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}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5842)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 120, 360, 120
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*720a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      64 facets:
         56 of {6}*12
         8 of {3}*6
      60 vertex figures:
         60 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      60 facets:
         60 of {6}*12
      64 vertex figures:
         56 of {6}*12
         8 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2> of order 3.
      44 facets:
         38 of {6}*12
         6 of {2}*4
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s1*s2*s1*s2> of order 3.
      40 facets:
         40 of {6}*12
      44 vertex figures:
         6 of {2}*4
         38 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 6.
      26 facets:
         8 of {3}*6
         15 of {6}*12
         3 of {2}*4
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 6.
      20 facets:
         20 of {6}*12
      26 vertex figures:
         15 of {6}*12
         8 of {3}*6
         3 of {2}*4
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0> of order 9.
      16 facets:
         12 of {6}*12
         4 of {2}*4
      16 vertex figures:
         4 of {2}*4
         12 of {6}*12

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,6}

Twisty Puzzle