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}*384b
if this polytope has a name.
Group : SmallGroup(384,5602)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 32, 96, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 768
Vertex Figure Of :
   {2,6,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*192a
   16-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*768e
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 2.
      20 facets:
         8 of {3}*6
         12 of {6}*12
      20 vertex figures:
         12 of {6}*12
         8 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      16 facets:
         16 of {6}*12
      16 vertex figures:
         16 of {6}*12
   P/N, where N=<s0*s1*s0*s1> of order 3.
      12 facets:
         2 of {2}*4
         10 of {6}*12
      12 vertex figures:
         10 of {6}*12
         2 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s2, s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      12 facets:
         4 of {6}*12
         8 of {3}*6
      12 vertex figures:
         4 of {6}*12
         8 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2> of order 8.
      7 facets:
         6 of {3}*6
         1 of {6}*12
      7 vertex figures:
         6 of {3}*6
         1 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s1*s2> of order 24.
      3 facets:
         2 of {3}*6
         1 of {2}*4
      3 vertex figures:
         2 of {3}*6
         1 of {2}*4

Permutation Representation (GAP) :

s0 := (3,5)(4,6);;
s1 := (3,4)(5,8)(6,7);;
s2 := (1,7)(2,8)(3,4)(5,6);;
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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(3,5)(4,6);
s1 := Sym(8)!(3,4)(5,8)(6,7);
s2 := Sym(8)!(1,7)(2,8)(3,4)(5,6);
poly := sub<Sym(8)|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, 
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0 >;

References : None.
to this polytope

Polytope of Type {6,6}

Twisty Puzzle