Polytope of Type {6,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*576c
if this polytope has a name.
Group : SmallGroup(576,8654)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 48, 144, 48
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 1152
Vertex Figure Of :
   {2,6,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*1152g, {6,6}*1152h, {6,6}*1152j
   3-fold covers : {6,18}*1728b, {18,6}*1728c, {6,6}*1728d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1> of order 2.
      24 facets:
         24 of {6}*12
      24 vertex figures:
         24 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2, s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 4.
      12 facets:
         12 of {6}*12
      12 vertex figures:
         12 of {6}*12

Permutation Representation (GAP) : 
s0 := ( 2, 3)( 7, 8)(10,12);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s2 := ( 5,11)( 6, 9)( 7,10)( 8,12);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(12)!( 2, 3)( 7, 8)(10,12);
s1 := Sym(12)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);
s2 := Sym(12)!( 5,11)( 6, 9)( 7,10)( 8,12);
poly := sub<Sym(12)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0 >;
References : None.
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