Chiral polytopes with up to 2000 flags (ordered by type for each rank) ...................................................................... Below is a complete list of all abstract chiral polytopes (with maximum symmetry) up to 2000 flags, up to isomorphism, reflection and duality. Note that the automorphism group of each such polytope has two orbits on flags, with any two adjacent flags lying in different orbits. Hence the number of flags is twice the order of the automorphism group. The list is ordered first by rank, and then within each rank (from 3 to 5) by Coxeter type (Schlaefli symbol), and then by the number of flags. Also each entry in the list indicates whether the polytope is properly self-dual ('PSD'), meaning that there exists a duality of the polytope that preserves each of the two flag orbits, or improperly self-dual ('ISD'), meaning that there exists a duality of the polytope that interchanges the two flag orbits, or otherwise non-self-dual ('NSD'). If the polytope is not self-dual, then its dual does not appear elsewhere in the list. Finally, in each case some defining relations are given for the automorphism group of the polytope, in terms of the Coxeter generators. If the rank is n, then the generators are A.1, A.2, ..., A.(n-1), which are automorphisms having the property that A.i has order p_i (for all i), where [p_1,p_2,...,p_{n-1}] is the Coxeter type (Schlaefli symbol) of the polytope, and (A.i*A.(i+1)*...*A.j)^2 = 1 whenever j > i. This list was created by finding and analysing all normal subgroups of index up to 1000 in the relevant Coxeter groups, with the help of the MAGMA system. Note that up to isomorphism, reflection and duality there is just one chiral 5-polytope with at most 2000 flags (namely an ISD 5-polytope of type [3,4,4,3]), and there are none of rank 6 or more. Marston Conder September 2012 Rank 3 ...... Chiral 3-polytope with group of order 42 NSD Type [ 3, 6 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, A.2^6, A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 78 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 114 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 126 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 168 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 186 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 222 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 234 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 258 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^2 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 294 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 312 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 342 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 366 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 378 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 402 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 438 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 456 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 474 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 504 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 546 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 546 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 558 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 582 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 618 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 654 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 666 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 672 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 702 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 744 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-3 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 762 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 774 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 798 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 798 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 834 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 882 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 888 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 906 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 936 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 942 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 978 NSD Type [ 3, 6 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 432 NSD Type [ 3, 8 ] [ A.1^3, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^2 * A.2^-2 * A.1 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 336 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-5)^2, A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 504 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, A.2^12, (A.2^2 * A.1^-1 * A.2^2)^3, A.2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 624 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-5)^2, A.2^2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 768 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, A.2^12, A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 912 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-5)^2, A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 936 NSD Type [ 3, 12 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, A.2^12, (A.2^2 * A.1^-1 * A.2^2)^3, A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 486 NSD Type [ 3, 18 ] [ A.1^3, (A.1^-1 * A.2^-1)^2, (A.2^2 * A.1^-1 * A.2^2)^3, A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^-4 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 20 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 40 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 52 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 68 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 80 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 100 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 104 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 116 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 136 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 148 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 160 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 164 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 180 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 200 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 208 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 212 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 232 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 244 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 260 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 260 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 272 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 292 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 296 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 320 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 328 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 340 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 340 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 ] Chiral 3-polytope with group of order 356 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 360 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 388 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 400 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 404 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 416 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 424 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 436 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 452 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-2 ] Chiral 3-polytope with group of order 464 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 468 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 488 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 500 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 500 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 520 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 520 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 544 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 548 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 580 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 580 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 584 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 592 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 596 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 612 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 628 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 640 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 656 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 676 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 680 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 680 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 692 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 712 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 720 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 724 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 740 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 740 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 772 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 776 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 788 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 800 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 808 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 820 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 820 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 832 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 848 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 872 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 884 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 884 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 900 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 904 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 916 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 928 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 932 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 936 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 964 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 976 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 980 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^-2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 1000 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 1000 ISD Type [ 4, 4 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2^-2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1^2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 384 NSD Type [ 4, 6 ] [ A.1^4, A.2^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, (A.1 * A.2^-2)^4 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 6 ] [ A.1^4, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.1^-1 * A.2^-3 * A.1^-2 * A.2^-3 * A.1^2 * A.2^3 * A.1^2 * A.2^3 * A.1^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 6 ] [ A.1^4, A.2^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-1 * A.2 * A.1^2 * A.2^3 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 144 NSD Type [ 4, 8 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^8, A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 160 NSD Type [ 4, 8 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^8, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 160 NSD Type [ 4, 8 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^8, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 288 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1^-1 * A.2 * A.1^2 * A.2^4 * A.1 ] Chiral 3-polytope with group of order 320 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 320 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 320 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^5, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 416 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 416 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 432 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^4 * A.1 ] Chiral 3-polytope with group of order 544 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 544 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 576 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-2, A.1 * A.2^-4 * A.1^-1 * A.2 * A.1^2 * A.2^4 * A.1^2 * A.2^-1, A.2^2 * A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^2 * A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-4 * A.1^2 * A.2^4 * A.1^-1, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-4 * A.1^2 * A.2^4 * A.1^-1, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^4 * A.1^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^5, A.1^-1 * A.2^-4 * A.1 * A.2^-1 * A.1^-2 * A.2^4 * A.1^2 * A.2, A.2^-3 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^4 * A.1 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1 * A.2^-4 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^-3 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 832 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 832 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 864 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, (A.1 * A.2^-1)^6 ] Chiral 3-polytope with group of order 928 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 928 NSD Type [ 4, 8 ] [ A.1^4, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 120 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 240 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^12 ] Chiral 3-polytope with group of order 312 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 408 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 480 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^3 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 480 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 540 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4, A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 600 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 600 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1, A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^3 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 624 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 696 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 720 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^3 * A.1 * A.2^-1 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.2^12, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, (A.1 * A.2^-2)^4, (A.1 * A.2^-5)^2, A.2^12 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, (A.1 * A.2^-5)^2, A.2^12, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 816 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 888 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, (A.1 * A.2^-2)^4, A.2^12, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-3 * A.1^2 * A.2 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1 * A.2^-1)^2, A.2^-4 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 972 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1 * A.2^-1)^2, A.2^12, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^3 ] Chiral 3-polytope with group of order 984 NSD Type [ 4, 12 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^12, A.1 * A.2^3 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 256 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 320 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 320 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^16 ] Chiral 3-polytope with group of order 576 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^-3 * A.1 * A.2^-1, A.2^16 ] Chiral 3-polytope with group of order 576 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^16 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 832 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^16 ] Chiral 3-polytope with group of order 832 NSD Type [ 4, 16 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 200 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^-2 * A.2^-5 ] Chiral 3-polytope with group of order 400 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^20 ] Chiral 3-polytope with group of order 520 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 680 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^20 ] Chiral 3-polytope with group of order 1000 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, (A.1 * A.2^-2)^4, A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 1000 NSD Type [ 4, 20 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 432 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^-3 * A.1 * A.2^-1, A.2^2 * A.1 * A.2^-5 * A.1 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 480 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^24 ] Chiral 3-polytope with group of order 480 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-6 ] Chiral 3-polytope with group of order 864 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2, A.2^24 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.2^24 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-6 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 24 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2^3 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 280 NSD Type [ 4, 28 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^5 * A.1 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 560 NSD Type [ 4, 28 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^28 ] Chiral 3-polytope with group of order 728 NSD Type [ 4, 28 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^2, A.1 * A.2^-6 * A.1^-1 * A.2 * A.1^-2 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 952 NSD Type [ 4, 28 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-6 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 32 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1 * A.2^-6 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 640 NSD Type [ 4, 32 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^32 ] Chiral 3-polytope with group of order 360 NSD Type [ 4, 36 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^-10 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 720 NSD Type [ 4, 36 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^36 ] Chiral 3-polytope with group of order 936 NSD Type [ 4, 36 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^2, A.2^-1 * A.1^-1 * A.2^6 * A.1 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2^6 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 720 NSD Type [ 4, 40 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2, A.2^-10 * A.1^2 * A.2^-2 * A.1 * A.2^4 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 40 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.2^-9 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-6 ] Chiral 3-polytope with group of order 800 NSD Type [ 4, 40 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^40 ] Chiral 3-polytope with group of order 440 NSD Type [ 4, 44 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^11 * A.1^2 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^8 ] Chiral 3-polytope with group of order 880 NSD Type [ 4, 44 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^44 ] Chiral 3-polytope with group of order 768 NSD Type [ 4, 48 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2^4 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 48 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^48 ] Chiral 3-polytope with group of order 960 NSD Type [ 4, 48 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.2^-10 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-8 ] Chiral 3-polytope with group of order 520 NSD Type [ 4, 52 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^13 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-5 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 600 NSD Type [ 4, 60 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^15 * A.1^2 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^12 ] Chiral 3-polytope with group of order 680 NSD Type [ 4, 68 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^17 * A.1^2 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^14 ] Chiral 3-polytope with group of order 760 NSD Type [ 4, 76 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^19 * A.1^2 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^16 ] Chiral 3-polytope with group of order 840 NSD Type [ 4, 84 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^21 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-5 * A.1 * A.2^14 ] Chiral 3-polytope with group of order 920 NSD Type [ 4, 92 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^23 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-5 * A.1 * A.2^16 ] Chiral 3-polytope with group of order 1000 NSD Type [ 4, 100 ] [ A.1^4, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^25 * A.1^2 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^22 ] Chiral 3-polytope with group of order 960 ISD Type [ 5, 5 ] [ A.1^5, A.2^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^6, A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 960 NSD Type [ 5, 6 ] [ A.1^5, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^5, A.2^-1 * A.1^-2 * A.2^-3 * A.1^2 * A.2 * A.1^-1 * A.2^3 * A.1, A.2 * A.1^-2 * A.2^-3 * A.1^2 * A.2^-1 * A.1 * A.2^3 * A.1^-1 ] Chiral 3-polytope with group of order 110 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 110 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 ] Chiral 3-polytope with group of order 310 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 310 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 410 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2^-2 * A.1^2 ] Chiral 3-polytope with group of order 410 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 550 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 550 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 610 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1 * A.2^-3 ] Chiral 3-polytope with group of order 610 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 710 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^-4 ] Chiral 3-polytope with group of order 710 NSD Type [ 5, 10 ] [ A.1^5, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 84 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^3 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 156 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 192 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2 ] Chiral 3-polytope with group of order 228 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-2 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 252 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 252 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 336 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 372 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 384 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, (A.1 * A.2^-1 * A.1)^4 ] Chiral 3-polytope with group of order 384 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^3 * A.1 ] Chiral 3-polytope with group of order 444 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^3 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 468 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 468 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 516 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-2 * A.1^-2 ] Chiral 3-polytope with group of order 576 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^4, A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 576 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2 * A.1^-1 * A.2^-3 * A.1^3 * A.2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 588 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-3 * A.1^-1 * A.2 * A.1^2 * A.2^3 * A.1^-2 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 588 PSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 588 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 624 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-2 * A.1^-2 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 648 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.2^-1 * A.1^-3 * A.2^-3 * A.1^3 * A.2^3 * A.1^3 * A.2^-2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^2 * A.2^3 * A.1^-1, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 684 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2, A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 684 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-2 * A.1^-1 * A.2 * A.1^2 ] Chiral 3-polytope with group of order 720 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^5, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 732 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1^-2 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, A.1^-1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 768 ISD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.1 * A.2^-1 * A.1^-3 * A.2^-3 * A.1^-2 * A.2^3 * A.1^3 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 PSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2^3 * A.1 * A.2^-1, (A.2^-1 * A.1^2 * A.2^-1)^3 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-3 * A.1^3 * A.2^3 * A.1^-2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^4, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 804 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 ] Chiral 3-polytope with group of order 876 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 ] Chiral 3-polytope with group of order 912 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 948 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2 * A.1^-2 * A.2^-2 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 6 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-2 * A.2 * A.1^3 * A.2^3 * A.1^-1 * A.2, (A.1 * A.2^-1)^6, A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 384 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-3 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 432 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.2 * A.1^-1 * A.2)^3, A.1 * A.2^-4 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-3 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^3 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2 * A.1^-1, A.1^-1 * A.2^-4 * A.1^3 * A.2^4 * A.1^-2 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, (A.1 * A.2^-1 * A.1)^4, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-4 * A.1^3 * A.2^4 * A.1^-2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1^-2 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^3 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2 * A.1^-1, A.2^-2 * A.1^-2 * A.2 * A.1^3 * A.2^4 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 8 ] [ A.1^6, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1 * A.2^-1 * A.1^-1 * A.2^2 * A.1^-1 * A.2^3 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 54 NSD Type [ 6, 9 ] [ (A.1^-1 * A.2^-1)^2, A.1^6, (A.1 * A.2^-2)^2, A.2 * A.1^-3 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 216 NSD Type [ 6, 9 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-9, A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 378 NSD Type [ 6, 9 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-9, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 378 NSD Type [ 6, 9 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-9, A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 ] Chiral 3-polytope with group of order 378 NSD Type [ 6, 9 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-9, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 486 NSD Type [ 6, 9 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-9, A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^2 ] Chiral 3-polytope with group of order 702 NSD Type [ 6, 9 ] [ A.1^6, A.2^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-2 ] Chiral 3-polytope with group of order 702 NSD Type [ 6, 9 ] [ A.1^6, A.2^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 702 NSD Type [ 6, 9 ] [ A.1^6, A.2^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-2 * A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 9 ] [ A.1^6, A.2^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 168 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 168 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 312 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 312 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 384 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 384 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-2, A.2^-2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 456 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 456 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 504 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 504 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1, A.2^12 ] Chiral 3-polytope with group of order 504 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^-2 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-2 ] Chiral 3-polytope with group of order 504 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^-2 * A.2^3 * A.1^-1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-5)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 744 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 744 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-2, (A.1 * A.2^-1 * A.1)^4 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1, A.1 * A.2^-3 * A.1^-2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 888 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2^2 * A.1 ] Chiral 3-polytope with group of order 888 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2^2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 936 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^12, A.1 * A.2^2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 936 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-2, A.2^12, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-2 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 936 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^12, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 936 NSD Type [ 6, 12 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 210 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 390 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2^2 ] Chiral 3-polytope with group of order 480 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 570 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 630 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-1 * A.1^2 * A.2^2, A.2^-15 ] Chiral 3-polytope with group of order 840 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 930 NSD Type [ 6, 15 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-15, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2^-2 ] Chiral 3-polytope with group of order 108 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-2 * A.2^-4 ] Chiral 3-polytope with group of order 324 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-4 ] Chiral 3-polytope with group of order 432 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1 * A.2^-4 * A.1^2 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1, A.2^18 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^18 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2 * A.1^-2 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-2 * A.1^3 * A.2^2 * A.1^-1, A.2^-1 * A.1^-2 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2^3 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^-3 * A.1 * A.2^-1, A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-3 * A.1 * A.2 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 18 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 294 NSD Type [ 6, 21 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^3 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2^2 ] Chiral 3-polytope with group of order 546 NSD Type [ 6, 21 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 798 NSD Type [ 6, 21 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 882 NSD Type [ 6, 21 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-2 * A.2^-1 * A.1^2 * A.2^-1 * A.1, A.2^-21 ] Chiral 3-polytope with group of order 882 NSD Type [ 6, 21 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1^-2 * A.2)^3, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.2^3 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1 * A.2 ] Chiral 3-polytope with group of order 336 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 336 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-5 ] Chiral 3-polytope with group of order 624 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-4 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 624 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-5, A.1 * A.2^-3 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, A.1 * A.2^-4 * A.1^2 * A.2^-1 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 768 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 912 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 912 NSD Type [ 6, 24 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-5, A.2^2 * A.1 * A.2^-2 * A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 162 NSD Type [ 6, 27 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^3 * A.1^-2 * A.2 * A.1^2 * A.2^5 ] Chiral 3-polytope with group of order 648 NSD Type [ 6, 27 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-3 ] Chiral 3-polytope with group of order 420 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^3 * A.1 * A.2^-2 * A.1 * A.2^3 * A.1^-2 * A.2^2 ] Chiral 3-polytope with group of order 420 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2^-6 ] Chiral 3-polytope with group of order 780 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2^4 * A.1 * A.2^-1 * A.1^-3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 780 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-3 * A.1, A.2^-1 * A.1^-1 * A.2^4 * A.1^2 * A.2^4 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 960 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, (A.1 * A.2^-2 * A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^4, A.2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-1 * A.1^2 * A.2 * A.1^-2 * A.2, A.2^-1 * A.1^-1 * A.2^4 * A.1^2 * A.2 * A.1^-1 * A.2^-4 ] Chiral 3-polytope with group of order 960 NSD Type [ 6, 30 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1, A.2^2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-2 * A.1^2 * A.2, A.2^-1 * A.1^-1 * A.2^4 * A.1^2 * A.2^4 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 462 NSD Type [ 6, 33 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-7 ] Chiral 3-polytope with group of order 858 NSD Type [ 6, 33 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2^-5 * A.1^2 * A.2^-1 * A.1^-3 * A.2 * A.1^-2 * A.2^4 ] Chiral 3-polytope with group of order 216 NSD Type [ 6, 36 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-6 * A.1^3 * A.2 * A.1^-1 * A.2^-5 ] Chiral 3-polytope with group of order 648 NSD Type [ 6, 36 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^2 * A.1 * A.2^-4 * A.1^-2 * A.2^-2 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 36 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-1 * A.2^3 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^5 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 36 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 546 NSD Type [ 6, 39 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2, A.2^-1 * A.1^-1 * A.2^4 * A.1^-2 * A.2 * A.1^3 * A.2^-7 ] Chiral 3-polytope with group of order 588 NSD Type [ 6, 42 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1, A.2^-6 * A.1^2 * A.2^-1 * A.1^2 * A.2^-7 ] Chiral 3-polytope with group of order 588 NSD Type [ 6, 42 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^-3 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-7 ] Chiral 3-polytope with group of order 270 NSD Type [ 6, 45 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^7 * A.1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-4 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 48 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^2 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-1 * A.1^2 * A.2^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2^6 * A.1^-2 * A.2 * A.1^-2 * A.2^7 ] Chiral 3-polytope with group of order 672 NSD Type [ 6, 48 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^7 * A.1^-2 * A.2 * A.1^2 * A.2 * A.1^-2 * A.2^7 ] Chiral 3-polytope with group of order 714 NSD Type [ 6, 51 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2, A.2^-7 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2^6 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 324 NSD Type [ 6, 54 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^9 * A.1 * A.2^-1 * A.1^2 * A.2^-3 * A.1 * A.2^5 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 54 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^2 * A.1^2 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 * A.1^2 * A.2, A.2^7 * A.1 * A.2^-1 * A.1^-1 * A.2^3 * A.1^-2 * A.2^7 ] Chiral 3-polytope with group of order 798 NSD Type [ 6, 57 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-10 * A.1^2 * A.2^-1 * A.1^2 * A.2^-6 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 840 NSD Type [ 6, 60 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^10 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^7 ] Chiral 3-polytope with group of order 840 NSD Type [ 6, 60 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^-3 * A.1, A.2^10 * A.1^2 * A.2 * A.1^-1 * A.2^-3 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 378 NSD Type [ 6, 63 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-11 * A.1^2 * A.2^-1 * A.1 * A.2^4 * A.1^-1 * A.2^-5 ] Chiral 3-polytope with group of order 924 NSD Type [ 6, 66 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2^11 * A.1^2 * A.2^4 * A.1^-1 * A.2^-1 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 924 NSD Type [ 6, 66 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^11 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 966 NSD Type [ 6, 69 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-12 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-7 ] Chiral 3-polytope with group of order 432 NSD Type [ 6, 72 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^12 * A.1^2 * A.2 * A.1^-2 * A.2^11 ] Chiral 3-polytope with group of order 486 NSD Type [ 6, 81 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-14 * A.1^2 * A.2^-1 * A.1 * A.2^4 * A.1^-1 * A.2^-8 ] Chiral 3-polytope with group of order 540 NSD Type [ 6, 90 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^15 * A.1^3 * A.2^-1 * A.1 * A.2^14 ] Chiral 3-polytope with group of order 594 NSD Type [ 6, 99 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-17 * A.1^3 * A.2 * A.1^-1 * A.2^-15 ] Chiral 3-polytope with group of order 648 NSD Type [ 6, 108 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^18 * A.1 * A.2^-1 * A.1 * A.2^5 * A.1^-1 * A.2^-1 * A.1 * A.2^11 ] Chiral 3-polytope with group of order 702 NSD Type [ 6, 117 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-20 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^5 * A.1^-1 * A.2^-12 ] Chiral 3-polytope with group of order 756 NSD Type [ 6, 126 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^21 * A.1^2 * A.2 * A.1^-2 * A.2^20 ] Chiral 3-polytope with group of order 810 NSD Type [ 6, 135 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-23 * A.1^2 * A.2^-1 * A.1 * A.2^4 * A.1^-1 * A.2^-17 ] Chiral 3-polytope with group of order 864 NSD Type [ 6, 144 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^24 * A.1^2 * A.2 * A.1^-1 * A.2^-5 * A.1 * A.2^18 ] Chiral 3-polytope with group of order 918 NSD Type [ 6, 153 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-26 * A.1^3 * A.2 * A.1^-1 * A.2^-24 ] Chiral 3-polytope with group of order 972 NSD Type [ 6, 162 ] [ A.1^6, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^27 * A.1^2 * A.2 * A.1^-2 * A.2^26 ] Chiral 3-polytope with group of order 56 PSD Type [ 7, 7 ] [ (A.1^-1 * A.2^-1)^2, A.1^-7, A.2 * A.1^-3 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 112 NSD Type [ 7, 14 ] [ (A.1^-1 * A.2^-1)^2, A.1^-7, A.2^2 * A.1^-2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 406 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 406 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^2, A.2 * A.1 * A.2^-1 * A.1^-3 * A.2^4 * A.1^-1 ] Chiral 3-polytope with group of order 406 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^-3 * A.2^2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 602 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 602 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 602 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2^3 * A.1^-3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 784 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^3 * A.2^2 * A.1^-1 * A.2^-1 * A.1, A.2^4 * A.1^3 * A.2^-1 * A.1^2 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 896 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^-3 * A.2^3 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 994 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.1 * A.2^-3 * A.1^-2 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 994 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 994 NSD Type [ 7, 14 ] [ A.1^7, (A.1^-1 * A.2^-1)^2, A.2^-4 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1^2 ] Chiral 3-polytope with group of order 72 ISD Type [ 8, 8 ] [ (A.1^-1 * A.2^-1)^2, A.1^8, A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 136 NSD Type [ 8, 8 ] [ (A.1^-1 * A.2^-1)^2, A.1^8, A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 144 ISD Type [ 8, 8 ] [ (A.1^-1 * A.2^-1)^2, A.1^8, A.1 * A.2^-1 * A.1^3 * A.2^-3 ] Chiral 3-polytope with group of order 200 PSD Type [ 8, 8 ] [ (A.1^-1 * A.2^-1)^2, A.1^8, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1^-1 * A.2 * A.1^4 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 216 ISD Type [ 8, 8 ] [ (A.1^-1 * A.2^-1)^2, A.1^8, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^2 * A.1^4 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 272 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 288 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2 * A.1^-3 * A.2 * A.1^2 * A.2^4 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2 ] Chiral 3-polytope with group of order 320 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 320 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 320 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 320 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 328 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1^-2 * A.2^-4 * A.1^4 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 400 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, (A.1 * A.2^-1)^4, A.1^-2 * A.2^-4 * A.1^4 * A.2^2 ] Chiral 3-polytope with group of order 400 PSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1^-2 * A.2^-4 * A.1^4 * A.2^-2 ] Chiral 3-polytope with group of order 432 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.2 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2 ] Chiral 3-polytope with group of order 512 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2^-4 * A.1^2 * A.2^4 * A.1^-1, A.2^-1 * A.1^3 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^3 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^2 * A.1^-1 * A.2^2, A.2^-1 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-1 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 512 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2^2 * A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 512 PSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 544 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1^-2 * A.2 * A.1^-3 * A.2^4 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 576 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-4 * A.1^-2 * A.2^-2 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 576 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^3 * A.2^-1 * A.1^-2 * A.2^4 * A.1 ] Chiral 3-polytope with group of order 576 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-2 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^3 * A.2 ] Chiral 3-polytope with group of order 576 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^3 * A.2^-1 * A.1^-4 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 584 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 640 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 640 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^2 * A.2^-2 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2^3 * A.1^3 * A.2^3 * A.1^-1, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2^3 * A.1^3 * A.2^3 * A.1^-1, A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 640 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.2 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-2 * A.2^2, (A.1 * A.2^-1 * A.1)^4 ] Chiral 3-polytope with group of order 640 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 640 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1^3 * A.2^-2 * A.1^2 ] Chiral 3-polytope with group of order 648 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^3 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 656 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-4 * A.1^-2 * A.2^-1 * A.1 * A.2^-3 ] Chiral 3-polytope with group of order 712 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2^-2 * A.1 * A.2^-1 * A.1^3 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 720 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^3 * A.2^-1 * A.1^-2 * A.2^4 * A.1, A.2 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-2 * A.2^2, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-2 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 720 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 776 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-4 * A.1^-2 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 800 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, (A.1 * A.2^-1)^4, A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^4 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 800 PSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^3 * A.2^-1 * A.1^-4 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 832 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 832 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 832 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 864 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1^-3 * A.2 * A.1^2 * A.2^4 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2 ] Chiral 3-polytope with group of order 904 NSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1^-4 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 968 ISD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2 * A.1)^2, (A.1 * A.2^-1)^4, A.1 * A.2^-1 * A.1^-3 * A.2 * A.1^4 * A.2 * A.1^-3 * A.2^2 ] Chiral 3-polytope with group of order 1000 PSD Type [ 8, 8 ] [ A.1^8, A.2^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-2 * A.1^-1 * A.2 * A.1^-1 * A.2^4 * A.1, A.1^-1 * A.2 * A.1^4 * A.2^-1 * A.1^2 * A.2 ] Chiral 3-polytope with group of order 432 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^3 * A.2^-1 * A.1^-4 * A.2^-1 * A.1 * A.2^-1, A.2^2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 432 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 432 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1^3 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 480 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.2^12 ] Chiral 3-polytope with group of order 480 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 * A.2 * A.1^-1, A.2^12 ] Chiral 3-polytope with group of order 768 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1^3, A.2^-2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^12 ] Chiral 3-polytope with group of order 768 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 768 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.1^-2 * A.2^2 * A.1^3 * A.2^-1 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 768 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1^3, A.2^2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 864 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2^-1, A.2^12 ] Chiral 3-polytope with group of order 864 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 864 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, (A.1 * A.2^-1 * A.1)^4, A.1 * A.2^-1 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1, (A.1 * A.2^-1)^6 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2, A.2^-5 * A.1^2 * A.2^-2 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2, A.1^-1 * A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^5 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^12, A.2^2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 12 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^12, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^2, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2^2 * A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4, A.2^-1 * A.1^3 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^3 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^2 * A.1^-1 * A.2^2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4, A.2^-1 * A.1^3 * A.2^-1 * A.1^-2 * A.2^-1 * A.1^3 * A.2^-1, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^2 * A.1^-1 * A.2^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^2 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 * A.2 * A.1^-1, A.2^16 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 640 NSD Type [ 8, 16 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.2^16 ] Chiral 3-polytope with group of order 720 NSD Type [ 8, 20 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-4 * A.2^-1 * A.1^3 * A.2^-1, A.1 * A.2^-2 * A.1^-1 * A.2 * A.1^-3 * A.2^-1 * A.1 * A.2^6 ] Chiral 3-polytope with group of order 800 NSD Type [ 8, 20 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2 * A.1^2 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 * A.2 * A.1^-1, A.2^20 ] Chiral 3-polytope with group of order 800 NSD Type [ 8, 20 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^-1 * A.1 * A.2^-2 * A.1^3 * A.2^-5 ] Chiral 3-polytope with group of order 800 NSD Type [ 8, 20 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.2^20 ] Chiral 3-polytope with group of order 432 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^4 ] Chiral 3-polytope with group of order 816 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1^3 * A.2^-1, A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 816 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^-2 * A.2 * A.1^-3 * A.2^-1 * A.1^3 * A.2^-1, A.2^2 * A.1 * A.2^-4 * A.1^-2 * A.2^-2 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.1^-1 * A.2^5 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1, A.2^24 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1, A.2^24 ] Chiral 3-polytope with group of order 960 NSD Type [ 8, 24 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-6 ] Chiral 3-polytope with group of order 256 NSD Type [ 8, 32 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1, A.2^-4 * A.1^3 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 720 NSD Type [ 8, 40 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1)^4, A.2^-1 * A.1^-2 * A.2 * A.1^-3 * A.2^-1 * A.1^3 * A.2^-1, A.2 * A.1 * A.2^-3 * A.1^3 * A.2^6 ] Chiral 3-polytope with group of order 512 NSD Type [ 8, 64 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1, A.2^-8 * A.1^2 * A.2^-2 * A.1 * A.2 * A.1^-1 * A.2^-5 ] Chiral 3-polytope with group of order 768 NSD Type [ 8, 96 ] [ A.1^8, (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1, A.2^12 * A.1^3 * A.2^-2 * A.1 * A.2^10 ] Chiral 3-polytope with group of order 216 NSD Type [ 9, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.1 * A.2^-3 * A.1^-2 * A.2^5 ] Chiral 3-polytope with group of order 432 NSD Type [ 9, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, (A.1 * A.2^-5)^2, A.2^-2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 864 NSD Type [ 9, 12 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^12, A.2^2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 162 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, A.1^-9, A.2 * A.1^-4 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 342 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, A.1^-9, A.2^2 * A.1^-3 * A.2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 342 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, A.1^-9, A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^4 ] Chiral 3-polytope with group of order 342 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1^-9, A.1^-2 * A.2 * A.1^-2 * A.2^2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 486 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, (A.2 * A.1^-1 * A.2)^3, A.2^2 * A.1 * A.2^-5 * A.1^-2 * A.2^5 ] Chiral 3-polytope with group of order 486 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-2 * A.2^-2 * A.1 * A.2^-2, A.2^2 * A.1 * A.2^-5 * A.1^-2 * A.2^5 ] Chiral 3-polytope with group of order 486 NSD Type [ 9, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.1^-1 * A.2 * A.1 * A.2^-5 * A.1^-1 * A.2^6 ] Chiral 3-polytope with group of order 648 NSD Type [ 9, 18 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2^-2 * A.1 * A.2^-2 * A.1^-2 * A.2^-1 * A.1 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 666 NSD Type [ 9, 18 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, (A.2 * A.1^-1 * A.2)^3, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2 * A.1^-2 ] Chiral 3-polytope with group of order 666 NSD Type [ 9, 18 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, (A.2 * A.1^-1 * A.2)^3, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^4 * A.1^-1, A.2 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 666 NSD Type [ 9, 18 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, (A.2 * A.1^-1 * A.2)^3, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 432 NSD Type [ 9, 24 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1^-9, A.1 * A.2^-3 * A.1^-2 * A.2^5 ] Chiral 3-polytope with group of order 864 NSD Type [ 9, 24 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.2^-6 * A.1^-1 * A.2^2 * A.1^-3 * A.2^5 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 648 NSD Type [ 9, 36 ] [ A.1^9, (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-4 ] Chiral 3-polytope with group of order 220 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 220 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.2^-1 * A.1^5 * A.2^-1 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 620 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 620 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^10, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 820 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-1 * A.1^3)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^5 * A.1^-1 ] Chiral 3-polytope with group of order 820 NSD Type [ 10, 10 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-1 * A.1^3)^2, (A.1 * A.2^-3 * A.1)^2, (A.1 * A.2^-2 * A.1 * A.2^-1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 330 NSD Type [ 10, 15 ] [ (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 330 NSD Type [ 10, 15 ] [ (A.1^-1 * A.2^-1)^2, A.1^-5 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 930 NSD Type [ 10, 15 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^-2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 930 NSD Type [ 10, 15 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1^2 * A.2^-2 ] Chiral 3-polytope with group of order 440 NSD Type [ 10, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.1 * A.2^-3 * A.1^2 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 440 NSD Type [ 10, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.2^-2 * A.1^4 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 440 NSD Type [ 10, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-2 * A.1^3 * A.2^-1 * A.1^2 * A.2^-1, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-4 ] Chiral 3-polytope with group of order 440 NSD Type [ 10, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-4 ] Chiral 3-polytope with group of order 250 NSD Type [ 10, 25 ] [ (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^-3 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 250 NSD Type [ 10, 25 ] [ (A.1^-1 * A.2^-1)^2, A.1 * A.2^-2 * A.1^-2 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 660 NSD Type [ 10, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^-2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 660 NSD Type [ 10, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2^3 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 660 NSD Type [ 10, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 660 NSD Type [ 10, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1 * A.2^-1, (A.1 * A.2^-3 * A.1)^2 ] Chiral 3-polytope with group of order 770 NSD Type [ 10, 35 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.2^2 * A.1^-5 * A.2^-3 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 770 NSD Type [ 10, 35 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.1^-1 * A.2^3 * A.1^-2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 880 NSD Type [ 10, 40 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1^-1 * A.2^3 * A.1^2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 880 NSD Type [ 10, 40 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.2 * A.1 * A.2^-1 * A.1^5 * A.2^6 ] Chiral 3-polytope with group of order 880 NSD Type [ 10, 40 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1 * A.2^-1, A.2^-1 * A.1^-1 * A.2^3 * A.1^2 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 880 NSD Type [ 10, 40 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1 * A.2^-1, A.2 * A.1 * A.2^-2 * A.1^3 * A.2^5 ] Chiral 3-polytope with group of order 990 NSD Type [ 10, 45 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1, A.2^-1 * A.1^-1 * A.2^3 * A.1^-2 * A.2^2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 990 NSD Type [ 10, 45 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, (A.1 * A.2^-2 * A.1^2)^2, (A.1 * A.2^-1 * A.1 * A.2^-1 * A.1)^2, A.2^-3 * A.1^5 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-1 * A.1, A.1^-1 * A.2^3 * A.1^-4 * A.2 * A.1^-1 * A.2^-5 ] Chiral 3-polytope with group of order 500 NSD Type [ 10, 50 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2 * A.1 * A.2^-3 * A.1^3 * A.2^6 ] Chiral 3-polytope with group of order 500 NSD Type [ 10, 50 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2^-2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-6 ] Chiral 3-polytope with group of order 750 NSD Type [ 10, 75 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2^3 * A.1 * A.2^-1 * A.1^-1 * A.2^3 * A.1^-2 * A.2^8 ] Chiral 3-polytope with group of order 750 NSD Type [ 10, 75 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2^-6 * A.1^2 * A.2^-2 * A.1^-2 * A.2^-7 ] Chiral 3-polytope with group of order 1000 NSD Type [ 10, 100 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2^10 * A.1 * A.2^-2 * A.1 * A.2^2 * A.1^-1 * A.2^-2 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 1000 NSD Type [ 10, 100 ] [ (A.1^-1 * A.2^-1)^2, A.1^10, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2, A.2^10 * A.1^2 * A.2^3 * A.1^-2 * A.2^7 ] Chiral 3-polytope with group of order 506 NSD Type [ 11, 22 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^-11 ] Chiral 3-polytope with group of order 506 NSD Type [ 11, 22 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.1^-11, A.2 * A.1^-5 * A.2^3 * A.1^-2 ] Chiral 3-polytope with group of order 506 NSD Type [ 11, 22 ] [ (A.1^-1 * A.2^-1)^2, A.1^-11, A.2 * A.1^-5 * A.2^2 * A.1^-1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 506 NSD Type [ 11, 22 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^3 * A.1^-1, A.1^-11 ] Chiral 3-polytope with group of order 506 NSD Type [ 11, 22 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.1^-11 ] Chiral 3-polytope with group of order 156 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^-1 * A.2 * A.1^4 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 240 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^-1 * A.1^5 * A.2 * A.1^-1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 300 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.2^-2 * A.1^4 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 312 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.1^12 ] Chiral 3-polytope with group of order 336 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.1^12 ] Chiral 3-polytope with group of order 360 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2 * A.1^-3, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.1^12 ] Chiral 3-polytope with group of order 360 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.2 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 444 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, A.1 * A.2^-1 * A.1^5 * A.2^-3 * A.1^2 ] Chiral 3-polytope with group of order 480 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.1^12, A.1 * A.2^-1 * A.1^5 * A.2^-2 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 588 PSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, (A.1 * A.2^-2 * A.1^3)^2, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2^3 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 600 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.1 * A.2^-1 * A.1^5 * A.2^-5, (A.1 * A.2^-2 * A.1^3)^2, A.2^-1 * A.1 * A.2^-2 * A.1^3 * A.2^-3 * A.1^2 ] Chiral 3-polytope with group of order 624 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^2 * A.2^-2 * A.1^2 * A.2^-1 * A.1 * A.2^2, A.1^12 ] Chiral 3-polytope with group of order 624 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^12, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 624 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, (A.1 * A.2^-2 * A.1^3)^2, A.1^-2 * A.2 * A.1^5 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 624 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1 * A.2, A.1^12, A.2^-1 * A.1^6 * A.2^-3 * A.1^2 ] Chiral 3-polytope with group of order 672 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.1^12, A.2^-1 * A.1^6 * A.2^-1 * A.1 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 720 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4, A.1^12, A.1^2 * A.2^-1 * A.1^4 * A.2^-3 * A.1^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 720 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.2^12 ] Chiral 3-polytope with group of order 732 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, (A.1 * A.2^-2 * A.1^3)^2, A.1^-1 * A.2 * A.1^6 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.2^-1 * A.1 * A.2^-1 * A.1^4 * A.2^-4 * A.1, A.1^2 * A.2^-2 * A.1^3 * A.2^-1 * A.1 * A.2^-3 ] Chiral 3-polytope with group of order 768 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.2^-1 * A.1 * A.2^-1 * A.1^4 * A.2^-4 * A.1, A.2 * A.1 * A.2^-2 * A.1^3 * A.2^-2 * A.1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 768 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.2^-3 * A.1^4 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 768 PSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, A.1^2 * A.2^-1 * A.1^4 * A.2^2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 768 PSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-2 * A.1^5 * A.2^-2 * A.1 * A.2^-1 * A.1, A.1^2 * A.2^-1 * A.1^4 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 780 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 780 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1, A.2^-4 * A.1^2 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 816 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-2 * A.1^5 * A.2^-3 * A.1 * A.2^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^3, A.2^-1 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 840 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2^-2, A.1^12, A.2^-2 * A.1^5 * A.2^-3 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 840 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1, A.1^12 ] Chiral 3-polytope with group of order 876 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.1)^3, A.1^12, (A.1 * A.2^-2 * A.1^3)^2, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 888 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.1 * A.2^-1 * A.1^5 * A.2^-3 * A.1^2 ] Chiral 3-polytope with group of order 912 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^12, A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^-1 * A.1^-3 * A.2^-1 * A.1 * A.2^2 * A.1^-1 ] Chiral 3-polytope with group of order 936 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2 * A.1^-3, A.1^12, A.2^-2 * A.1^5 * A.2^-3 * A.1 * A.2^-1, A.2^12, A.2^-1 * A.1^-1 * A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 936 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.2^12, A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^2 * A.2^-1 * A.1^-2 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 936 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.1^12, A.1^2 * A.2^-1 * A.1^4 * A.2^-1 * A.1 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 936 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1, A.1^12, A.2^-2 * A.1^5 * A.2^-2 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 960 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-2 * A.1^5 * A.2^-3 * A.1 * A.2^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^3, (A.1 * A.2^-1 * A.1 * A.2^-2 * A.1)^2 ] Chiral 3-polytope with group of order 960 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-2 * A.1^5 * A.2^-1 * A.1 * A.2^-1 * A.1^2, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^3 ] Chiral 3-polytope with group of order 960 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1^12, A.2 * A.1^-1 * A.2 * A.1^4 * A.2^-1 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 960 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-2, A.1^12, (A.1 * A.2^-2 * A.1^3)^2 ] Chiral 3-polytope with group of order 972 NSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.1^12, A.2^2 * A.1^5 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 972 PSD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2 * A.1^6 * A.2^-1 * A.1^2 * A.2 * A.1^-1, (A.1 * A.2^-2 * A.1^3)^2 ] Chiral 3-polytope with group of order 972 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-1 * A.1^6 * A.2 * A.1^-2 * A.2^-1 * A.1, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2 * A.1^-1 * A.2^-1 * A.1^2 ] Chiral 3-polytope with group of order 972 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 972 ISD Type [ 12, 12 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.1 * A.2^-1 * A.1^5 * A.2^2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 768 NSD Type [ 12, 16 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2^-1 * A.1 * A.2^-2, A.1^12 ] Chiral 3-polytope with group of order 960 NSD Type [ 12, 16 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1, A.2^16 ] Chiral 3-polytope with group of order 960 NSD Type [ 12, 16 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.1 * A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 216 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-4 ] Chiral 3-polytope with group of order 432 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.1^12, A.2 * A.1 * A.2^-1 * A.1^5 * A.2 * A.1^-2 * A.2^3 ] Chiral 3-polytope with group of order 648 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-4, A.1^12 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1^3, A.2 * A.1 * A.2^-1 * A.1^5 * A.2 * A.1^-1 * A.2^-2 * A.1 * A.2 ] Chiral 3-polytope with group of order 600 NSD Type [ 12, 20 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^3 * A.2 * A.1^-1 * A.2^-6 ] Chiral 3-polytope with group of order 672 NSD Type [ 12, 24 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, A.2^-1 * A.1^6 * A.2^-1 * A.1 * A.2^-2 * A.1, A.2^-2 * A.1^5 * A.2^-3 * A.1 * A.2^-1, A.1 * A.2^-2 * A.1^4 * A.2^-1 * A.1^2 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 672 NSD Type [ 12, 24 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^3 * A.2^4 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 672 NSD Type [ 12, 24 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.1 * A.2^-2 * A.1^4 * A.2^-1 * A.1 * A.2^-3, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-5 ] Chiral 3-polytope with group of order 672 NSD Type [ 12, 24 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.1^12, A.1 * A.2^-2 * A.1^4 * A.2^-1 * A.1 * A.2^-3 ] Chiral 3-polytope with group of order 648 NSD Type [ 12, 27 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.1^12, A.1 * A.2^-4 * A.1^-5 * A.2 * A.1^-1 * A.2^-4 * A.1 ] Chiral 3-polytope with group of order 840 NSD Type [ 12, 28 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1^12, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^-2 * A.2^-1, A.2^2 * A.1 * A.2^-5 * A.1^-3 * A.2^2 * A.1^-2 * A.2^5 ] Chiral 3-polytope with group of order 840 NSD Type [ 12, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^-3 * A.2^6 ] Chiral 3-polytope with group of order 840 NSD Type [ 12, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^12, (A.1 * A.2^-1 * A.1^4)^2, A.2^-1 * A.1 * A.2^-1 * A.1^4 * A.2^-2 * A.1 * A.2^-2, A.2 * A.1 * A.2^-4 * A.1^2 * A.2^-2 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 432 NSD Type [ 12, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^12, A.2^6 * A.1^-3 * A.2^-1 * A.1 * A.2^5 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^12, A.2^-1 * A.1^6 * A.2^-1 * A.1 * A.2^-2 * A.1, A.1^-1 * A.2 * A.1 * A.2^-5 * A.1^-1 * A.2^4 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^3 * A.1^-1, A.1^12, A.2^-1 * A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1^3, A.1^-2 * A.2 * A.1^5 * A.2^-1 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 36 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-2)^2, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1, A.1^12, A.1 * A.2^-4 * A.1^-1 * A.2 * A.1^-5 * A.2^-7 * A.1 ] Chiral 3-polytope with group of order 648 NSD Type [ 12, 54 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^12, A.2^9 * A.1^2 * A.2 * A.1^-1 * A.2^-5 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 72 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^12, A.2^-1 * A.1^6 * A.2^-1 * A.1 * A.2^-2 * A.1, A.2^2 * A.1 * A.2^-4 * A.1^-2 * A.2^-2 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 864 NSD Type [ 12, 72 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^12, A.2^12 * A.1^-1 * A.2^-1 * A.1^2 * A.2^-4 * A.1 * A.2^7 ] Chiral 3-polytope with group of order 702 NSD Type [ 13, 26 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.1^-13 ] Chiral 3-polytope with group of order 702 NSD Type [ 13, 26 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1^-13 ] Chiral 3-polytope with group of order 224 PSD Type [ 14, 14 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^5 * A.2 * A.1^-1 * A.2^2, A.1^-14 ] Chiral 3-polytope with group of order 812 NSD Type [ 14, 14 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.1^-2 * A.2^2 * A.1^3 * A.2 * A.1^-1 * A.2^-3, A.1^14, A.1 * A.2^-1 * A.1^6 * A.2^-2 * A.1^3 * A.2^-1 ] Chiral 3-polytope with group of order 812 NSD Type [ 14, 14 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.2 * A.1^-1 * A.2 * A.1^4 * A.2^-1 * A.1 * A.2 * A.1^-2, A.1^14 ] Chiral 3-polytope with group of order 812 NSD Type [ 14, 14 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-2 * A.2, A.2^3 * A.1^4 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2, A.1^14 ] Chiral 3-polytope with group of order 896 PSD Type [ 14, 14 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1, A.1^14, A.2^-1 * A.1^7 * A.2^-1 * A.1 * A.2^-1 * A.1^3 ] Chiral 3-polytope with group of order 336 NSD Type [ 14, 21 ] [ (A.1^-1 * A.2^-1)^2, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1^-5 * A.2^-1 * A.1 * A.2 * A.1^-2 ] Chiral 3-polytope with group of order 448 NSD Type [ 14, 28 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.1^14 ] Chiral 3-polytope with group of order 560 NSD Type [ 14, 35 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-5 * A.2^3 * A.1^-1 * A.2^-1 ] Chiral 3-polytope with group of order 672 NSD Type [ 14, 42 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^4, A.2^3 * A.1^4 * A.2^-1 * A.1 * A.2^2 * A.1^-1, A.1^14 ] Chiral 3-polytope with group of order 686 NSD Type [ 14, 49 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^3 * A.1^-3 * A.2^-1 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 686 NSD Type [ 14, 49 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1 * A.2^-3 * A.1^-2 * A.2^-4 * A.1 ] Chiral 3-polytope with group of order 686 NSD Type [ 14, 49 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^2 * A.2^-2 * A.1^-2 * A.2^-5 ] Chiral 3-polytope with group of order 896 NSD Type [ 14, 56 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^3 * A.1^-1 * A.2, A.1^-2 * A.2 * A.1^4 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2, A.2 * A.1 * A.2^-2 * A.1^3 * A.2^5, A.1^14 ] Chiral 3-polytope with group of order 240 PSD Type [ 15, 15 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^5 * A.2^2 * A.1^-2, A.1^-1 * A.2^2 * A.1^-9 * A.2 * A.1^-1 * A.2 ] Chiral 3-polytope with group of order 960 PSD Type [ 15, 15 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1 * A.1, A.2 * A.1^7 * A.2 * A.1^-2 * A.2^3, A.1^-15 ] Chiral 3-polytope with group of order 480 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.1^-15 ] Chiral 3-polytope with group of order 930 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^4 * A.1^-1, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^3 * A.1^-1 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2^-1, A.1^-15 ] Chiral 3-polytope with group of order 930 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2 * A.1^-1 * A.2^2, A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2, A.1^-15 ] Chiral 3-polytope with group of order 930 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^2 * A.1^-2 * A.2^-1, A.2 * A.1^7 * A.2^3 * A.1^-3, A.1^-15 ] Chiral 3-polytope with group of order 930 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^4, A.2 * A.1^7 * A.2 * A.1^-1 * A.2^2 * A.1^-2, A.1^-15 ] Chiral 3-polytope with group of order 990 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2 * A.1^-2 * A.2^-1, A.2 * A.1^7 * A.2^2 * A.1^-2 * A.2 * A.1^-1, A.1^-15 ] Chiral 3-polytope with group of order 990 NSD Type [ 15, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2^3 * A.1^-1 * A.2^-1, A.2 * A.1^7 * A.2^2 * A.1^-1 * A.2^3, A.1^-15 ] Chiral 3-polytope with group of order 272 NSD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1^2 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 272 NSD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2^-3 * A.1^2 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 544 NSD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^2 * A.1^-1 * A.2^2, A.1 * A.2^-1 * A.1^9 * A.2^-2 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 544 NSD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2^3 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2 * A.1^-1 * A.2^2, A.1 * A.2^-1 * A.1^8 * A.2^-1 * A.1 * A.2^-4 ] Chiral 3-polytope with group of order 784 ISD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^-2 * A.1^2 * A.2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^-1 * A.1^2 ] Chiral 3-polytope with group of order 784 ISD Type [ 16, 16 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1^7 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 512 NSD Type [ 16, 32 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.1^2 * A.2^-1 * A.1^10 * A.2^-3 ] Chiral 3-polytope with group of order 512 NSD Type [ 16, 32 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2^-4 * A.1^3 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 512 NSD Type [ 16, 32 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2^4 * A.1^3 * A.2^-2 * A.1 * A.2^2, A.1^16 ] Chiral 3-polytope with group of order 324 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^3 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2^-1 * A.1^2 * A.2^-2 * A.1^9 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 684 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2 * A.1^6 * A.2^2 * A.1^-1 * A.2 * A.1^-1, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-7 * A.2^2 * A.1^-1 * A.2 * A.1^-1 ] Chiral 3-polytope with group of order 684 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1 * A.2^-2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.2^3 * A.1^-9 * A.2 * A.1^-3 * A.2^2 ] Chiral 3-polytope with group of order 684 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^-1 * A.1 * A.2, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.2 * A.1^-3 * A.2^2 * A.1^-6 * A.2 * A.1^-1 * A.2^4 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.2^3 * A.1^4 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^-7 * A.2 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1 * A.2^-3 * A.1^2 * A.2^-1 * A.1 * A.2^2, A.1^18 ] Chiral 3-polytope with group of order 972 ISD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^4)^2, A.1 * A.2^-2 * A.1^4 * A.2^-4 * A.1, A.1^-2 * A.2 * A.1^4 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 972 PSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^4)^2, A.1^-2 * A.2 * A.1^4 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.2^3 * A.1^4 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1^-1 * A.2 * A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^-2 * A.2^4 * A.1^-1 * A.2^2, A.2^-5 * A.1^5 * A.2^5 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.2^-5 * A.1^5 * A.2^5 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 18 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.1 * A.2^-2 * A.1^4 * A.2^-2 * A.1 * A.2^-2, A.1 * A.2^-1 * A.1^-1 * A.2^3 * A.1 * A.2^-1 * A.1^-2 * A.2^-3 * A.1 * A.2^2, A.2^2 * A.1 * A.2^-2 * A.1^-1 * A.2^2 * A.1 * A.2^-3 * A.1 * A.2^3 ] Chiral 3-polytope with group of order 432 NSD Type [ 18, 24 ] [ (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^4 * A.2^-2 * A.1 * A.2^-1, A.2^-2 * A.1^2 * A.2^-1 * A.1^2 * A.2^-5 ] Chiral 3-polytope with group of order 864 NSD Type [ 18, 24 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^3 * A.1^5 * A.2^-4 * A.1 * A.2 ] Chiral 3-polytope with group of order 864 NSD Type [ 18, 24 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^2 * A.1^-1 * A.2, A.2^3 * A.1^5 * A.2^-4 * A.1 * A.2 ] Chiral 3-polytope with group of order 486 NSD Type [ 18, 27 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^4 * A.1^-3 * A.2^-1 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 486 NSD Type [ 18, 27 ] [ (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^-3 * A.2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 486 NSD Type [ 18, 27 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-4 * A.2^2 * A.1^-2 ] Chiral 3-polytope with group of order 486 NSD Type [ 18, 27 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^-2 * A.2^3 * A.1^-1 ] Chiral 3-polytope with group of order 540 NSD Type [ 18, 30 ] [ (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^4 * A.2^-2 * A.1 * A.2^-1, A.2^2 * A.1 * A.2^-3 * A.1^2 * A.2^-3 * A.1 * A.2^2 ] Chiral 3-polytope with group of order 648 NSD Type [ 18, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2^4 * A.1 * A.2^-1 * A.1^-2 * A.2^-5 * A.1 * A.2^2, (A.1^4 * A.2^-2 * A.1^3)^2 ] Chiral 3-polytope with group of order 648 NSD Type [ 18, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^2 * A.1^-2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2^4, A.2 * A.1 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^2 * A.1^-1 * A.2, A.1 * A.2^-1 * A.1^-8 * A.2^-1 * A.1 * A.2^-2 * A.1^2, A.2^-2 * A.1^5 * A.2^-1 * A.1^3 * A.2^-1 * A.1^3 * A.2^-2 * A.1 ] Chiral 3-polytope with group of order 756 NSD Type [ 18, 42 ] [ (A.1^-1 * A.2^-1)^2, A.1^-1 * A.2 * A.1^4 * A.2^-2 * A.1 * A.2^-1, A.2^-6 * A.1^2 * A.2^-1 * A.1^2 * A.2^-7 ] Chiral 3-polytope with group of order 810 NSD Type [ 18, 45 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, (A.1^-4 * A.2^2 * A.1^-3)^2, A.2^-3 * A.1^-1 * A.2^4 * A.1^-2 * A.2^6 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 864 NSD Type [ 18, 48 ] [ (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^4 * A.2 * A.1^-1 * A.2^-1 * A.1, A.2^-8 * A.1^-2 * A.2^-4 * A.1 * A.2 * A.1^-1 * A.2^-3 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 54 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-9 * A.2^2 * A.1^-2, A.2^-2 * A.1^-1 * A.2^5 * A.1 * A.2^-1 * A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-1 * A.2^-8 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 54 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.1^2 * A.2^-6 * A.1^7 * A.2^-1 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 54 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-2 * A.2 * A.1^-1, A.2^3 * A.1^4 * A.2 * A.1^-1 * A.2^-1 * A.1 * A.2, A.1^-18 ] Chiral 3-polytope with group of order 972 NSD Type [ 18, 54 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^3 * A.2^4, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.1^-1 * A.2 * A.1^-2 * A.2 * A.1^-9 * A.2^2 * A.1^-2 ] Chiral 3-polytope with group of order 500 ISD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.1 * A.2^-2 * A.1^3 * A.2^-3 * A.1, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 500 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^6 * A.2^-1 * A.1 * A.2^-2 ] Chiral 3-polytope with group of order 500 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^4 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 820 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1 * A.2^-1 * A.1^4 * A.2^-2 * A.1^2 ] Chiral 3-polytope with group of order 820 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2^-2 * A.1^4 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 880 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2^2, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.1^-1 * A.2^2 * A.1^-1 * A.2 * A.1^-9 * A.2 * A.1^-1 * A.2^2 * A.1^-2 ] Chiral 3-polytope with group of order 880 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2^2 * A.1^-1 * A.2 * A.1^2 * A.2^-2 * A.1 * A.2, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2 * A.1^-3 * A.2^-1, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-2 * A.1^9 * A.2^-2 * A.1^2 ] Chiral 3-polytope with group of order 1000 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-3 * A.1 * A.2^4, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^2 * A.1^-3, A.2 * A.1^2 * A.2^-1 * A.1^3 * A.2^2 * A.1^-1 * A.2^2, A.2 * A.1^-1 * A.2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^2 * A.1^-1, A.2 * A.1^7 * A.2 * A.1^-1 * A.2^2 * A.1^-2, A.1^3 * A.2^-3 * A.1^8 * A.2^-1 * A.1^5 ] Chiral 3-polytope with group of order 1000 ISD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.2^-3)^2, A.1 * A.2^-2 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-1, A.1^-1 * A.2^4 * A.1^-6 * A.2^2 * A.1^-1 * A.2^-1 * A.1 * A.2 * A.1^-1 * A.2^-2 ] Chiral 3-polytope with group of order 1000 ISD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2 * A.1^-2 * A.2 * A.1^3 * A.2^-2 * A.1 * A.2^2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^2 * A.1^-2 * A.2^-1, A.1^2 * A.2^-1 * A.1^12 * A.2^-3 * A.1^2 ] Chiral 3-polytope with group of order 1000 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.1^-2 * A.2 * A.1^3 * A.2 * A.1^-1 * A.2^-2, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^3, A.1^2 * A.2^-5 * A.1^11 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 1000 NSD Type [ 20, 20 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2^2 * A.1^2 * A.2^-2 * A.1 * A.2, A.2 * A.1 * A.2^-1 * A.1^4 * A.2 * A.1^-1 * A.2^3, A.1^3 * A.2^-2 * A.1^9 * A.2^-3 * A.1 * A.2^-1 * A.1 ] Chiral 3-polytope with group of order 1000 NSD Type [ 20, 50 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^3 * A.1^-1 * A.2, A.2^-3 * A.1^-1 * A.2 * A.1^3 * A.2^-6 ] Chiral 3-polytope with group of order 1000 NSD Type [ 20, 50 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^3 * A.1^-1 * A.2, A.2^-1 * A.1^-1 * A.2 * A.1 * A.2^-2 * A.1^2 * A.2^-6 ] Chiral 3-polytope with group of order 672 PSD Type [ 21, 21 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-3 * A.2, A.1^-2 * A.2 * A.1^-1 * A.2^4 * A.1^-1 * A.2 * A.1^-6 * A.2^2 * A.1^-1 * A.2^2 ] Chiral 3-polytope with group of order 600 NSD Type [ 24, 24 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^-1 * A.2 * A.1^3 * A.2^-1 * A.1 * A.2 * A.1^-1, A.2^-1 * A.1^6 * A.2^-4 * A.1 ] Chiral 3-polytope with group of order 864 ISD Type [ 24, 24 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2, A.2^-2 * A.1^5 * A.2^-1 * A.1^2 * A.2^-2, A.2^-2 * A.1^-1 * A.2 * A.1^3 * A.2^2 * A.1^-2 * A.2^-1 ] Chiral 3-polytope with group of order 768 NSD Type [ 24, 32 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1 * A.2^-1, A.2 * A.1 * A.2^-1 * A.1^4 * A.2^2 * A.1^-3, A.2^-3 * A.1^-1 * A.2^11 * A.1^-1 * A.2^-2, A.1 * A.2^-1 * A.1^-9 * A.2^6 * A.1^-2 * A.2 ] Chiral 3-polytope with group of order 864 NSD Type [ 24, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2^2 * A.1^-1 * A.2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1 * A.2^-1 * A.1^-1 * A.2^4 * A.1^-2 * A.2^7 ] Chiral 3-polytope with group of order 864 NSD Type [ 24, 36 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2 * A.1^-1, A.1^7 * A.2^-2 * A.1 * A.2^-2, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^2 * A.1^-1, A.2^2 * A.1 * A.2^-4 * A.1^-2 * A.2^-2 * A.1 * A.2^4 ] Chiral 3-polytope with group of order 812 NSD Type [ 28, 28 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^5 * A.2 * A.1^-1 * A.2^2, A.1^-1 * A.2 * A.1^-1 * A.2 * A.1^3 * A.2^-2 * A.1 * A.2^2, A.1^8 * A.2^-1 * A.1 * A.2^-4 ] Chiral 3-polytope with group of order 812 NSD Type [ 28, 28 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2^2 * A.1^2 * A.2 * A.1^-1 * A.2^-2, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.1^8 * A.2^-1 * A.1 * A.2^-1 * A.1^2 * A.2^-1 ] Chiral 3-polytope with group of order 812 NSD Type [ 28, 28 ] [ (A.1^-1 * A.2^-1)^2, A.2 * A.1^6 * A.2^2 * A.1^-1 * A.2 * A.1^-1, A.2^-1 * A.1^-1 * A.2 * A.1^4 * A.2 * A.1^-3 * A.2^-1, A.1^8 * A.2^-1 * A.1 * A.2^-4 ] Chiral 3-polytope with group of order 896 PSD Type [ 28, 28 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-2 * A.2^2, A.1 * A.2^-1 * A.1 * A.2^-9 * A.1 * A.2^-1 * A.1^10 * A.2^-3 * A.1 ] Chiral 3-polytope with group of order 960 PSD Type [ 30, 30 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2 * A.1^-1 * A.2, A.1 * A.2^-1 * A.1^2 * A.2^-10 * A.1 * A.2^-2 * A.1^9 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 992 PSD Type [ 31, 31 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2 * A.1^-2, A.1^4 * A.2^-14 * A.1^9 * A.2^-2 * A.1 * A.2^-1 ] Chiral 3-polytope with group of order 992 PSD Type [ 31, 31 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2^3 * A.1^-1 * A.2, A.1 * A.2^-1 * A.1^2 * A.2^-1 * A.1^10 * A.2^-1 * A.1^2 * A.2^-1 * A.1^7 * A.2^-4 * A.1 ] Chiral 3-polytope with group of order 992 PSD Type [ 31, 31 ] [ (A.1^-1 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^2 * A.2 * A.1^-1 * A.2^-1, A.2 * A.1^6 * A.2 * A.1^-1 * A.2^3, A.1 * A.2^-1 * A.1 * A.2^-1 * A.1^11 * A.2^-1 * A.1 * A.2^-1 * A.1^8 * A.2^-1 * A.1^3 * A.2^-1 ] Rank 4 ...... Chiral 4-polytope with group of order 336 NSD Type [ 3, 3, 6 ] [ A.1^3, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.3^-2 * A.2 * A.3^-1 * A.2 * A.3^3 * A.2 ] Chiral 4-polytope with group of order 192 NSD Type [ 3, 3, 8 ] [ A.1^3, A.2^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 3, 8 ] [ A.1^3, A.2^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.3 * A.1^-1 * A.3)^3 ] Chiral 4-polytope with group of order 120 NSD Type [ 3, 4, 4 ] [ A.1^3, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.3^-2 * A.2^2 * A.3, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1 ] Chiral 4-polytope with group of order 240 NSD Type [ 3, 4, 4 ] [ A.1^3, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.3^2 * A.1, A.3^-1 * A.1^-1 * A.3^-1 * A.1^-1 * A.3^2 * A.2^2 * A.1 ] Chiral 4-polytope with group of order 480 NSD Type [ 3, 4, 4 ] [ A.1^3, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1^-1 * A.3^-1 * A.1^-1 * A.3^2 * A.2^2 * A.1 ] Chiral 4-polytope with group of order 720 NSD Type [ 3, 4, 4 ] [ A.1^3, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.3^2 * A.1 ] Chiral 4-polytope with group of order 576 NSD Type [ 3, 4, 6 ] [ A.1^3, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2 * A.3^-1 * A.2 * A.1 * A.3^-2 * A.1^-1, A.2^-1 * A.3^-3 * A.2 * A.1^-1 * A.3^3 * A.1 ] Chiral 4-polytope with group of order 960 NSD Type [ 3, 4, 8 ] [ A.1^3, A.2^4, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2^-1 * A.3 * A.1^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 720 NSD Type [ 3, 4, 12 ] [ A.1^3, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^2 * A.1 * A.3^-1, (A.2 * A.3^-3)^2 ] Chiral 4-polytope with group of order 720 NSD Type [ 3, 4, 12 ] [ A.1^3, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1^-1 * A.3^-1)^4, (A.2 * A.3^-3)^2, A.3^-1 * A.1^-1 * A.3^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.2^-1 * A.3^-1 ] Chiral 4-polytope with group of order 720 NSD Type [ 3, 4, 12 ] [ A.1^3, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2^-1 * A.3 * A.1^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3, A.3^-2 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.3^-2 * A.1 * A.3^-1 ] Chiral 4-polytope with group of order 336 PSD Type [ 3, 6, 3 ] [ A.1^3, A.2^6, A.3^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1, A.2 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 672 PSD Type [ 3, 6, 3 ] [ A.1^3, A.2^6, A.3^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1, A.3^-1 * A.2^-2 * A.3 * A.2^3 * A.3^-1 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 6, 4 ] [ A.1^3, A.2^6, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.3^-2 * A.2 * A.1 * A.3^2 * A.2, A.2^-1 * A.3 * A.2 * A.1^-1 * A.3 * A.2^-2 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 672 NSD Type [ 3, 6, 6 ] [ A.1^3, A.2^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.2^-1 * A.3^2 * A.2 * A.1^-1 * A.3^3 * A.1 * A.3 ] Chiral 4-polytope with group of order 672 NSD Type [ 3, 6, 6 ] [ A.1^3, A.2^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1, (A.1 * A.2^-1 * A.3 * A.2^-1)^2 ] Chiral 4-polytope with group of order 672 NSD Type [ 3, 6, 6 ] [ A.1^3, A.2^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.2^-2 * A.1 * A.2^-1 * A.1 * A.2^3 * A.1, A.2 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 384 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 384 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1, A.2^2 * A.3^-1 * A.2^2 * A.3^3 ] Chiral 4-polytope with group of order 384 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.3 * A.1^-1 * A.3 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2 * A.3^-1 * A.2 * A.1 * A.3^2 * A.1^-1, (A.2 * A.3^-1 * A.1^-1 * A.3^-1)^2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 6, 8 ] [ A.1^3, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, (A.3 * A.1^-1 * A.3)^3, (A.3 * A.2^-1 * A.3)^3 ] Chiral 4-polytope with group of order 162 NSD Type [ 3, 6, 9 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.3^-1 * A.1)^3 ] Chiral 4-polytope with group of order 486 NSD Type [ 3, 6, 9 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2 * A.3^-1 * A.2^3 * A.3 ] Chiral 4-polytope with group of order 324 NSD Type [ 3, 6, 18 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.1^-1 * A.3 * A.1^-1 * A.3 * A.1^-1 * A.3^4 ] Chiral 4-polytope with group of order 972 NSD Type [ 3, 6, 18 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.3 * A.1^-1 * A.3)^3, A.3^-1 * A.1 * A.3 * A.2^-2 * A.1^-1 * A.3^-1 * A.2 * A.3^-1 * A.2, A.1 * A.3 * A.2 * A.3^-1 * A.2 * A.1^-1 * A.3^4 ] Chiral 4-polytope with group of order 972 NSD Type [ 3, 6, 18 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.1^-1 * A.2^-2 * A.3 * A.2 * A.1^-1 * A.2^3 * A.3^-1, A.3^-1 * A.2^2 * A.1^-1 * A.3^-1 * A.1 * A.3^-4 ] Chiral 4-polytope with group of order 486 NSD Type [ 3, 6, 27 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^3 * A.1^-1 * A.3 * A.2 * A.1^2 * A.2 * A.3^5 ] Chiral 4-polytope with group of order 648 NSD Type [ 3, 6, 36 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^4 * A.1^-1 * A.3 * A.1 * A.3 * A.1^-1 * A.3^2 * A.1 * A.3^4 ] Chiral 4-polytope with group of order 810 NSD Type [ 3, 6, 45 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^-8 * A.1 * A.3^-1 * A.1 * A.3^-1 * A.1 * A.3^-5 ] Chiral 4-polytope with group of order 972 NSD Type [ 3, 6, 54 ] [ A.1^3, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^9 * A.1^-1 * A.3 * A.1^-1 * A.3 * A.1^-1 * A.3^7 ] Chiral 4-polytope with group of order 576 PSD Type [ 3, 8, 3 ] [ A.1^3, A.2^8, A.3^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-3)^2, (A.2 * A.3^-1 * A.2^2)^2, A.2^2 * A.1 * A.3 * A.2^2 * A.1 * A.3 * A.2^-2 * A.1 * A.3 ] Chiral 4-polytope with group of order 864 NSD Type [ 3, 8, 4 ] [ A.1^3, A.2^8, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-3)^2, A.2 * A.1 * A.3 * A.2^-1 * A.1 * A.2^-2 * A.3^-1, A.1^-1 * A.3 * A.2^-1 * A.3^-2 * A.1^-1 * A.3^2 * A.2 * A.3^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 3, 8, 4 ] [ A.1^3, A.2^8, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.3 * A.1 * A.2^-1 * A.1 * A.3^2 * A.2^-1 * A.3, (A.1 * A.2^-3)^2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 8, 8 ] [ A.1^3, A.2^8, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-3)^2, A.2 * A.1 * A.3 * A.2^-1 * A.1 * A.2^-2 * A.3^-1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 8, 8 ] [ A.1^3, A.2^8, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-3)^2, A.2 * A.1 * A.3 * A.2^-1 * A.1 * A.2^-2 * A.3^-1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1 ] Chiral 4-polytope with group of order 720 NSD Type [ 3, 12, 4 ] [ A.1^3, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.3 * A.1 * A.2^-1 * A.1 * A.3^2 * A.2^-1 * A.3, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.2^-1 * A.3^2 * A.1, (A.2 * A.3^-1 * A.2^2)^2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 4 ] [ A.1^3, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.3^-2 * A.2 * A.1 * A.3^2 * A.2, A.1 * A.3 * A.1 * A.2^-1 * A.1 * A.3^2 * A.2^-1 * A.3, A.2 * A.1 * A.2^-2 * A.1 * A.2^3 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3^-1 * A.1 * A.2^-2 * A.1 * A.3^-1 * A.2^2, A.3 * A.2 * A.3^-1 * A.2 * A.1 * A.3^-2 * A.1^-1 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3 * A.2 * A.3^-1 * A.2 * A.1 * A.3^-2 * A.1^-1, A.3^-1 * A.1^-1 * A.3 * A.2 * A.1^-1 * A.3 * A.2^-1 * A.3^-1 * A.1^-1 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1, A.2^2 * A.3^-1 * A.2^2 * A.3^3 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3^-1 * A.1 * A.2^-2 * A.1 * A.3^-1 * A.2^2, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, (A.1^-1 * A.3^-1)^4 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1, (A.1^-1 * A.3^-1)^4 ] Chiral 4-polytope with group of order 768 NSD Type [ 3, 12, 8 ] [ A.1^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1 * A.2^-2 * A.1 * A.2^3, A.2^2 * A.3^-1 * A.2^2 * A.3^3, (A.1 * A.3^-1)^4 ] Chiral 4-polytope with group of order 336 NSD Type [ 4, 3, 6 ] [ A.1^4, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.2 ] Chiral 4-polytope with group of order 576 NSD Type [ 4, 3, 6 ] [ A.1^4, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.3 * A.1^-2 * A.3 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 672 NSD Type [ 4, 3, 6 ] [ A.1^4, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.3^2 * A.2 * A.3^-1 * A.1^-1 * A.3^3 * A.1, A.3 * A.2 * A.1^-2 * A.3 * A.2^-1 * A.3^-1 * A.1^2 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 4, 3, 6 ] [ A.1^4, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, A.1 * A.3^-3 * A.2 * A.1 * A.3^3 * A.2, (A.1^-1 * A.3^-1)^4 ] Chiral 4-polytope with group of order 120 PSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.1^-1 * A.2^-2 * A.1^2 * A.2, A.2 * A.3^-2 * A.2^2 * A.3^-1, A.3 * A.2 * A.1^-1 * A.3^2 * A.1, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1 ] Chiral 4-polytope with group of order 240 NSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2 * A.3^-2 * A.2^2 * A.3^-1, A.3 * A.2 * A.1^-1 * A.3^2 * A.1, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 4-polytope with group of order 400 ISD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.3 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.3^2 * A.1, A.1 * A.3^-2 * A.2 * A.1^-1 * A.2^2 * A.3^2 * A.2 ] Chiral 4-polytope with group of order 480 PSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^2 * A.3^-1, A.3^-1 * A.1^-1 * A.3 * A.1 * A.2^-1 * A.3^2 * A.2 ] Chiral 4-polytope with group of order 480 NSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.2 * A.3^-2 * A.2^2 * A.3^-1, A.3 * A.2 * A.1^-1 * A.3^2 * A.1, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1 ] Chiral 4-polytope with group of order 800 NSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-1 * A.1 * A.2^-1 * A.1^-2 * A.2^2 * A.1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.3^2 * A.2^2 * A.3^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^2 * A.3^-1, A.3^-1 * A.1^-1 * A.3 * A.1 * A.2^-1 * A.3^2 * A.2 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.1^-1 * A.3^-2 * A.2 * A.1^2 * A.3^2 * A.2 * A.1^-1 ] Chiral 4-polytope with group of order 960 PSD Type [ 4, 4, 4 ] [ A.1^4, A.2^4, A.3^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.3^-1 * A.1^-1 * A.3 * A.1 * A.2^-1 * A.3^2 * A.2 ] Chiral 4-polytope with group of order 240 NSD Type [ 4, 4, 6 ] [ A.1^4, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.1^-1 * A.2^-2 * A.1^2 * A.2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2 ] Chiral 4-polytope with group of order 480 NSD Type [ 4, 4, 6 ] [ A.1^4, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^2 * A.3^-1, (A.2 * A.3^-2)^2 ] Chiral 4-polytope with group of order 480 NSD Type [ 4, 4, 6 ] [ A.1^4, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.1^-1 * A.2^-2 * A.1^2 * A.2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2 * A.3^-1 * A.1^2 * A.3^2 * A.1^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 6 ] [ A.1^4, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.1^-1 * A.2 * A.1^-1 * A.2^-2 * A.1^-2 * A.2^2 * A.1^2 * A.2, A.1^-1 * A.2^-1 * A.3 * A.2^-1 * A.1^-2 * A.2^2 * A.1^-1 * A.3^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 6 ] [ A.1^4, A.2^4, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, A.1^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^2 * A.3^-1, A.1^-1 * A.3^-3 * A.1^2 * A.3^3 * A.1^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 8 ] [ A.1^4, A.2^4, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.1^-1 * A.2^-2 * A.1^2 * A.2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-3)^2 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 12 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, (A.2 * A.3^-2)^2, A.3^-1 * A.2^-1 * A.3 * A.1^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^2 * A.3^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 12 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-1 * A.2 * A.1^2 * A.2^2 * A.1^-1, (A.1 * A.3^2 * A.2^-1)^2, (A.1 * A.3^-1)^4, A.1^-1 * A.3^-1 * A.2^-1 * A.3 * A.2 * A.1^-1 * A.2^-1 * A.3^-1 * A.2 * A.3^-1 ] Chiral 4-polytope with group of order 960 NSD Type [ 4, 4, 12 ] [ A.1^4, A.2^4, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.1^-1 * A.2^-2 * A.1^2 * A.2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^2 * A.1^-2 * A.3 * A.2^-1 * A.3^-1 * A.1 * A.3^2 ] Chiral 4-polytope with group of order 672 NSD Type [ 4, 6, 6 ] [ A.1^4, A.2^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.1 * A.3 * A.2^-1 * A.1^2 * A.2 * A.3^-1 * A.2 ] Chiral 4-polytope with group of order 672 NSD Type [ 4, 6, 6 ] [ A.1^4, A.2^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.3^-1 * A.1^-1 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.2 ] Chiral 4-polytope with group of order 672 NSD Type [ 6, 3, 6 ] [ A.1^6, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-1 * A.1)^2, A.3^-2 * A.2 * A.3^-1 * A.2 * A.3^3 * A.2 ] Chiral 4-polytope with group of order 672 PSD Type [ 6, 3, 6 ] [ A.1^6, A.2^3, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.3^-2 * A.1)^2, A.2^-1 * A.1^-2 * A.2 * A.1^3 * A.2^-1 * A.1 ] Chiral 4-polytope with group of order 384 NSD Type [ 6, 3, 8 ] [ A.1^6, A.2^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 384 NSD Type [ 6, 3, 8 ] [ A.1^6, A.2^3, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-1 * A.1)^2, A.3 * A.1^-1 * A.3 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3^-2 * A.2 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.1 * A.3 * A.2^-1 * A.1 * A.3 * A.2^-1 * A.3^-1, A.2^2 * A.3^-1 * A.2^2 * A.3^3 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.3 * A.1^-1 * A.3 * A.2 * A.1^-1 * A.3^-1 * A.1^-1 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, (A.2 * A.3^-3)^2, A.1 * A.3 * A.2 * A.1^-2 * A.3^-2 * A.1 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, (A.2 * A.3^-3)^2, A.1 * A.3 * A.2^-1 * A.1^-2 * A.3 * A.2^-1 * A.3^2 ] Chiral 4-polytope with group of order 768 NSD Type [ 6, 6, 8 ] [ A.1^6, A.2^6, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^2 * A.3^-1 * A.2^2 * A.3^3, A.1 * A.3 * A.2^-1 * A.1^-2 * A.3 * A.2^-1 * A.3^-2 ] Chiral 4-polytope with group of order 324 NSD Type [ 6, 6, 9 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^-1 * A.2^-1 * A.3 * A.1 * A.2^-1 * A.1 * A.3^-1 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 6, 9 ] [ A.1^6, A.2^6, A.3^9, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3 * A.2 * A.3^-1 * A.2^3 * A.3, A.2 * A.1 * A.2^-1 * A.1^2 * A.2^2 * A.1^-1 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 6, 9 ] [ A.1^6, A.2^6, A.3^9, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^-1 * A.2^-1 * A.3 * A.2^3 * A.3^-1 ] Chiral 4-polytope with group of order 648 NSD Type [ 6, 6, 18 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.1^-1 * A.3^-1 * A.1^-1 * A.3^-1 * A.1^2 * A.3^-4 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 6, 27 ] [ A.1^6, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^-4 * A.1^-1 * A.3^-1 * A.1^2 * A.3^-1 * A.1^-1 * A.3^-3 ] Chiral 4-polytope with group of order 324 PSD Type [ 6, 9, 6 ] [ A.1^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1, (A.2 * A.3^-1 * A.2)^2, A.1 * A.3^-3 * A.2 * A.1^-1 * A.3^-1 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 9, 6 ] [ A.1^6, A.2^9, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.1 * A.3^-3 * A.2 * A.1^-1 * A.3^-1, A.2^-1 * A.1^2 * A.2^-1 * A.1^2 * A.2 * A.1^-1 * A.2^-1 * A.1 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 9, 6 ] [ A.1^6, A.2^9, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1, (A.2 * A.3^-1 * A.2)^2, A.3 * A.2^-1 * A.3^-3 * A.1^-1 * A.3^3 * A.1 * A.3 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 9, 6 ] [ A.1^6, A.2^9, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1, (A.2 * A.3^-1 * A.2)^2, A.3^-1 * A.1 * A.3^2 * A.2 * A.1 * A.3^-2 * A.2 * A.3^-1 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 9, 6 ] [ A.1^6, A.2^9, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.1 * A.3 * A.2^-1)^2, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1, A.3 * A.2^-1 * A.3^-3 * A.1^-1 * A.3^3 * A.1 * A.3 ] Chiral 4-polytope with group of order 972 NSD Type [ 6, 9, 18 ] [ A.1^6, A.2^9, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2^-1 * A.1^-1 * A.2 * A.1^3 * A.2^-1, A.3 * A.2 * A.3^-1 * A.2 * A.1 * A.3^-2 * A.1^-1 ] Chiral 4-polytope with group of order 648 PSD Type [ 6, 18, 6 ] [ A.1^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.1 * A.3 * A.2 * A.1^2 * A.2^-1 * A.3^-1 * A.1, A.3^-1 * A.1 * A.3^-1 * A.1^2 * A.3^-1 * A.1 * A.3^-1, A.1 * A.3 * A.2^2 * A.1 * A.2^-1 * A.3^-1 * A.2 ] Chiral 4-polytope with group of order 972 PSD Type [ 6, 27, 6 ] [ A.1^6, A.3^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-2)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-1 * A.2)^2, A.1 * A.3 * A.2 * A.1^2 * A.2^-1 * A.3^-1 * A.1, A.3^-1 * A.1 * A.3^-1 * A.1^2 * A.3^-1 * A.1 * A.3^-1, A.3^-1 * A.2 * A.1 * A.3 * A.2 * A.1^-1 * A.2^-5 ] Chiral 4-polytope with group of order 504 PSD Type [ 7, 7, 7 ] [ A.1^7, A.2^7, A.3^7, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.2 * A.1^-3 * A.2^2 * A.1^-1, A.1 * A.3 * A.1^-2 * A.3 * A.2^-1 * A.3 ] Chiral 4-polytope with group of order 768 NSD Type [ 8, 3, 12 ] [ A.1^8, A.2^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-1 * A.1^2)^2, (A.1 * A.3^2 * A.2^-1)^2, (A.1 * A.3^-1)^4 ] Chiral 4-polytope with group of order 768 NSD Type [ 8, 3, 12 ] [ A.1^8, A.2^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2 * A.1^-1 * A.3 * A.1, (A.1 * A.2^-1 * A.1^2)^2, A.1 * A.3 * A.2 * A.1^2 * A.2^-1 * A.3^-1 * A.1, A.3 * A.2 * A.3^-2 * A.2 * A.3^3 ] Chiral 4-polytope with group of order 720 PSD Type [ 8, 8, 8 ] [ A.1^8, A.2^8, A.3^8, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.2^-1 * A.1^3 * A.2 * A.1^-1 * A.2^-1, A.2^2 * A.3^-1 * A.1^2 * A.3^2 * A.1^-1 ] Chiral 4-polytope with group of order 486 NSD Type [ 9, 6, 9 ] [ A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.3^-1 * A.2^-1 * A.3 * A.1 * A.2^-1 * A.1 * A.3^-1, A.1^-9 ] Chiral 4-polytope with group of order 486 PSD Type [ 9, 6, 9 ] [ A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.2^-3 * A.1^-2 * A.2^-1, (A.3^-1 * A.1)^3 ] Chiral 4-polytope with group of order 486 ISD Type [ 9, 6, 9 ] [ A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.2^-3 * A.1^-2 * A.2^-1, (A.2 * A.3^-2)^2, A.3^-1 * A.2^-1 * A.3 * A.2^3 * A.3^-1 ] Chiral 4-polytope with group of order 648 NSD Type [ 9, 6, 12 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.2^3 * A.3^-1 * A.2, A.1^-1 * A.2^-3 * A.1^2 * A.2, A.3^12 ] Chiral 4-polytope with group of order 810 NSD Type [ 9, 6, 15 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.2^3 * A.3^-1 * A.2, A.1 * A.2^-3 * A.1^-2 * A.2^-1, A.3^-15 ] Chiral 4-polytope with group of order 972 NSD Type [ 9, 6, 18 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.2^-1 * A.1 * A.2^-1 * A.1 * A.2^-2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, (A.2 * A.3^-2)^2, A.1^-1 * A.3^-1 * A.1^-1 * A.3^-1 * A.1^2 * A.3^-4 ] Chiral 4-polytope with group of order 972 NSD Type [ 9, 6, 18 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.3^-1 * A.2^3 * A.3^-1 * A.2, A.1 * A.2^-3 * A.1^-2 * A.2^-1, A.3^18 ] Chiral 4-polytope with group of order 972 NSD Type [ 9, 6, 18 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.2^-3 * A.1^-2 * A.2^-1, (A.2 * A.3^-2)^2, A.1^-1 * A.3 * A.1^-1 * A.3 * A.1^-1 * A.3^4 ] Chiral 4-polytope with group of order 972 NSD Type [ 9, 6, 18 ] [ A.1^9, A.2^6, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1 * A.2^-1 * A.1)^2, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.1 * A.2^-3 * A.1^-2 * A.2^-1, (A.2 * A.3^-2)^2, (A.3^-1 * A.1^-1 * A.3^-1)^3 ] Rank 5 ...... Chiral 5-polytope with group of order 720 ISD Type [ 3, 4, 4, 3 ] [ A.1^3, A.2^4, A.3^4, A.4^3, (A.1^-1 * A.2^-1)^2, (A.2^-1 * A.3^-1)^2, (A.1, A.4), (A.3^-1 * A.4^-1)^2, A.2^-1 * A.3^-2 * A.2^2 * A.3, A.3^-1 * A.2^-2 * A.1^-1 * A.3 * A.1, A.4^-1 * A.3^-2 * A.2^-1 * A.4 * A.2 ]