Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*432h
if this polytope has a name.
Group : SmallGroup(432,741)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 18, 108, 36
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,12,2} of size 864
   {6,12,4} of size 1728
Vertex Figure Of :
   {2,6,12} of size 864
   {4,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4}*144
   6-fold quotients : {6,4}*72
   27-fold quotients : {2,4}*16
   54-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*864j, {6,24}*864g
   3-fold covers : {6,12}*1296k, {6,12}*1296m, {6,12}*1296n, {6,12}*1296s, {6,12}*1296u
   4-fold covers : {24,12}*1728q, {24,12}*1728r, {6,48}*1728g, {12,24}*1728s, {12,24}*1728t, {12,12}*1728q, {6,12}*1728j
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);;
s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(14,15)(17,18);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(18)!( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,11)( 8,10)( 9,12);
s2 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(14,15)(17,18);
poly := sub<Sym(18)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope