Polytope of Type {12,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope