Magma V2.15-15 Thu Feb 16 2012 15:25:31 on mcon007-01 [Seed = 1847412742] Type ? for help. Type -D to quit. > > > //////////////////////// > // Dihedral group D_5 // > //////////////////////// > > G:=Group; > print Order(G); 10 > > > ////////////////////////// > // Free group of rank 3 // > ////////////////////////// > > G:=FreeGroup(3); > print Order(G); Infinity > G:=FreeGroup(3); > print Order(G); Infinity > G:=FreeGroup(3); > G; Finitely presented group G on 3 generators (free) > > > /////////////////////////////// > // Spherical triangle groups // > /////////////////////////////// > > for p in [2..6] do for q in [p..6] do for r in [q..6] do for|for|for> if (1/p)+(1/q)+(1/r) gt 1 then for|for|for|if> G:=Group; for|for|for|if> print p,q,r,":",Order(G); for|for|for|if> end if; for|for|for> end for;end for;end for; 2 2 2 : 4 2 2 3 : 6 2 2 4 : 8 2 2 5 : 10 2 2 6 : 12 2 3 3 : 12 2 3 4 : 24 2 3 5 : 60 > > > ////////////////////////////////////// > // Modular group C2 * C3 = PSL(2,Z) // > ////////////////////////////////////// > > G:=Group< x,y | x^2, y^3 >; > print AbelianQuotient(G); Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 > print AbelianQuotientInvariants(G); [ 6 ] > > H:=sub; > print Index(G,H); 6 > > print CosetTable(G,H); Mapping from: Cartesian Product<{ 1 .. 6 }, GrpFP: G> to { 1 .. 6 } $1 $2 -$2 1. 2 3 4 2. 1 5 6 3. 5 4 1 4. 6 1 3 5. 3 6 2 6. 4 2 5 > f:=CosetAction(G,H); P:=Image(f); print P; Permutation group P acting on a set of cardinality 6 (1, 2)(3, 5)(4, 6) (1, 3, 4)(2, 5, 6) > S:=SchreierGraph(G,H); print S; Edges(S); Digraph Vertex Neighbours 1 2 3 ; 2 1 5 ; 3 4 5 ; 4 1 6 ; 5 3 6 ; 6 2 4 ; {@ [1, 2], [1, 3], [2, 1], [2, 5], [3, 4], [3, 5], [4, 1], [4, 6], [5, 3], [5, 6], [6, 2], [6, 4] @} > > > print Order(G); 0 > K:=Rewrite(G,H); print K; Finitely presented group K on 2 generators Generators as words in group G K.1 = y * x * y^-1 * x K.2 = y^-1 * x * y * x > Relations(K); [] > print AbelianQuotientInvariants(K); [ 0, 0 ] > > > ///////////////////// > // Mystery example // > ///////////////////// > > G:=Group b^-1*a*b*a^-3, c^-1*b*c*b^-2, a*c^2*a*c^2*a*c^-2, > (a*c*a^-1*c*a*b^-1*c^-1)^2, (a*c^-1*a^-1*c^-1*a*c*b)^2, > a*c*a^2*c^-2*a^-1*c*a^-2*c*a^2*b*c^-1 >; > > G; Finitely presented group G on 3 generators Relations a^11 = Id(G) b^5 = Id(G) c^4 = Id(G) (a * c)^7 = Id(G) (a * c^-1)^7 = Id(G) b^-1 * a * b * a^-3 = Id(G) c^-1 * b * c * b^-2 = Id(G) a * c^2 * a * c^2 * a * c^-2 = Id(G) (a * c * a^-1 * c * a * b^-1 * c^-1)^2 = Id(G) (a * c^-1 * a^-1 * c^-1 * a * c * b)^2 = Id(G) a * c * a^2 * c^-2 * a^-1 * c * a^-2 * c * a^2 * b * c^-1 = Id(G) > print Order(G); 0 > n,ct:=ToddCoxeter(G,sub: CosetLimit:=2000000); > Q:=CosetImage(G,sub); > n; 443520 > print Degree(Q),Order(Q); print CompositionFactors(Q); 8064 443520 G | M22 1 > > > /////////////////// > // Trivial group // > /////////////////// > > G:=Group< x | x^67741 = x^84053 = 1 >; > print Order(G); 1 > > > //////////////////////////// > // (2,3,6) Triangle group // > //////////////////////////// > > G:=Group< x,y,z | x*y*z, x^2, y^3, z^6 >; > > G:=Rewrite(G,G); print G; Finitely presented group G on 2 generators Relations G.1^3 = Id(G) (G.2^-1 * G.1^-1)^2 = Id(G) G.2^6 = Id(G) > > > H:=sub; > print Index(G,H); CosetTable(G,H); 6 Mapping from: Cartesian Product<{ 1 .. 6 }, GrpFP: G> to { 1 .. 6 } $1 $2 -$1 -$2 1. 2 3 4 5 2. 4 6 1 3 3. 6 2 5 1 4. 1 5 2 6 5. 3 1 6 4 6. 5 4 3 2 > f:=CosetAction(G,H); P:=Image(f); print P; Permutation group P acting on a set of cardinality 6 (1, 2, 4)(3, 6, 5) (1, 3, 2, 6, 4, 5) > > print Order(G); 0 > > > K:=Rewrite(G,H); print K; Finitely presented group K on 2 generators Generators as words in group G K.1 = (G.2^-1, G.1^-1) K.2 = G.2^2 * G.1^-1 Relations (K.1^-1, K.2^-1) = Id(K) > print AbelianQuotientInvariants(K); [ 0, 0 ] > > > //////////////////////////// > // (2,3,6) Triangle group // > //////////////////////////// > > G:=Group< x,y,z | x*y*z, x^2, y^3, z^6 >; > > L:=LowIndexSubgroups(G,18); > print #L; 43 > > L:=LowIndexSubgroups(G,180); > print #L; 2234 > for i in [1..#L] do Q:=CosetImage(G,L[i]); for> if Index(G,L[i]) in [15,16,17,18] then print Degree(Q), Order(Q); for|if> end if; end for; 15 150 15 150 16 96 18 18 18 54 18 54 18 54 18 216 18 216 18 216 18 216 18 72 18 72 18 216 18 216 > > > ///////////////////////////////////// > // Extended (2,3,7) triangle group // > ///////////////////////////////////// > > G:=Group< a,b,c | a^2, b^2, c^2, (a*b)^2, (b*c)^3, (a*c)^7 >; > > L:=LowIndexSubgroups(G,15); > print #L; 9 > for i in [1..#L] do Q:=CosetImage(G,L[i]); for> print Degree(Q), Order(Q), FactoredOrder(Q); for> end for; 1 1 [] 2 2 [ <2, 1> ] 8 336 [ <2, 4>, <3, 1>, <7, 1> ] 9 504 [ <2, 3>, <3, 2>, <7, 1> ] 14 2184 [ <2, 3>, <3, 1>, <7, 1>, <13, 1> ] 14 2184 [ <2, 3>, <3, 1>, <7, 1>, <13, 1> ] 14 336 [ <2, 4>, <3, 1>, <7, 1> ] 14 1092 [ <2, 2>, <3, 1>, <7, 1>, <13, 1> ] 15 653837184000 [ <2, 10>, <3, 6>, <5, 3>, <7, 2>, <11, 1>, <13, 1> ] > > > ////////////////////////////////////// > // Modular group C2 * C3 = PSL(2,Z) // > ////////////////////////////////////// > > G:=Group< x,y | x^2, y^3 >; > > for n in [1..10] do L:=LowIndexSubgroups(G,n); for> print "Index up to",n," Number of classes of subgroups =",#L; for> end for; Index up to 1 Number of classes of subgroups = 1 Index up to 2 Number of classes of subgroups = 2 Index up to 3 Number of classes of subgroups = 4 Index up to 4 Number of classes of subgroups = 6 Index up to 5 Number of classes of subgroups = 7 Index up to 6 Number of classes of subgroups = 15 Index up to 7 Number of classes of subgroups = 21 Index up to 8 Number of classes of subgroups = 28 Index up to 9 Number of classes of subgroups = 42 Index up to 10 Number of classes of subgroups = 69 > for n in [11..20] do L:=LowIndexSubgroups(G,n); for> print "Index up to",n," Number of classes of subgroups =",#L; for> end for; Index up to 11 Number of classes of subgroups = 95 Index up to 12 Number of classes of subgroups = 175 Index up to 13 Number of classes of subgroups = 308 Index up to 14 Number of classes of subgroups = 478 Index up to 15 Number of classes of subgroups = 826 Index up to 16 Number of classes of subgroups = 1591 Index up to 17 Number of classes of subgroups = 2593 Index up to 18 Number of classes of subgroups = 4769 Index up to 19 Number of classes of subgroups = 9451 Index up to 20 Number of classes of subgroups = 16382 > > > ////////////////////////////////////// > // Modular group C2 * C3 = PSL(2,Z) // > ////////////////////////////////////// > > G:=Group< x,y | x^2, y^3 >; > > n:=20; > L:=LowIndexNormalSubgroups(G,n); > print "Index up to",n," Number of normal subgroups =",#L; Index up to 20 Number of normal subgroups = 7 > for n in [20*t : t in [1..15]] do for> L:=LowIndexNormalSubgroups(G,n); for> print "Index up to",n," Number of normal subgroups =",#L; for> end for; Index up to 20 Number of normal subgroups = 7 Index up to 40 Number of normal subgroups = 9 Index up to 60 Number of normal subgroups = 15 Index up to 80 Number of normal subgroups = 19 Index up to 100 Number of normal subgroups = 21 Index up to 120 Number of normal subgroups = 24 Index up to 140 Number of normal subgroups = 26 Index up to 160 Number of normal subgroups = 30 Index up to 180 Number of normal subgroups = 36 Index up to 200 Number of normal subgroups = 40 Index up to 220 Number of normal subgroups = 42 Index up to 240 Number of normal subgroups = 47 Index up to 260 Number of normal subgroups = 49 Index up to 280 Number of normal subgroups = 49 Index up to 300 Number of normal subgroups = 56 > > > ///////////////////////////////////// > // The Djokovic-Miller amalgam G_5 // > ///////////////////////////////////// > > G5:=Group (p,q),(p,r),(p,s),(q,r),(q,s),p*q*(r*s)^2, > (h,p),h^-1*q*h*r,h^-1*r*h*p*q*r,(s*h)^2, a*p*a*q,a*r*a*s>; > > > > n:=4800; > L:=LowIndexNormalSubgroups(G5,n); > > print "Index up to",n," Number of normal subgroups =",#L; Index up to 4800 Number of normal subgroups = 7 > for i in [1..#L] do Q:=CosetImage(G5,L[i]`Group); for> print i,Order(Q),FactoredOrder(Q); end for; 1 1 [] 2 2 [ <2, 1> ] 3 2 [ <2, 1> ] 4 2 [ <2, 1> ] 5 4 [ <2, 2> ] 6 1440 [ <2, 5>, <3, 2>, <5, 1> ] 7 4320 [ <2, 5>, <3, 3>, <5, 1> ] > > > ////////////////////////////////////////////// > // Reflexible regular maps of genus 2 to 15 // > ////////////////////////////////////////////// > > maxgenus:=15; maxo:=4*maxgenus+2; > > for p in [2..maxo] do for q in [p..maxo] do if (1/p+1/q lt 1/2) then for|for|if> ratio:=(1/2-(1/p+1/q)); lcm:=LCM(2,LCM(p,q)); for|for|if> maxn:=(Floor(4*(maxgenus-1)/ratio) div lcm)*lcm; for|for|if> if maxn gt 0 then for|for|if|if> F:=Group; for|for|if|if> L:=LowIndexNormalSubgroups(F,maxn); for|for|if|if> // print p,q,":",#L,"normal subgroups of index up to",ma\ xn; for|for|if|if> for i in [1..#L] do f:=CosetAction(F,L[i]`Group); Q:=Ima\ ge(f); for|for|if|if|for> if [Order(f(x)) : x in [a,b,c,a*c,a*b,b*c]] eq [2,\ 2,2,2,p,q] then for|for|if|if|for|if> if Index(Q,sub) eq 2 th\ en for|for|if|if|for|if|if> n:=Order(Q); chi:=(n div (2*p)) - (n div 4\ ) + (n div (2*q)); for|for|if|if|for|if|if> g:=(2-chi) div 2; for|for|if|if|for|if|if> print "Genus",g,"map of type",[p,q]; print\ FPGroup(Q); for|for|if|if|for|if|if> end if;end if; for|for|if|if|for> end for; for|for|if|if> end if; for|for|if> end if; end for;end for; Genus 3 map of type [ 3, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^7 = Id($) $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 7 map of type [ 3, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^7 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 14 map of type [ 3, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^7 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 14 map of type [ 3, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^7 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 14 map of type [ 3, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^7 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 2 map of type [ 3, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 = Id($) Genus 3 map of type [ 3, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.2 * $.3)^8 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 = Id($) Genus 5 map of type [ 3, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.2 * $.3)^8 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 8 map of type [ 3, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.2 * $.3)^8 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 8 map of type [ 3, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.2 * $.3)^8 = Id($) $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 10 map of type [ 3, 9 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^9 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 15 map of type [ 3, 9 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.3 * $.2)^9 = Id($) $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 5 map of type [ 3, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 6 map of type [ 3, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^10 = Id($) Genus 13 map of type [ 3, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) ($.2 * $.3)^10 = Id($) $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 3 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 4 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 7 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 9 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 10 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^12 = Id($) Genus 13 map of type [ 3, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.2 * $.3)^12 = Id($) Genus 15 map of type [ 3, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^14 = Id($) Genus 10 map of type [ 3, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 10 map of type [ 3, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 15 map of type [ 3, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 10 map of type [ 3, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 4 map of type [ 4, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2)^5 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 5 map of type [ 4, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2)^5 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) Genus 9 map of type [ 4, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2)^5 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 10 map of type [ 4, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2)^5 = Id($) ($.3 * $.2 * $.1 * $.2)^5 = Id($) Genus 2 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) Genus 3 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) Genus 4 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^6 = Id($) Genus 5 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 6 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2 * $.1 * $.2)^3 = Id($) ($.2 * $.3)^6 = Id($) Genus 9 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 = Id($) Genus 10 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2)^2 = Id($) Genus 10 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 11 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 = Id($) Genus 15 map of type [ 4, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^6 = Id($) ($.2 * $.3 * $.2 * $.1 * $.2 * $.3)^3 = Id($) Genus 10 map of type [ 4, 7 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2 * $.1 * $.2)^3 = Id($) ($.3 * $.2)^7 = Id($) Genus 2 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 3 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^8 = Id($) Genus 3 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 5 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) ($.2 * $.3)^8 = Id($) Genus 5 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) Genus 9 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^8 = Id($) Genus 9 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^8 = Id($) $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 9 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^8 = Id($) Genus 9 map of type [ 4, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.2 * $.3)^8 = Id($) $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 6 map of type [ 4, 9 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.3 * $.2)^9 = Id($) Genus 4 map of type [ 4, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^10 = Id($) Genus 3 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 5 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^12 = Id($) Genus 9 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^12 = Id($) Genus 9 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) Genus 9 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) ($.2 * $.3)^12 = Id($) Genus 10 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.3 * $.2 * $.1 * $.2)^3 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 13 map of type [ 4, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2 * $.3 * $.2)^6 = Id($) Genus 6 map of type [ 4, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^14 = Id($) Genus 12 map of type [ 4, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.3 * $.2)^15 = Id($) Genus 4 map of type [ 4, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 7 map of type [ 4, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^16 = Id($) Genus 7 map of type [ 4, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 4, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) ($.2 * $.3)^16 = Id($) Genus 13 map of type [ 4, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 8 map of type [ 4, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^18 = Id($) Genus 15 map of type [ 4, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^18 = Id($) Genus 5 map of type [ 4, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 9 map of type [ 4, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^20 = Id($) Genus 10 map of type [ 4, 22 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^22 = Id($) Genus 6 map of type [ 4, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 11 map of type [ 4, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^24 = Id($) Genus 11 map of type [ 4, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 12 map of type [ 4, 26 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^26 = Id($) Genus 7 map of type [ 4, 28 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 13 map of type [ 4, 28 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^28 = Id($) Genus 14 map of type [ 4, 30 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^30 = Id($) Genus 8 map of type [ 4, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 15 map of type [ 4, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^32 = Id($) Genus 15 map of type [ 4, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 9 map of type [ 4, 36 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 10 map of type [ 4, 40 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 11 map of type [ 4, 44 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 12 map of type [ 4, 48 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 13 map of type [ 4, 52 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 14 map of type [ 4, 56 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 15 map of type [ 4, 60 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^4 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 4 map of type [ 5, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) ($.3 * $.2)^5 = Id($) ($.3 * $.2 * $.1 * $.2)^3 = Id($) Genus 5 map of type [ 5, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) ($.3 * $.2)^5 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 5, 5 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) ($.3 * $.2)^5 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 9 map of type [ 5, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) Genus 9 map of type [ 5, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.3)^6 = Id($) Genus 2 map of type [ 5, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.1)^5 = Id($) Genus 6 map of type [ 5, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 5, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.2 * $.1)^5 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 2 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2)^6 = Id($) Genus 3 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^6 = Id($) Genus 4 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) Genus 4 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) Genus 4 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) Genus 5 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.3 * $.2 * $.1 * $.2)^3 = Id($) Genus 9 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 10 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 10 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.3 = Id($) Genus 10 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 10 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 11 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 13 map of type [ 6, 6 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) ($.2 * $.3)^6 = Id($) $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 6 map of type [ 6, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 6 map of type [ 6, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^8 = Id($) Genus 11 map of type [ 6, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 11 map of type [ 6, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 = Id($) Genus 7 map of type [ 6, 9 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) ($.3 * $.2)^9 = Id($) Genus 8 map of type [ 6, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^10 = Id($) Genus 15 map of type [ 6, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 4 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^6 = Id($) Genus 7 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 = Id($) Genus 10 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^6 = Id($) Genus 10 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^12 = Id($) Genus 10 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^12 = Id($) Genus 13 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) Genus 13 map of type [ 6, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 12 map of type [ 6, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^14 = Id($) Genus 5 map of type [ 6, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 13 map of type [ 6, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) ($.3 * $.2)^15 = Id($) Genus 14 map of type [ 6, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^6 = Id($) ($.2 * $.3)^16 = Id($) Genus 7 map of type [ 6, 21 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 8 map of type [ 6, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 10 map of type [ 6, 30 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 11 map of type [ 6, 33 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 6, 39 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 14 map of type [ 6, 42 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^6 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 3 map of type [ 7, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) ($.2 * $.1)^7 = Id($) Genus 15 map of type [ 7, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.2 * $.1)^7 = Id($) Genus 2 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 3 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 3 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2)^8 = Id($) Genus 5 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 5 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^8 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) ($.2 * $.3)^8 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^8 = Id($) ($.2 * $.3)^8 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^8 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 = Id($) Genus 9 map of type [ 8, 8 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^8 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2)^2 = Id($) Genus 12 map of type [ 8, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) ($.2 * $.3)^10 = Id($) Genus 8 map of type [ 8, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 = Id($) Genus 15 map of type [ 8, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 15 map of type [ 8, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) ($.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 15 map of type [ 8, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) ($.2 * $.3)^12 = Id($) Genus 15 map of type [ 8, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^8 = Id($) ($.2 * $.3)^12 = Id($) Genus 11 map of type [ 8, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 11 map of type [ 8, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^8 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 14 map of type [ 8, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) ($.1 * $.2)^8 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 8, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 9 map of type [ 8, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^8 = Id($) Genus 15 map of type [ 8, 40 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^8 = Id($) $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 15 map of type [ 8, 40 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^8 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 6 map of type [ 9, 9 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 = Id($) Genus 4 map of type [ 9, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) ($.1 * $.2)^9 = Id($) Genus 10 map of type [ 9, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) ($.2 * $.1)^9 = Id($) Genus 13 map of type [ 9, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) ($.2 * $.1)^9 = Id($) Genus 4 map of type [ 10, 10 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 6 map of type [ 10, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 8 map of type [ 10, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 12 map of type [ 10, 30 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) ($.1 * $.2)^10 = Id($) Genus 14 map of type [ 10, 35 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 5 map of type [ 11, 22 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 3 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 5 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 9 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 9 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 9 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) Genus 13 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) Genus 13 map of type [ 12, 12 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) ($.1 * $.2)^12 = Id($) Genus 10 map of type [ 12, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 6 map of type [ 13, 26 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 6 map of type [ 14, 14 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 9 map of type [ 14, 21 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 12 map of type [ 14, 28 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 15 map of type [ 14, 35 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 = Id($) Genus 12 map of type [ 15, 15 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) Genus 7 map of type [ 15, 30 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 4 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 7 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 7 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 13 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 16, 16 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.3 * $.2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 = Id($) Genus 8 map of type [ 17, 34 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 8 map of type [ 18, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 15 map of type [ 18, 18 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 9 map of type [ 19, 38 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 5 map of type [ 20, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) Genus 9 map of type [ 20, 20 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 10 map of type [ 21, 42 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 10 map of type [ 22, 22 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 15 map of type [ 22, 33 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 11 map of type [ 23, 46 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 6 map of type [ 24, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 11 map of type [ 24, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 11 map of type [ 24, 24 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 12 map of type [ 25, 50 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 12 map of type [ 26, 26 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 27, 54 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 7 map of type [ 28, 28 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 13 map of type [ 28, 28 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 14 map of type [ 29, 58 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 14 map of type [ 30, 30 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 15 map of type [ 31, 62 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 8 map of type [ 32, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 15 map of type [ 32, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.2 * $.1 * $.3 * $.2 * $.1 * $.2 = Id($) $.3 * $.1 * $.2 * $.3 * $.2 * $.1 * $.3 * $.2 * $.3 * $.2 = Id($) $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 = Id($) Genus 15 map of type [ 32, 32 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 9 map of type [ 36, 36 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 = Id($) Genus 10 map of type [ 40, 40 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 11 map of type [ 44, 44 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 12 map of type [ 48, 48 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 13 map of type [ 52, 52 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 14 map of type [ 56, 56 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) Genus 15 map of type [ 60, 60 ] Finitely presented group on 3 generators Relations $.1^2 = Id($) $.2^2 = Id($) $.3^2 = Id($) ($.1 * $.3)^2 = Id($) $.3 * $.1 * $.2 * $.1 * $.3 * $.2 = Id($) $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.1 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.3 * $.2 * $.1 * $.2 = Id($) > > F:=Group; > L:=LowIndexNormalSubgroups(F,24); > > graphs:=[];print ""; > for t in [1..#L] do for> rep:=L[t]`Group; f:=CosetAction(F,rep); Q:=Image(f); for> if (Order(Q) in [20..24]) and (#{1,1^f(a),1^f(b),1^f(c)} eq 4) then for|if> edges:={{1,1^f(u)}^g : u in [a,b,c], g in Q}; for|if> cgs:=Graph; okm:=false; for|if> for gr in graphs do if IsIsomorphic(cgs,gr) then okm:=true;brea\ k gr;end if;end for; for|if> if not(okm) then Append(~graphs,cgs); for|if|if> print #graphs,": Cayley graph of order",Order(cgs), for|if|if|print> "valency",Degree(Rep(VertexSet(cgs))),"girth",Girth(\ cgs),"diameter",Diameter(cgs); for|if|if> end if; for|if> end if; for> end for; 1 : Cayley graph of order 20 valency 3 girth 4 diameter 5 2 : Cayley graph of order 20 valency 3 girth 6 diameter 4 3 : Cayley graph of order 20 valency 3 girth 4 diameter 6 4 : Cayley graph of order 20 valency 3 girth 4 diameter 5 5 : Cayley graph of order 22 valency 3 girth 4 diameter 6 6 : Cayley graph of order 22 valency 3 girth 6 diameter 5 7 : Cayley graph of order 24 valency 3 girth 4 diameter 6 8 : Cayley graph of order 24 valency 3 girth 4 diameter 6 9 : Cayley graph of order 24 valency 3 girth 6 diameter 5 10 : Cayley graph of order 24 valency 3 girth 6 diameter 5 11 : Cayley graph of order 24 valency 3 girth 6 diameter 4 12 : Cayley graph of order 24 valency 3 girth 6 diameter 5 13 : Cayley graph of order 24 valency 3 girth 4 diameter 7 14 : Cayley graph of order 24 valency 3 girth 6 diameter 4 15 : Cayley graph of order 24 valency 3 girth 4 diameter 4 16 : Cayley graph of order 24 valency 3 girth 4 diameter 6 > > F:=Group; > L:=LowIndexNormalSubgroups(F,24); > > graphs2:=[];print ""; > for t in [1..#L] do for> rep:=L[t]`Group; f:=CosetAction(F,rep); Q:=Image(f); for> if (Order(Q) in [20..24]) and (#{1,1^f(x),1^f(y),1^f(y^-1)} eq 4) th\ en for|if> edges:={{1,1^f(u)}^g : u in [x,y,y^-1], g in Q}; for|if> cgs:=Graph; okm:=false; for|if> for gr in graphs2 do if IsIsomorphic(cgs,gr) then okm:=true;bre\ ak gr;end if;end for; for|if> if not(okm) then Append(~graphs2,cgs); for|if|if> print #graphs2,": Cayley graph of order",Order(cgs), for|if|if|print> "valency",Degree(Rep(VertexSet(cgs))),"girth",Girth(\ cgs),"diameter",Diameter(cgs); for|if|if> end if; for|if> end if; for> end for; 1 : Cayley graph of order 20 valency 3 girth 4 diameter 4 2 : Cayley graph of order 20 valency 3 girth 4 diameter 5 3 : Cayley graph of order 20 valency 3 girth 4 diameter 6 4 : Cayley graph of order 22 valency 3 girth 4 diameter 6 5 : Cayley graph of order 22 valency 3 girth 4 diameter 6 6 : Cayley graph of order 24 valency 3 girth 6 diameter 4 7 : Cayley graph of order 24 valency 3 girth 3 diameter 6 8 : Cayley graph of order 24 valency 3 girth 6 diameter 4 9 : Cayley graph of order 24 valency 3 girth 4 diameter 7 10 : Cayley graph of order 24 valency 3 girth 6 diameter 5 11 : Cayley graph of order 24 valency 3 girth 4 diameter 6 12 : Cayley graph of order 24 valency 3 girth 4 diameter 6 13 : Cayley graph of order 24 valency 3 girth 4 diameter 6 > > for i in [1..#graphs] do for j in [1..#graphs2] do for|for> if IsIsomorphic(graphs[i],graphs2[j]) then for|for|if> print "F1 graph",i,"of order",Order(graphs[i]), for|for|if|print> "isomorphic to F2 graph",j,"of order",Order(graphs2[\ j]); for|for|if> end if; for|for> end for;end for; F1 graph 3 of order 20 isomorphic to F2 graph 3 of order 20 F1 graph 4 of order 20 isomorphic to F2 graph 2 of order 20 F1 graph 5 of order 22 isomorphic to F2 graph 4 of order 22 F1 graph 7 of order 24 isomorphic to F2 graph 12 of order 24 F1 graph 8 of order 24 isomorphic to F2 graph 13 of order 24 F1 graph 11 of order 24 isomorphic to F2 graph 6 of order 24 F1 graph 12 of order 24 isomorphic to F2 graph 10 of order 24 F1 graph 13 of order 24 isomorphic to F2 graph 9 of order 24 F1 graph 14 of order 24 isomorphic to F2 graph 8 of order 24 F1 graph 16 of order 24 isomorphic to F2 graph 11 of order 24 > > > //////////////////////////////// > // Cayley graphs of order 128 // > //////////////////////////////// > > graphs:=[]; > > F:=Group; > L:=LowIndexNormalSubgroups(F,128); > print ""; > > for t in [1..#L] do for> rep:=L[t]`Group; f:=CosetAction(F,rep); Q:=Image(f); for> if (Order(Q) eq 128) and (#{1,1^f(x),1^f(y),1^f(y^-1)} eq 4) then for|if> edges:={{1,1^f(u)}^g : u in [x,y,y^-1], g in Q}; for|if> cgs:=Graph; okm:=false; for|if> for gr in graphs do if IsIsomorphic(cgs,gr) then okm:=true;brea\ k gr;end if;end for; for|if> if not(okm) then Append(~graphs,cgs); for|if|if> print #graphs,": Cayley graph of order",Order(cgs), for|if|if|print> "valency",Degree(Rep(VertexSet(cgs))),"girth",Girth(\ cgs),"diameter",Diameter(cgs); for|if|if> end if; for|if> end if; for> end for; 1 : Cayley graph of order 128 valency 3 girth 4 diameter 32 2 : Cayley graph of order 128 valency 3 girth 4 diameter 33 3 : Cayley graph of order 128 valency 3 girth 6 diameter 17 4 : Cayley graph of order 128 valency 3 girth 6 diameter 18 5 : Cayley graph of order 128 valency 3 girth 8 diameter 10 6 : Cayley graph of order 128 valency 3 girth 6 diameter 10 7 : Cayley graph of order 128 valency 3 girth 8 diameter 10 8 : Cayley graph of order 128 valency 3 girth 8 diameter 10 9 : Cayley graph of order 128 valency 3 girth 8 diameter 10 10 : Cayley graph of order 128 valency 3 girth 6 diameter 12 11 : Cayley graph of order 128 valency 3 girth 10 diameter 8 12 : Cayley graph of order 128 valency 3 girth 10 diameter 8 13 : Cayley graph of order 128 valency 3 girth 8 diameter 9 14 : Cayley graph of order 128 valency 3 girth 8 diameter 10 15 : Cayley graph of order 128 valency 3 girth 8 diameter 10 16 : Cayley graph of order 128 valency 3 girth 8 diameter 10 17 : Cayley graph of order 128 valency 3 girth 10 diameter 8 18 : Cayley graph of order 128 valency 3 girth 8 diameter 8 19 : Cayley graph of order 128 valency 3 girth 8 diameter 10 20 : Cayley graph of order 128 valency 3 girth 10 diameter 9 21 : Cayley graph of order 128 valency 3 girth 6 diameter 11 22 : Cayley graph of order 128 valency 3 girth 10 diameter 9 23 : Cayley graph of order 128 valency 3 girth 6 diameter 16 24 : Cayley graph of order 128 valency 3 girth 8 diameter 9 25 : Cayley graph of order 128 valency 3 girth 10 diameter 9 26 : Cayley graph of order 128 valency 3 girth 8 diameter 9 27 : Cayley graph of order 128 valency 3 girth 4 diameter 10 28 : Cayley graph of order 128 valency 3 girth 4 diameter 16 29 : Cayley graph of order 128 valency 3 girth 8 diameter 8 30 : Cayley graph of order 128 valency 3 girth 8 diameter 9 31 : Cayley graph of order 128 valency 3 girth 4 diameter 9 32 : Cayley graph of order 128 valency 3 girth 8 diameter 9 33 : Cayley graph of order 128 valency 3 girth 4 diameter 12 34 : Cayley graph of order 128 valency 3 girth 6 diameter 16 35 : Cayley graph of order 128 valency 3 girth 4 diameter 32 > > > ////////////////////////////////////////////////////// > // Reflexible regular maps of genus 2 to 15 (cont.) // > ////////////////////////////////////////////////////// > > maxgenus:=15; maxo:=4*maxgenus+2; > > for p in [2..maxo] do for q in [p..maxo] do if (1/p+1/q lt 1/2) then for|for|if> ratio:=(1/2-(1/p+1/q)); lcm:=LCM(2,LCM(p,q)); for|for|if> maxn:=(Floor(4*(maxgenus-1)/ratio) div lcm)*lcm; for|for|if> if maxn gt 0 then for|for|if|if> F:=Group; for|for|if|if> L:=LowIndexNormalSubgroups(F,maxn); for|for|if|if> // print p,q,":",#L,"normal subgroups of index up to",ma\ xn; for|for|if|if> for i in [1..#L] do f:=CosetAction(F,L[i]`Group); Q:=Ima\ ge(f); for|for|if|if|for> if [Order(f(x)) : x in [a,b,c,a*c,a*b,b*c]] eq [2,\ 2,2,2,p,q] then for|for|if|if|for|if> if Index(Q,sub) eq 2 th\ en for|for|if|if|for|if|if> n:=Order(Q); chi:=(n div (2*p)) - (n div 4\ ) + (n div (2*q)); for|for|if|if|for|if|if> g:=(2-chi) div 2; for|for|if|if|for|if|if> print "Genus",g,"map of type",[p,q]; // FP\ Group(Q); for|for|if|if|for|if|if> end if;end if; for|for|if|if|for> end for; for|for|if|if> end if; for|for|if> end if; end for;end for; Genus 3 map of type [ 3, 7 ] Genus 7 map of type [ 3, 7 ] Genus 14 map of type [ 3, 7 ] Genus 14 map of type [ 3, 7 ] Genus 14 map of type [ 3, 7 ] Genus 2 map of type [ 3, 8 ] Genus 3 map of type [ 3, 8 ] Genus 5 map of type [ 3, 8 ] Genus 8 map of type [ 3, 8 ] Genus 8 map of type [ 3, 8 ] Genus 10 map of type [ 3, 9 ] Genus 15 map of type [ 3, 9 ] Genus 5 map of type [ 3, 10 ] Genus 6 map of type [ 3, 10 ] Genus 13 map of type [ 3, 10 ] Genus 3 map of type [ 3, 12 ] Genus 4 map of type [ 3, 12 ] Genus 7 map of type [ 3, 12 ] Genus 9 map of type [ 3, 12 ] Genus 10 map of type [ 3, 12 ] Genus 13 map of type [ 3, 12 ] Genus 15 map of type [ 3, 14 ] Genus 10 map of type [ 3, 15 ] Genus 10 map of type [ 3, 18 ] Genus 15 map of type [ 3, 20 ] Genus 10 map of type [ 3, 24 ] Genus 4 map of type [ 4, 5 ] Genus 5 map of type [ 4, 5 ] Genus 9 map of type [ 4, 5 ] Genus 10 map of type [ 4, 5 ] Genus 2 map of type [ 4, 6 ] Genus 3 map of type [ 4, 6 ] Genus 4 map of type [ 4, 6 ] Genus 5 map of type [ 4, 6 ] Genus 6 map of type [ 4, 6 ] Genus 9 map of type [ 4, 6 ] Genus 9 map of type [ 4, 6 ] Genus 10 map of type [ 4, 6 ] Genus 10 map of type [ 4, 6 ] Genus 11 map of type [ 4, 6 ] Genus 15 map of type [ 4, 6 ] Genus 10 map of type [ 4, 7 ] Genus 2 map of type [ 4, 8 ] Genus 3 map of type [ 4, 8 ] Genus 3 map of type [ 4, 8 ] Genus 5 map of type [ 4, 8 ] Genus 5 map of type [ 4, 8 ] Genus 9 map of type [ 4, 8 ] Genus 9 map of type [ 4, 8 ] Genus 9 map of type [ 4, 8 ] Genus 9 map of type [ 4, 8 ] Genus 6 map of type [ 4, 9 ] Genus 4 map of type [ 4, 10 ] Genus 3 map of type [ 4, 12 ] Genus 5 map of type [ 4, 12 ] Genus 9 map of type [ 4, 12 ] Genus 9 map of type [ 4, 12 ] Genus 9 map of type [ 4, 12 ] Genus 10 map of type [ 4, 12 ] Genus 13 map of type [ 4, 12 ] Genus 6 map of type [ 4, 14 ] Genus 12 map of type [ 4, 15 ] Genus 4 map of type [ 4, 16 ] Genus 7 map of type [ 4, 16 ] Genus 7 map of type [ 4, 16 ] Genus 13 map of type [ 4, 16 ] Genus 13 map of type [ 4, 16 ] Genus 8 map of type [ 4, 18 ] Genus 15 map of type [ 4, 18 ] Genus 5 map of type [ 4, 20 ] Genus 9 map of type [ 4, 20 ] Genus 10 map of type [ 4, 22 ] Genus 6 map of type [ 4, 24 ] Genus 11 map of type [ 4, 24 ] Genus 11 map of type [ 4, 24 ] Genus 12 map of type [ 4, 26 ] Genus 7 map of type [ 4, 28 ] Genus 13 map of type [ 4, 28 ] Genus 14 map of type [ 4, 30 ] Genus 8 map of type [ 4, 32 ] Genus 15 map of type [ 4, 32 ] Genus 15 map of type [ 4, 32 ] Genus 9 map of type [ 4, 36 ] Genus 10 map of type [ 4, 40 ] Genus 11 map of type [ 4, 44 ] Genus 12 map of type [ 4, 48 ] Genus 13 map of type [ 4, 52 ] Genus 14 map of type [ 4, 56 ] Genus 15 map of type [ 4, 60 ] Genus 4 map of type [ 5, 5 ] Genus 5 map of type [ 5, 5 ] Genus 9 map of type [ 5, 5 ] Genus 9 map of type [ 5, 6 ] Genus 9 map of type [ 5, 6 ] Genus 2 map of type [ 5, 10 ] Genus 6 map of type [ 5, 10 ] Genus 13 map of type [ 5, 10 ] Genus 2 map of type [ 6, 6 ] Genus 3 map of type [ 6, 6 ] Genus 4 map of type [ 6, 6 ] Genus 4 map of type [ 6, 6 ] Genus 4 map of type [ 6, 6 ] Genus 5 map of type [ 6, 6 ] Genus 9 map of type [ 6, 6 ] Genus 9 map of type [ 6, 6 ] Genus 10 map of type [ 6, 6 ] Genus 10 map of type [ 6, 6 ] Genus 10 map of type [ 6, 6 ] Genus 10 map of type [ 6, 6 ] Genus 11 map of type [ 6, 6 ] Genus 13 map of type [ 6, 6 ] Genus 13 map of type [ 6, 6 ] Genus 6 map of type [ 6, 8 ] Genus 6 map of type [ 6, 8 ] Genus 11 map of type [ 6, 8 ] Genus 11 map of type [ 6, 8 ] Genus 7 map of type [ 6, 9 ] Genus 8 map of type [ 6, 10 ] Genus 15 map of type [ 6, 10 ] Genus 4 map of type [ 6, 12 ] Genus 7 map of type [ 6, 12 ] Genus 10 map of type [ 6, 12 ] Genus 10 map of type [ 6, 12 ] Genus 10 map of type [ 6, 12 ] Genus 13 map of type [ 6, 12 ] Genus 13 map of type [ 6, 12 ] Genus 12 map of type [ 6, 14 ] Genus 5 map of type [ 6, 15 ] Genus 13 map of type [ 6, 15 ] Genus 14 map of type [ 6, 16 ] Genus 7 map of type [ 6, 21 ] Genus 8 map of type [ 6, 24 ] Genus 10 map of type [ 6, 30 ] Genus 11 map of type [ 6, 33 ] Genus 13 map of type [ 6, 39 ] Genus 14 map of type [ 6, 42 ] Genus 3 map of type [ 7, 14 ] Genus 15 map of type [ 7, 14 ] Genus 2 map of type [ 8, 8 ] Genus 3 map of type [ 8, 8 ] Genus 3 map of type [ 8, 8 ] Genus 5 map of type [ 8, 8 ] Genus 5 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 9 map of type [ 8, 8 ] Genus 12 map of type [ 8, 10 ] Genus 8 map of type [ 8, 12 ] Genus 15 map of type [ 8, 12 ] Genus 15 map of type [ 8, 12 ] Genus 15 map of type [ 8, 12 ] Genus 15 map of type [ 8, 12 ] Genus 11 map of type [ 8, 16 ] Genus 11 map of type [ 8, 16 ] Genus 14 map of type [ 8, 20 ] Genus 9 map of type [ 8, 24 ] Genus 9 map of type [ 8, 24 ] Genus 15 map of type [ 8, 40 ] Genus 15 map of type [ 8, 40 ] Genus 6 map of type [ 9, 9 ] Genus 4 map of type [ 9, 18 ] Genus 10 map of type [ 9, 18 ] Genus 13 map of type [ 9, 18 ] Genus 4 map of type [ 10, 10 ] Genus 6 map of type [ 10, 15 ] Genus 8 map of type [ 10, 20 ] Genus 12 map of type [ 10, 30 ] Genus 14 map of type [ 10, 35 ] Genus 5 map of type [ 11, 22 ] Genus 3 map of type [ 12, 12 ] Genus 5 map of type [ 12, 12 ] Genus 9 map of type [ 12, 12 ] Genus 9 map of type [ 12, 12 ] Genus 9 map of type [ 12, 12 ] Genus 13 map of type [ 12, 12 ] Genus 13 map of type [ 12, 12 ] Genus 13 map of type [ 12, 12 ] Genus 10 map of type [ 12, 24 ] Genus 6 map of type [ 13, 26 ] Genus 6 map of type [ 14, 14 ] Genus 9 map of type [ 14, 21 ] Genus 12 map of type [ 14, 28 ] Genus 15 map of type [ 14, 35 ] Genus 12 map of type [ 15, 15 ] Genus 7 map of type [ 15, 30 ] Genus 4 map of type [ 16, 16 ] Genus 7 map of type [ 16, 16 ] Genus 7 map of type [ 16, 16 ] Genus 13 map of type [ 16, 16 ] Genus 13 map of type [ 16, 16 ] Genus 13 map of type [ 16, 16 ] Genus 13 map of type [ 16, 16 ] Genus 8 map of type [ 17, 34 ] Genus 8 map of type [ 18, 18 ] Genus 15 map of type [ 18, 18 ] Genus 9 map of type [ 19, 38 ] Genus 5 map of type [ 20, 20 ] Genus 9 map of type [ 20, 20 ] Genus 10 map of type [ 21, 42 ] Genus 10 map of type [ 22, 22 ] Genus 15 map of type [ 22, 33 ] Genus 11 map of type [ 23, 46 ] Genus 6 map of type [ 24, 24 ] Genus 11 map of type [ 24, 24 ] Genus 11 map of type [ 24, 24 ] Genus 12 map of type [ 25, 50 ] Genus 12 map of type [ 26, 26 ] Genus 13 map of type [ 27, 54 ] Genus 7 map of type [ 28, 28 ] Genus 13 map of type [ 28, 28 ] Genus 14 map of type [ 29, 58 ] Genus 14 map of type [ 30, 30 ] Genus 15 map of type [ 31, 62 ] Genus 8 map of type [ 32, 32 ] Genus 15 map of type [ 32, 32 ] Genus 15 map of type [ 32, 32 ] Genus 9 map of type [ 36, 36 ] Genus 10 map of type [ 40, 40 ] Genus 11 map of type [ 44, 44 ] Genus 12 map of type [ 48, 48 ] Genus 13 map of type [ 52, 52 ] Genus 14 map of type [ 56, 56 ] Genus 15 map of type [ 60, 60 ] > > quit; Total time: 579.439 seconds, Total memory usage: 77.40MB