-1 * x * y^-1 * z^-7 * x * y^-1 * z^-2 ] T101.25 : Triangle type {2,4,54} Group order 864 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-35 * x * z^9 * y * x * z^2 * y^-1 * z^-6 ] T101.26 : Triangle type {2,4,84} Group order 840 Chiral action Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-17 * x * z^9 * y * x * z^2 * y * x * z^7 * y^-1 * z^-4 ] T101.27 : Triangle type {2,4,104} Group order 832 Reflexible action Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-86 * x * z^7 * y * z^-2 * x * z^2 * y^-1 * z^-5 ] T101.28 : Triangle type {2,4,104} Group order 832 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-36 * x * z^7 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-4 ] T101.29 : Triangle type {2,4,204} Group order 816 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-204 ] T101.30 : Triangle type {2,4,404} Group order 808 Reflexible action Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-53 * x * y^-1 * z^-148 ] T101.31 : Triangle type {2,5,20} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, x * z * y^2 * x * y^-2 * z^-1 * x * y^-2 * z^-1 * y ] T101.32 : Triangle type {2,6,6} Group order 1200 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z * y^-1 * z * y * x * z * y * x * y^-1 * z * y^-2 * z * y^-2 * z * y^-2 * z^-1 * y * z^-1 * x * z * y^-1 * z * y * x * z ] T101.33 : Triangle type {2,6,8} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^3 * z^-2 * x * y^-1 * z^-1 ] T101.34 : Triangle type {2,6,8} Group order 960 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T101.35 : Triangle type {2,6,15} Group order 750 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y^-2 * z)^5 ] T101.36 : Triangle type {2,6,15} Group order 750 Reflexible action Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y, y^-1 * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 * z * y^-2 * z ] T101.37 : Triangle type {2,6,28} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-8 * x * z^5 * y * x * z^3 * y * z^-2 * x * y^-1 * z^-2 * x * z * y^-1 * z^-3 ] T101.38 : Triangle type {2,6,28} Group order 672 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z, x * z * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T101.39 : Triangle type {2,6,78} Group order 624 Reflexible action Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-2 * x * z^3 * y * z^-1 * x * z^2 * y * z^-6 * x * z^2 * y^-1 * z^-4 ] T101.40 : Triangle type {2,6,303} Group order 606 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^83 * y * x * y^-1 * z^-9 * x * z^7 ] T101.41 : Triangle type {2,8,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^2 * y^3 * x * z * y * x * y^-1 * z^-1 * x * z, y^-2 * z * y^-4 * z^-1 * y * x * y^-1 * z * y^-1 ] T101.42 : Triangle type {2,8,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1)^4, z^8, y^-1 * z * y * z^-1 * x * y^-1 * z^2 * y^-1 * z^3 * y^-1 ] T101.43 : Triangle type {2,8,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * z^-1 * y * x * y^-1 * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T101.44 : Triangle type {2,8,8} Group order 800 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y * z^-1 * y * x * y^-1 * z^2 * y * x * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x * z ] T101.45 : Triangle type {2,8,8} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y ] T101.46 : Triangle type {2,8,8} Group order 800 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y^-1 * z^2 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T101.47 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, x * z^3 * y^-1 * z^-4, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T101.48 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, x * z^3 * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, z * y^2 * x * y^-2 * z^-1 * x * y^-1 * z^-1 * x ] T101.49 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-2 * x * z * y * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-2 ] T101.50 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T101.51 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * x * z * y * z^-1 * y^2 * z^-1 * x * z * y^-1 * z^-1 ] T101.52 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z * y * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-2 ] T101.53 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-2 * y * x * y^-1 * z^-2 ] T101.54 : Triangle type {2,8,16} Group order 640 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T101.55 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-13 * x * z^2 * y * x * z^6 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-3 * x * z^3 * y^-1 * z^-1 ] T101.56 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-17 * x * z^4 * y * x * z^2 * y * z^-3 * x * z * y * z^-6 ] T101.57 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z^3 * y * z^-4 * x * y^-1 * x * z^4 * y^-1 * z^-1 ] T101.58 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-1 * x * z^10 * y * z^-1 * x * y^-1 * z^-4 ] T101.59 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z^3 * y * z^-4 * x * y^-2 * z^3 * y^-1 * z^-3 ] T101.60 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, z^-3 * x * z^3 * y^-2 * z * y * z^-4 * x * z^2 * y^-1 * z^-3 ] T101.61 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-8 * x * z^4 * y * x * z^18 * y^-1 * z^-2 * x * y^-1 * z^-1 ] T101.62 : Triangle type {2,8,36} Group order 576 Reflexible action Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-11 * x * z * y * z^-4 * x * z^5 * y * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-2 ] T101.63 : Triangle type {2,8,56} Group order 560 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, x * z^6 * y * x * y^-1 * z^-6 ] T101.64 : Triangle type {2,8,56} Group order 560 Chiral action Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^3 * y * z^-2 * x * z * y^-1 * z^-6 * x ] T101.65 : Triangle type {2,8,136} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^45 * y * x * z * y * z^-10 * x * z^10 ] T101.66 : Triangle type {2,8,136} Group order 544 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-31 * x * z^20 * y * x * z^2 * y^-1 * z^-3 * x * z^2 * y^-1 * z^-7 ] T101.67 : Triangle type {2,10,15} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^10, y^2 * z^-1 * y^4 * z^-1 * x * z * y^-1 * z^-1 ] T101.68 : Triangle type {2,10,15} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^10, (y * z^-1 * y^3)^2, y^-1 * z * y^-1 * z * y^3 * x * y^-1 * z * y^-1 * z ] T101.69 : Triangle type {2,12,12} Group order 600 Chiral action Defining relators: [ x^2, x * y * z, y * x * y^-1 * z * y^2 * z^-1 * x * z^2, z^-2 * x * y^-3 * z * y^-1 * z^-2 * y, x * z^2 * y^-3 * z^-1 * y^2 * z^-2, y^12 ] T101.70 : Triangle type {2,12,12} Group order 600 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T101.71 : Triangle type {2,12,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, y^12, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T101.72 : Triangle type {2,12,12} Group order 600 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, z * y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T101.73 : Triangle type {2,16,48} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-1 * y^3, y^-16 ] T101.74 : Triangle type {2,16,48} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z * y * x * z * y^2 * z^-1 * x * z * y^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, y^-1 * z^2 * y^-3 * z^-1 * x * z^2 * y^-1 ] T101.75 : Triangle type {2,20,20} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^2 * z^-2 * y^2 * z^-2 * y * z^-1 * y ] T101.76 : Triangle type {2,20,20} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, x * z^2 * y^-2 * z^-2 * y * z^-1, y^6 * z^-1 * y * z^-2 ] T101.77 : Triangle type {2,20,20} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, y * z^-1 * y^4 * z^-1 * y^2 * z^-1 ] T101.78 : Triangle type {2,20,20} Group order 500 Chiral action Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-2 * y^3 * z^-3 * y, y * z^-1 * x * z * y^2 * x * z * y^-1 * z ] T101.79 : Triangle type {2,20,20} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, (z^-1 * y)^5 ] T101.80 : Triangle type {2,20,20} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4, (z^-1 * y)^5 ] T101.81 : Triangle type {2,20,20} Group order 500 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, (z^-1 * y)^5 ] T101.82 : Triangle type {2,20,30} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z^2 * y^-2 * z^-3 * y, z^-2 * y^4 * z^-4 ] T101.83 : Triangle type {2,24,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^-5 * z^-1 * x * y^-1 * z ] T101.84 : Triangle type {2,24,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, y^-1 * z * y^-3 * z^-1 * x * z^2, x * y^-1 * z^2 * y^2 * x * y^-1 * z^-2 ] T101.85 : Triangle type {2,24,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, z^-1 * y * z^-1 * y^2 * z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-3 ] T101.86 : Triangle type {2,24,24} Group order 480 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-2 * y ] T101.87 : Triangle type {2,24,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z * y^3 * x * y^-1 * z^-1 * y, (z^-1 * y)^5, y^-1 * z * y^-4 * z^-3 * y * x ] T101.88 : Triangle type {2,24,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, z^-1 * x * z * y^2 * x * y^-1 * z^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-2 ] T101.89 : Triangle type {2,24,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * z * y^-3 * z * y^-1 * z^-2, z^-1 * y * x * y^-2 * z^-1 * y * z^-2 ] T101.90 : Triangle type {2,24,24} Group order 480 Reflexible action Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T101.91 : Triangle type {2,28,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * y * z^-2 * y^6 * z^-1 * y^2 * z^-1 * y * z^-4 * y^5 * z^-1 ] T101.92 : Triangle type {2,28,56} Group order 448 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-1 * y * z^-7 * y^3 * z^-1 * y^7 * z^-1 * y * z^-1 * y * z^-3 ] T101.93 : Triangle type {2,44,44} Group order 440 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z^-1 * y * z^-23 * y * z^-1 * y^8 * z^-1 * y * z^-2 * y * z^-1 * y * z^-1 * y ] T101.94 : Triangle type {2,54,54} Group order 432 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-37 * y^14 * z^-1 ] T101.95 : Triangle type {2,84,84} Group order 420 Chiral action Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y^20 * z^-4 * y * z^-1 * y^9 * z^-1 * y * z^-1 * y * z^-1 * y ] T101.96 : Triangle type {2,104,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^36 * z^-1 * y^9 * z^-2 * y ] T101.97 : Triangle type {2,104,104} Group order 416 Reflexible action Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-68 * y^36 ] T101.98 : Triangle type {2,203,406} Group order 406 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^134 * y^-68 ] T101.99 : Triangle type {2,204,204} Group order 408 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^69 * z^-134 * y ] T101.100 : Triangle type {2,404,404} Group order 404 Reflexible action Defining relators: [ x^2, x * y * z, x * z * y, y^68 * z^-133 * y ] T101.101 : Triangle type {3,3,4} Group order 2400 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 * x ] T101.102 : Triangle type {3,3,4} Group order 2400 Chiral action Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, (x * z * y)^4, y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * z^-1 * x * y^-1 * x * z^-1 * x^-1 * y^-1 * x * z * y * x^-1 ] T101.103 : Triangle type {3,3,28} Group order 672 Chiral action Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z * y * x * z^2 * y * z^-2 * x * z^5 ] T101.104 : Triangle type {3,4,4} Group order 1200 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, y^-1 * z^-1 * y * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 * z * y^-1 ] T101.105 : Triangle type {3,4,4} Group order 1200 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * x^-1 * y * z^-1 * y * x^-1 * z * y * x^-1 * z * y ] T101.106 : Triangle type {3,4,4} Group order 1200 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * x^-1 * y^-2 * z^-1 * x * y^-1 * x * z * y^-1 * z^2 * y ] T101.107 : Triangle type {3,4,4} Group order 1200 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * x * y^-1 * z ] T101.108 : Triangle type {3,4,4} Group order 1200 Chiral action Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z * y * x^-1 * z * y * x^-1 * z * y * z^-1 * x^-1 * y^-1 ] T101.109 : Triangle type {3,6,6} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y^-2 * z^2 * y^-2 * z^2 * y^-1 * z * y^-1 * z^2 * y^-2 * z^2 * y^-2 * z * y^-1 * z * y^-1 * z ] T101.110 : Triangle type {3,6,6} Group order 600 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y * x * z^-1 * x * z^-1 * x * z * y * x^-1 * y * x^-1 ] T101.111 : Triangle type {3,8,8} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^3 * x^-1 * z^3, y^8 ] T101.112 : Triangle type {3,8,8} Group order 480 Reflexible action Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * x * y^-2 * z ] T101.113 : Triangle type {3,15,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, x^-1 * y^2 * x^-1 * z * y^2, z^-3 * y * x^-1 * z^2 * y^-2, y^-1 * z^2 * y * x^-1 * z * y^-1 * z^2, x * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y ] T101.114 : Triangle type {3,15,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T101.115 : Triangle type {3,15,15} Group order 375 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, y^2 * z^-1 * y * x^-1 * z * y * x^-1 * z, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z ] T101.116 : Triangle type {3,28,28} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y * z^-8 * y * z^-2 * y * z^-1 * y * z^-2 * y^4 * z^-3 * y^3 * z^-1 ] T101.117 : Triangle type {3,28,28} Group order 336 Reflexible action Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^9 * z^-7 * y^8 * z^-1 * y^3 ] T101.118 : Triangle type {3,78,78} Group order 312 Reflexible action Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-1 * y^2 * z^-1 * y * z^-1 * y * z^-5 * y * z^-2 * y^3 * z^-1 * y^2 * z^-1 * y^2 * z^-1 ] T101.119 : Triangle type {3,303,303} Group order 303 Reflexible action Defining relators: [ x^3, x * y * z, x * z * y, y^9 * z^-1 * y^91 ] T101.120 : Triangle type {4,4,4} Group order 800 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-1 * z * x^-1 * y * x^-2 * z * x^-1 * y^-1 * z * x^-1, z^-1 * x^-1 * y * z^-1 * x^-2 * z * y^-1 * z^2 * y ] T101.121 : Triangle type {4,4,4} Group order 800 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1)^4, y * x * y^-1 * x * y^-1 * x * z * y * x * z^-1, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T101.122 : Triangle type {4,4,4} Group order 800 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, (x * y^-1)^4, x^-1 * y * z^-1 * x^-1 * y^-1 * x * z^-1 * x * z^2, y * z^-1 * y * z^-1 * y * x * z * y * x^-1 * z ] T101.123 : Triangle type {4,4,4} Group order 800 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * z * y * z^-1 * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y * x^-1 * z ] T101.124 : Triangle type {4,4,4} Group order 800 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * z * y * z^-1 * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y * x * z ] T101.125 : Triangle type {4,4,4} Group order 800 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y * x^-1 * y^-2 * z^-1 * x * y^-1 * z^-1 * x^-1 * z * y^-1 ] T101.126 : Triangle type {4,4,4} Group order 800 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y * x^-1 * y^-2 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 ] T101.127 : Triangle type {4,4,4} Group order 800 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x^-1 * z * x^-1 * y * x^-2 * z * y * x^-1 * z * y, x^-1 * y^-2 * z^-1 * y * x^-1 * y * z^-1 * x^-1 * y * z^-1 ] T101.128 : Triangle type {4,4,6} Group order 600 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z * x^-1 ] T101.129 : Triangle type {4,4,6} Group order 600 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4, x * y^-1 * z^-1 * x^-2 * z * y^-1 * z^-1 * y ] T101.130 : Triangle type {4,4,6} Group order 600 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, y^-1 * z^-1 * y * x^2 * y^-1 * z * y^-1, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T101.131 : Triangle type {4,4,6} Group order 600 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^6, z^-2 * x * y^-1 * x * z^2 * y^-1, z^-1 * x * z * y * x^-1 * y * x * z * y^-1 ] T101.132 : Triangle type {4,4,6} Group order 600 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^-2 * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T101.133 : Triangle type {4,4,6} Group order 600 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z^-1 * y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z * y * x * z * y ] T101.134 : Triangle type {4,4,10} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x * z * y * x^-2 * y^-1 * z * y * x * z ] T101.135 : Triangle type {4,4,10} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * y * x^-1 * y^-1 * z^-1 * x^-1, x * z^-1 * x^-1 * y^-1 * x * z^-1 * x^-1 * y ] T101.136 : Triangle type {4,4,10} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x, (x * z^-1)^4 ] T101.137 : Triangle type {4,4,10} Group order 500 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z * x^-1 ] T101.138 : Triangle type {4,4,10} Group order 500 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (y^-1 * x)^5 ] T101.139 : Triangle type {4,4,10} Group order 500 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z * y * x^-1 * y^-1)^2, (y^-1 * x)^5 ] T101.140 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * x^-1 * y * x^2 * z^2 * x^-1, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T101.141 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * x^-1 * y * x^2 * z^2 * x^-1, z^-1 * x^-1 * z * y * x * z^2 * y ] T101.142 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, x^-1 * z * y * z^-1 * y * x * z * y * z^-1 * y, z^-3 * x^-1 * z * y * x^-1 * y * z^-1 * x * z * y * z^-3 ] T101.143 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * y * x^-1 * y * x^2 * y^-1 * z * x^-1 * y^-1, z * y * x * z^2 * y * z^-1 * x^-1 * z * y * x^-1 * z^4 ] T101.144 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-1 * y^-1 * x * z^-1 * y * z^-1, x * z * x^-1 * y^-1 * x * z^-3 ] T101.145 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z * y * x^-1 * z^2 * x^-1, y * z^-2 * x^-1 * y * x * z^-1 ] T101.146 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T101.147 : Triangle type {4,4,12} Group order 480 Chiral action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, x^-1 * z * y * z^-1 * y * x * y^-1 * z^-2 * y, z^-3 * x * z * y * x^-1 * y * z^-1 * x * y^-1 * z^-4 ] T101.148 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T101.149 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T101.150 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^3 * x^-1 * z^2 * y^-1, (x * z * x^-1 * y^-1)^2 ] T101.151 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z * y^-1 ] T101.152 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-3 * x^-1 * z^2 * y^-1, (x * z^-2 * y)^2, z^-1 * x^-1 * y * x^-2 * y^-1 * z^-1 * x * z^-1 ] T101.153 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z * x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z * x^-1 * z ] T101.154 : Triangle type {4,4,12} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x * z^-1 * x^-2 * y^-1 * x^-1 * y * x * z^-1 * x * z^-1 ] T101.155 : Triangle type {4,4,22} Group order 440 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^6 * y^-1 * z^-4 * x^-1 * z * y * z^-7 * x * z^2 ] T101.156 : Triangle type {4,4,27} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^-13 * x * z^5 * y * x * z^4 * y * x^-1 * y * x^-1 * y * z^-1 ] T101.157 : Triangle type {4,4,27} Group order 432 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^8 * y * z^-1 * x * z^5 * y * x^-1 * y * z^-1 * x^-1 * z^9 ] T101.158 : Triangle type {4,4,42} Group order 420 Chiral action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^9 * y * x * z * y * z^-9 * x^-1 ] T101.159 : Triangle type {4,4,52} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-4 * y * x^2 * z^3 * y * z^-1 ] T101.160 : Triangle type {4,4,52} Group order 416 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z * y^-1 * z * y^-1 * z^-3 * x^2 * z^5 ] T101.161 : Triangle type {4,4,52} Group order 416 Reflexible action Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^10 * y * z^-4 * x^-1 * y * x^-1 * y * z^-7 * x * z^2 ] T101.162 : Triangle type {4,4,52} Group order 416 Reflexible action Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^38 * y^-1 * z^-4 * x * y^-1 * z^-8 * x ] T101.163 : Triangle type {4,4,52} Group order 416 Reflexible action Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^44 * y^-1 * x * y^-1 * z^-6 * x ] T101.164 : Triangle type {4,4,102} Group order 408 Chiral action Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, (x * z^2 * y^-1)^2, z^-3 * y * x^2 * z^2 * y * z^-1 ] T101.165 : Triangle type {4,4,102} Group order 408 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^86 * y^-1 * x^-1 * z^15 ] T101.166 : Triangle type {4,4,202} Group order 404 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^85 * y^-1 * x * z^15 ] T101.167 : Triangle type {4,6,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, (y * z^-2 * y)^2 ] T101.168 : Triangle type {4,6,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y^-1 * z^-1 * y^2 * x^-1 * z * y^-2 * z ] T101.169 : Triangle type {4,6,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^6, z * x^-1 * y * x^2 * z * y * x^-1, z * y^-1 * x * y^-1 * x * z * y^-2, (x^-1 * z * y^2)^2 ] T101.170 : Triangle type {4,6,6} Group order 480 Reflexible action Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^6, (y * z^-2 * y)^2 ] T101.171 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, (y * z^-1)^4, y * z^-3 * x^-1 * z^4 ] T101.172 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y^2 * x * z * y^2, z^-1 * y * z^-1 * y * x^-1 * y^2 * z^-1 * y, y * z^-3 * x^-1 * z^4 ] T101.173 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z, x^-1 * z * y * x^2 * z * y^-1 * z, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T101.174 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z^-1 * y^2 * x^-1 * y^3, x^-1 * z * y * x^2 * z * y * x^-1, (x^-1 * z^2 * y)^2 ] T101.175 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-4 * x^-1 * y * z^-3, z^-1 * x * z^2 * y * z^-2 * x^-1 * z^2 * y * z^-1 ] T101.176 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y^2)^2, x^-1 * z * y * x^-1 * y * x^-1 * z * y * z^-3 ] T101.177 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z * y * z^-1 * x^-1 * z^4 * y^-1 * x * y^-1 * z^-1 * x^-1 * z^2 * y * x^-1 * z^3 ] T101.178 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^2 * y * z^-2 * x^-1 * z^2 * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z^5 ] T101.179 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, y^6, y * z^-1 * x^-2 * z^2 * x^-1, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, z^2 * y * z^-1 * x^-1 * z^4 ] T101.180 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, z^2 * y * x^-2 * z^3 * x^-1, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T101.181 : Triangle type {4,6,16} Group order 384 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-6 * x * y^-1 * x * y^-1 * z^-3 * x * z^3 ] T101.182 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, z * y^-2 * x * z * x^-1, (x * z * y)^2, y * z^-1 * y * x^-1 * z * y * z^-1 ] T101.183 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^2 * z * y^-1, y^2 * x^-1 * y^-1 * x * z^-2 * y ] T101.184 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x * z * y)^2, x * z^-1 * x^-2 * z^2 * y ] T101.185 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * z * y)^2, y * x^-1 * y * x^2 * z * x^-1 * z ] T101.186 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-1 * z * y^-1 * z^2 * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T101.187 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, z * x^-1 * y * x^2 * z * y * x ] T101.188 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T101.189 : Triangle type {4,8,8} Group order 400 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-1 * z * y^-1 * z^-2 * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z * y^-1 ] T101.190 : Triangle type {4,8,8} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x^-1 * z ] T101.191 : Triangle type {4,8,8} Group order 400 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z^-2 * y * z^-1 * y * z^-1 * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x^-1 * z ] T101.192 : Triangle type {4,10,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-2 * z^2 * x^-1, z^-4 * x^-1 * z^3 * y^-1, y^10 ] T101.193 : Triangle type {4,10,40} Group order 320 Reflexible action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1, y * z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 ] T101.194 : Triangle type {4,12,14} Group order 336 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-2 * z * y^4 * x * y^-5, z^-4 * x^-1 * z * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x * z * y * z^-3 ] T101.195 : Triangle type {4,15,60} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-2 * z^6 * y^-1 * z * y^-1 * x * y^-1 * z * y^-1 * z ] T101.196 : Triangle type {4,15,60} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, x * y^-4 * z * x^-1 * z^-1 * y^4, y^-1 * z^5 * y^-6 * z^3 ] T101.197 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z * y^-1, y^-2 * z^4 * y^-10 ] T101.198 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T101.199 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^-1 * z^2, y^-2 * z^4 * y^-10 ] T101.200 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y^2 * x^-1 * y * z^-1 * y * z^-1 ] T101.201 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, z * y * x^-1 * z * y^2 * z^-1 * x^-1 * z * y^-1 ] T101.202 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2, z * y * x^-1 * z * y^2 * z^-1 * x * z * y^-1 ] T101.203 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3, z * y * x^-1 * z * y^2 * z^-1 * x^-1 * z * y^-1 ] T101.204 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T101.205 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-1 ] T101.206 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * y * x^-1 * z * y * z^-1 ] T101.207 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * z^-1 * x^-1 * y * z^-2 * y ] T101.208 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, z * y^-6 * z^2 * y^-1 * z * x^-1 * y^-1 * z * y^-1 * z^2 ] T101.209 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z^-1 * x * z^-1 * x^-1 * y * z^-1 * x ] T101.210 : Triangle type {4,16,16} Group order 320 Chiral action Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1, z * y^-1 * z^-1 * x^2 * z * y^-1 * z ] T101.211 : Triangle type {4,20,30} Group order 300 Chiral action Defining relators: [ x * y * z, x^4, z * y^2 * x^-1 * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * x^-1 * y * x^-1 * y * z^-1 * y ] T101.212 : Triangle type {4,20,30} Group order 300 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * y^3 * z^-3, z^-3 * x * z * y^-1 * z^-3 * x^-1 * z^2 * y^-1 * z^-4 ] T101.213 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^16 * z^-3 * y^2 * z^-1 * y^6 * z^-2 * y * z^-3 * y^2 ] T101.214 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-2 * y^8 * z^-4 * y * z^-1 ] T101.215 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-5 * y^5 * z^-7 * y^2 ] T101.216 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-2 * y^4 * z^-1 * y^2 * z^-5 * y * z^-1 ] T101.217 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^2 * z^-2 * y^4 * z^-1 * y^2 * z^-4 * y * z^-1 * y ] T101.218 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, y^8 * x * y^4 * z^-5 * y ] T101.219 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-9 * y^2 * z^-2 * y^6 * z^-1 * y * z^-7 * y^6 * z^-1 ] T101.220 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 * z^-2 * y * z^-1 * y^5 * z^-1 * y^3 * z^-1 * y^2 * z^-5 * y^7 ] T101.221 : Triangle type {4,36,36} Group order 288 Reflexible action Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y * z^-3 * y^4 * z^-1 * y^5 * z^-1 * y^2 * z^-1 ] T101.222 : Triangle type {4,56,56} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^4 * y^-1 * z * y^-3 * z^3 * y^-1 * z ] T101.223 : Triangle type {4,56,56} Group order 280 Chiral action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^-1 * z * y^-2 * z^3 * y^-2 * z^3 * y^-2 ] T101.224 : Triangle type {4,69,92} Group order 276 Reflexible action Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-4 * y^2 * z^-2 * y^2 * z^-9 * y^2 * z^-1 ] T101.225 : Triangle type {4,136,136} Group order 272 Reflexible action Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-34 * z^2 * y^-1 * z * y^-6 * z^2 * y^-7 * z * y^-14 ] T101.226 : Triangle type {4,136,136} Group order 272 Reflexible action Defining relators: [ x * y * z, x * z * y, x^4, y^-40 * z * y^-1 * z * y^-2 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-3 ] T101.227 : Triangle type {5,5,10} Group order 400 Reflexible action Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * z * y^-1, y^-5, y^-1 * z^-1 * y * x * z * x^-1, z * x^-2 * y^-1 * x^2 * y^-2 * x * y^-1 ] T101.228 : Triangle type {5,15,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x^2 * z * y^-2 ] T101.229 : Triangle type {5,15,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, x * z^-1 * x^2 * z * y^-1, y^2 * z^-1 * y * x * z^-1 * y * z^-1 ] T101.230 : Triangle type {5,15,15} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, z^-1 * y^3 * z^-2, z * y * x^-1 * y^-1 * x * z * y * x^-1 ] T101.231 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^6, x * z^-1 * y * x^-1 * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * y^-2 * x, z^-3 * x^-1 * y^2 * z^-1 ] T101.232 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^-1 * y * x^-1 * z^2, x^6 ] T101.233 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y * x^-1 * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3, x * z * y * x^2 * z^-2 * x ] T101.234 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-1 * y, z^-3 * x^-2 * y * z^-3 ] T101.235 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y^-1 * z^-1 * y * x^-1 * z * y * x^-1 ] T101.236 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^6, x * z^-1 * x^-2 * y^-1 * z^-2, y * z^-1 * x^-2 * y^2 * x^-1, z * y^2 * x^-1 * z * x^-1 * y^-1 ] T101.237 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^6, (z^-1 * y)^3, z^-1 * y * x^-2 * z * x^-1 * y^-1, z * y * x^-2 * y^-1 * z * x^-1 ] T101.238 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * x^-2 * y^2 * x ] T101.239 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, y * x^-3 * z * x^-2, y^-1 * z^-2 * x^-1 * z^3 ] T101.240 : Triangle type {6,6,14} Group order 336 Chiral action Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^3 * x^-1 * z * y^-1 * z ] T101.241 : Triangle type {6,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^2 * y * x * z^6 * y^-1 * z^-1 * x * z * y * x^-1 * z ] T101.242 : Triangle type {6,6,14} Group order 336 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, x^-1 * z * x^-1 * y^-1 * x * z * x^-1 * z, x^-1 * z^2 * y^-1 * x * z^3 ] T101.243 : Triangle type {6,6,39} Group order 312 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y^-1 * x * y^-1 * x^2 * y^-1 * x * y^-1, z^-1 * x^-1 * y^-1 * z^-3 * x * z * y * x^-1 * y * x * z * y * z^-3 ] T101.244 : Triangle type {6,12,12} Group order 300 Chiral action Defining relators: [ x * y * z, x^6, y^-1 * z^-1 * x^-2 * y^-1 * x * z, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T101.245 : Triangle type {6,12,12} Group order 300 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, z * y * x^-1 * z * y * x^-1 * z * y * x^-1 * z * y^-1 ] T101.246 : Triangle type {6,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, (z^-1 * y)^5 ] T101.247 : Triangle type {6,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z ] T101.248 : Triangle type {6,12,12} Group order 300 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, (z * y^-1)^5 ] T101.249 : Triangle type {6,22,33} Group order 264 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, z * x^-1 * z * y^-1 * z * y^-1 * z * x^-1 * y^-1 * z^2 * y^-1 * z ] T101.250 : Triangle type {6,82,123} Group order 246 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6, y^-7 * z^2 * y^-2 * z^6 * y^-2 * z * y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T101.251 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * y, x^8 ] T101.252 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^8 ] T101.253 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, x^8, y^8 ] T101.254 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * z^-2 * x^-1 * y^-2 * z, x^8, y * z^-1 * x * y^-1 * x * y^-2 * z^-1, y^8 ] T101.255 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * z^-1 * x^-1 * z * y^2, x^8 ] T101.256 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, y^3 * x^-1 * z^3, y * z^-1 * y * z^-1 * y * x * z * y * x^-1 * z ] T101.257 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, x * y^-1 * z^2 * y * x * y^-1 * z * y^-1 * z^-1 ] T101.258 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, x * y^-1 * z^2 * y * x^-1 * y^-1 * z^-2 * y ] T101.259 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, x^8, y * z^-1 * x^-1 * y^-1 * x * y^-2 * z^-1, y^8 ] T101.260 : Triangle type {8,8,8} Group order 320 Chiral action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, x^8, y^8 ] T101.261 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, x^8, z * y * z^-1 * x^-1 * y * x^-1 * z^5 ] T101.262 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^2 * z * y, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, x^8, z^-2 * x^-1 * z * y * x^-1 * z * y * z^-3 ] T101.263 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z * y^-1 * x * z * y * x^-1 * z^5 ] T101.264 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^-5 * x^-1 * z * y * z^-3 * x^-1 * z * y^-1 * x^-1 * z^2 * y * z^-3 ] T101.265 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, z^3 * y^-1 * z^-1 * x * z^4 ] T101.266 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^5 * y^-1 * z^-4 * x^-1 * y^-1 * x * y^-1 * x * z^6 ] T101.267 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y * x, z^9 * y * z^-2 * x^-1 * z^2 * y^-1 * z^-3 * x ] T101.268 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z * y^-1 * x * z^-1 * x, z * x^-3 * y^-3, y^2 * x^-2 * y^-1 * z * x^-1, y * z^-1 * x * z * y * x^-1 * z^5 ] T101.269 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z^8 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x^-1 * z ] T101.270 : Triangle type {8,8,18} Group order 288 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, x^-1 * z^5 * y * z^-1 * x^-1 * y * z^-5 * x * z * y * x^-1 * y * x^-1 * y * z^-1 ] T101.271 : Triangle type {8,8,28} Group order 280 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, z * x^-1 * y * x^-1 * y^2 * x, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-2 ] T101.272 : Triangle type {8,8,28} Group order 280 Chiral action Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, z * x^-3 * y^-3, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-1 * z^-1 * x^-1 * y * x^-1 * z^4 ] T101.273 : Triangle type {8,8,68} Group order 272 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^4 * x^-1 * z^2 * y^-1 * z ] T101.274 : Triangle type {8,8,68} Group order 272 Chiral action Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-3 * x^-1 * z^4 ] T101.275 : Triangle type {8,8,68} Group order 272 Reflexible action Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^24 * y * x^-1 * y * x^-1 * z^8 ] T101.276 : Triangle type {8,8,68} Group order 272 Reflexible action Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-12 * x^-1 * z * y^-1 * z^-5 * x * y^-1 * z^-6 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y ] T101.277 : Triangle type {8,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^-2 * x, x^8 ] T101.278 : Triangle type {8,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, y * x^-1 * y^-1 * x * z^2, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, x^8 ] T101.279 : Triangle type {8,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, z^-1 * y^2 * x * z^-1 * x, z^-1 * x^-3 * z * y * z^-1 ] T101.280 : Triangle type {8,16,32} Group order 256 Chiral action Defining relators: [ x * y * z, x * z * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T101.281 : Triangle type {8,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^2 * y^-1 * z^-5 * x^-1 * y * z^-6 * x * z ] T101.282 : Triangle type {8,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^2 * y^-1 * z^-6 * x^-1 * y^-1 * z^-4 * x * z^2 ] T101.283 : Triangle type {8,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^-10 * x^-1 * z^3 * y^-1 * z^-2 ] T101.284 : Triangle type {8,16,32} Group order 256 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, x^-1 * y^-1 * z^-3 * x * z * y^-1 * x^-1 * z * y * z^-4 * x^-1 * z^2 * y * z^-1 ] T101.285 : Triangle type {8,30,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^21 * y^-1 * z * y^-3 * z * y^-1 * z ] T101.286 : Triangle type {8,30,120} Group order 240 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-1 * z * y^-1 * z * y^-1 * z^6 * y^-8 * z * y^-1 * z * y^-1 * z ] T101.287 : Triangle type {8,40,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, x^8, z^-2 * y^4 * z^-4 ] T101.288 : Triangle type {8,40,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-2 * x * y^-1 * x * z * y^-1 * z^-1, y^7 * z^-1 * y * z^-1 ] T101.289 : Triangle type {8,48,48} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * z^-1 * x^-1 * z * y^-2, y * z^-2 * x^-1 * y^-2 * z, x^8, y^-2 * x * y^-1 * x * y^-2 * z ] T101.290 : Triangle type {8,48,48} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y * z^-1 * y^2 * z^-2, x^8 ] T101.291 : Triangle type {8,48,48} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x^-1 * y * z^-1 * y, x^8 ] T101.292 : Triangle type {8,116,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, z^7 * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^3 ] T101.293 : Triangle type {8,116,232} Group order 232 Reflexible action Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-7 * z * y^-1 * z^3 ] T101.294 : Triangle type {9,9,12} Group order 288 Reflexible action Defining relators: [ x * y * z, z * x^-2 * y^-2, z * y^2 * x^-1 * z^2, x^2 * y^-1 * x^2 * z^2 * y^-1, z * y * z^-1 * x^2 * y^-1 * z^-1 * x ] T101.295 : Triangle type {10,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * x^3 * z^-2 * x, z^-1 * x * z * y^-1 * z^-3 * x^-1 * z^4 * y * z^-1 ] T101.296 : Triangle type {10,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y^-1 * x^4 * y^-3, z^-1 * x * z^5 * y * x^-1 * y^-1 * z^-4 ] T101.297 : Triangle type {10,20,60} Group order 240 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^10, z * y^-1 * z^-4 * x^-1 * z * y * z^-1 * x * z^3 ] T101.298 : Triangle type {10,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^4 * x^-1 * y * z^-1 * y^2, x^10 ] T101.299 : Triangle type {10,24,40} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-1 * z^-1 * y, x^10 ] T101.300 : Triangle type {10,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^-3 * x^2 * y^-3, z^-3 * x^2 * z^-3 ] T101.301 : Triangle type {10,30,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, x^10 ] T101.302 : Triangle type {10,46,115} Group order 230 Reflexible action Defining relators: [ x * y * z, x * z * y, x^10, z^7 * y^-1 * z^5 * y^-7 * z^3 ] T101.303 : Triangle type {12,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y * x * z^-1 * y, x^-1 * y * x^-1 * y^3 * x^-6 * y ] T101.304 : Triangle type {12,15,60} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-2 * y * x * z^-1 * y, z^-1 * x^-3 * y^-1 * x^2, y * x^-1 * y * x^-1 * y^3 ] T101.305 : Triangle type {12,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2, x^-4 * z * x^-5 * y * x^-2 ] T101.306 : Triangle type {12,20,30} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^4 * z^-4, x^-12 ] T101.307 : Triangle type {12,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * x^-1 * y * x^-1 * z^2 * y * x^-1 ] T101.308 : Triangle type {12,24,24} Group order 240 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * y^-1 * z^-2, x^-12 ] T101.309 : Triangle type {14,32,224} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-6, x^3 * y^-4 * x^2 * z^-4 * x^5 ] T101.310 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1, (x * z^-4 * x^3)^2 ] T101.311 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y^-2, z^-2 * x^3 * z^-2 * x, (y * z^-1 * y^2)^2 ] T101.312 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * x^2 * y^-4, z * x^-1 * z^2 * x^-3 * z^5 ] T101.313 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2, y * z^-1 * y * x^-1 * y * x^-3 * y^2 * z^-1 * y ] T101.314 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x * z^-1 * x^8 * y^-3 * x * y^-2 * x ] T101.315 : Triangle type {14,56,56} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3, x * y^-4 * x^6 * y^-4 * x^3 ] T101.316 : Triangle type {15,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z * y^-1 * x^2 * z^2, y^2 * x^-2 * z^2 * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T101.317 : Triangle type {15,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z^2, x^-1 * z * x^-2 * z * y^-1 * z, (x * y^-1)^4 ] T101.318 : Triangle type {15,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, y * z^-1 * x^-1 * y * z^-1, x^-1 * z^2 * x * z^-2, z^-1 * y^2 * x^2 * z^-1 * x^2, y^3 * x^-2 * z * y^2 * x^-1 ] T101.319 : Triangle type {15,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-2 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z, y * x^-3 * y^3, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T101.320 : Triangle type {15,20,20} Group order 240 Reflexible action Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * x^-3 * y^3, z * x^-3 * z^3, z^-1 * x * z^-1 * x^2 * z * y^-1 * x ] T101.321 : Triangle type {15,45,45} Group order 225 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-4 * z^5 * y^-6, x^4 * y^-5 * x * z^-5 * x^5 ] T101.322 : Triangle type {16,16,24} Group order 240 Chiral action Defining relators: [ x * y * z, z * y * x^-1 * y * x, z^-2 * x^-2 * y^-1 * z * y, z^4 * x^-1 * z^3 * y^-1 ] T101.323 : Triangle type {16,16,24} Group order 240 Chiral action Defining relators: [ x * y * z, z * y * x^-2 * y^-1 * z^2, y^-1 * z^-1 * x^-2 * y * x * y^-1, z^-2 * x^-2 * z * y^-1 * x, z * x^-1 * y * x^-1 * y^2 * x ] T101.324 : Triangle type {16,16,24} Group order 240 Chiral action Defining relators: [ x * y * z, z * y * x^2 * z^-1 * x, z^-1 * y * x^-2 * z^2 * y^-1, y * x^-1 * y * x^-1 * y * z^-1 * y ] T101.325 : Triangle type {16,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-4 * z^2, x^4 * y^-4 * x^2 * z^-4 * x^6 ] T101.326 : Triangle type {16,28,112} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-7 * z * y, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-1 * z^3 ] T101.327 : Triangle type {18,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-3 * z^3, x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y^2 ] T101.328 : Triangle type {18,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^5 * x^-1 * z^5, y^-5 * z * y^-3 * x^5 * y^-3 ] T101.329 : Triangle type {18,108,108} Group order 216 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^2 * y^-8, z^4 * x^-1 * z * x^-1 * z^5 * x^-6 * z^2 ] T101.330 : Triangle type {20,44,55} Group order 220 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-1 * z^5 * x^-1 * z^5, y^3 * x^-5 * y^8 ] T101.331 : Triangle type {22,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^2 * x^-1 * y^2 * z^-1, z^-1 * x^4 * z^-3 ] T101.332 : Triangle type {22,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * z * y^-1, y^4 * x^-1 * y * x^-1 * y^2 * x^-1 * y^2 * x^-1 * y^3 ] T101.333 : Triangle type {22,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-2, z^-4 * x^2 * z^-4 ] T101.334 : Triangle type {22,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * y * x^-1 * y^-1 * z * y^-1, y * z^-2 * x^-1 * y^-2 * z, x * y^-1 * x^3 * y^-2 * z^-1, (y * z^-1 * y^2)^2 ] T101.335 : Triangle type {22,44,44} Group order 220 Chiral action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^10 * y^-1 * x^9 * z^-1 * x^2 ] T101.336 : Triangle type {27,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, x^-4 * z * x^-1 * z, y^4 * x^-1 * y^2 * z^-2 ] T101.337 : Triangle type {27,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, y * z^-1 * x^2 * z^-2, x^-2 * y^3 * x^-4 * y^3 ] T101.338 : Triangle type {27,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, (x * z * y)^2, z * y^-2 * z^3 * y^-1 * z^2 * x^-2 * y^-1 * z^2 * x^-1 * z^2 ] T101.339 : Triangle type {27,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^18 * z^-2 * x^6 * y^-1 * z^-1 * x ] T101.340 : Triangle type {27,54,54} Group order 216 Reflexible action Defining relators: [ x * y * z, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2, x^7 * z^-1 * x * z^-1 ] T101.341 : Triangle type {28,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-1 * z^3 * y^-5 * z^3 * y^-3 * x^2 * y^-1 ] T101.342 : Triangle type {28,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z * y^-3 * x * y^-1 * x * y^-1 * x^5 * y^-2 * z * y^-1 * z ] T101.343 : Triangle type {28,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * y^-2 * x, z^-1 * x^4 * z^-3, y^-2 * x * y^-1 * x * y^-3 ] T101.344 : Triangle type {28,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-1 * y * x^-6 * y * x^-1 * y^2, z * x^-1 * z^2 * x^-3 * z^5 ] T101.345 : Triangle type {28,28,28} Group order 224 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2, x^-1 * y * x^-1 * y * x^-5 * y * x^-1 * y ] T101.346 : Triangle type {30,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-5 * x^3 * y^-2, z^5 * x^-1 * z * x^-1 * z^5 * x^-6 * z^3 ] T101.347 : Triangle type {30,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z^5 * x^-5 * z, y^-6 * z^4 * y^-1 * x^5 * y^-1 * x * y^-2 ] T101.348 : Triangle type {30,105,210} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T101.349 : Triangle type {42,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^25 * y^-1 * x^9 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x^2 ] T101.350 : Triangle type {42,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^2 * x^-1 * z^15 * x^-1 * y^-2 * z^4 * x^-1 * z * x^-1 * z ] T101.351 : Triangle type {42,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-10 * z^3 * y^-2 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-1 ] T101.352 : Triangle type {42,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^5 * x^-6, y^4 * x^-3 * y * z^-5 * y * z^-1 * y^3 ] T101.353 : Triangle type {42,70,105} Group order 210 Reflexible action Defining relators: [ x * y * z, x * z * y, (x^-1 * z^5)^2, y^5 * x^-4 * y^3 * z^-1 * y^6 ] T101.354 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^-2 * z^3 * y^-1 * z * y^-2 * z * y^-1 * z^2 * y^-2 * x * y^-1 ] T101.355 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, x^2 * y^-3 * x * y^-1 * x^3 * y^-3 * z * y^-2 * x^2 * y^-2 * x ] T101.356 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2, x^-1 * y * x^-2 * y^2 * x^-9 * y ] T101.357 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-3 * x * z^-1 * x * z^-4, x^-1 * y * x^-7 * y^3 ] T101.358 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^6 * z^-3, x^-1 * y^3 * x^-5 * y^5 ] T101.359 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-11 * z * x^-2 * y^2 * x^-8 * z * x^-3 ] T101.360 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-5 * z, y^-5 * z^4 * y^-1 * x^5 * y^-1 * x * y^-1 ] T101.361 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^11 * y^-6 * x * y^-1 * x * y^-12 * x * y^-1 * x * y^-1 * x * y^-1 ] T101.362 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-4 * z^4 * x^-6, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x^3 * y^-4 ] T101.363 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^2 * y^-8, x^4 * y^-4 * x^2 * z^-5 * x * z^-1 * x * z^-1 * x * z^-1 * x ] T101.364 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x * y^-8 ] T101.365 : Triangle type {52,104,104} Group order 208 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^52 ] T101.366 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-9 * z^2 * y^-3 * x^3 * y^-8 ] T101.367 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-4 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x * y^-1 * x * y^-2 ] T101.368 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^8 * y^-1 * z^5, x^2 * y^-6 * x^7 ] T101.369 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^2 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^3 ] T101.370 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-1 * y^2 * z^-1 * y * z^-4 * y * z^-5 * x * y * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T101.371 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * z^-2 * x^3, z^4 * y^-1 * z^5 * y^-1 * z^5 ] T101.372 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^5, y^5 * x^-4 * y^6 * x^-1 * y^3 ] T101.373 : Triangle type {102,204,204} Group order 204 Reflexible action Defining relators: [ y^-1 * x^-1 * y^-1, x^17 * y^-1 * x^12 * y^-1 * x^72, y * z^-1 ] T101.374 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x^-2 * y^-1, y^77 * x^-1 * y^24, x * z^-1 ] T101.375 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-16 * y^3 * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * z * x^-6 ] T101.376 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^3, x^-6 * z * x^-1 * z * x^-1 * z^5 * x^-3 * z^3 * x^-6 ] T101.377 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * z^5 * y^-6, x^-5 * z^2 * x^-7 * y * x^-2 ] T101.378 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-3 * z^3 * x^-7, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-1 * x * y^-5 ] T101.379 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * z^4 * x^-1 * z^5, y^5 * x^-5 * y^3 * z^-2 * y^6 ] T101.380 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * y * x^-10, y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-2 * z^4 ] T101.381 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-1 * y * x^-5 * y^6 * x^-1, x^-2 * z * x^-1 * z * x^-1 * z^5 * x^-1 * z^5 ] T101.382 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x * y^-10, z^11 * x^-6 * z^2 ] T101.383 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-5 * y * x^-6 * y * x^-1 * y * x^-1 * y * x^-11 * y * x^-1 * y * x^-1 * y * x^-2 ] T101.384 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-8 * y^3, y * z^-1 * y^7 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T101.385 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-3 * x^3 * z^-5 * x * z^-1 * x * z^-1 * x, z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] T101.386 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^-2 * y * x^-1 * y * x^-1 * y * x^-5 * y^6 * x^-1 * y * x^-1 * y * x^-2 ] T101.387 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z * x^-32 * z^5 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * z^5 * x^-3 * z^4 * x^-1 * z * x^-1 * z ] T101.388 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^55 * x^-1 * y^12 ] T101.389 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, y^17 * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-9 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T101.390 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-2 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-8 * z^2 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T101.391 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4 * z^2, x^2 * y^-1 * x * y^-1 * x * y^-6 * x^5 * y^-1 * x * y^-1 * x^3 ] T101.392 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-1 * z^5 * y^-5 * z, x^-3 * y * x^-8 * y^2 * x^-2 ] T101.393 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * z^-2 * x^3, y^-2 * z * y^-1 * z * y^-1 * z^5 * y^-5 * z ] T101.394 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, y^-7 * x^4 * y^-2, z^5 * y^-1 * z^5 * y^-1 * z^5 ] T101.395 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, z^-5 * x * z^-4, y^5 * x^-5 * y^6 * x^-1 * y * x^-1 * y^2 ] T101.396 : Triangle type {203,203,203} Group order 203 Reflexible action Defining relators: [ x * y * z, x * z * y, x^-2 * z * x^-9, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^5 * y^-1 * z^5 ] Total number of triangle group actions in list above: 20810