Polytope of Type {8,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10}*960b
if this polytope has a name.
Group : SmallGroup(960,5713)
Rank : 3
Schlafli Type : {8,10}
Number of vertices, edges, etc : 48, 240, 60
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,10,2} of size 1920
Vertex Figure Of :
   {2,8,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*480a
   4-fold quotients : {4,10}*240b
   8-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,10}*1920a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 3.
      20 facets:
         20 of {8}*16
      16 vertex figures:
         16 of {10}*20
   P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 5.
      12 facets:
         12 of {8}*16
      16 vertex figures:
         8 of {10}*20
         8 of {2}*4

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,10}

Twisty Puzzle