Polytope of Type {5,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240996)
Rank : 3
Schlafli Type : {5,6}
Number of vertices, edges, etc : 160, 480, 192
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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) :
   16-fold quotients : {5,6}*120a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      96 facets:
         96 of {5}*10
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      96 facets:
         96 of {5}*10
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 3.
      64 facets:
         64 of {5}*10
      56 vertex figures:
         52 of {6}*12
         4 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      48 facets:
         48 of {5}*10
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1> of order 8.
      24 facets:
         24 of {5}*10
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 8.
      24 facets:
         24 of {5}*10
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      24 facets:
         24 of {5}*10
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 8.
      24 facets:
         24 of {5}*10
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
      24 facets:
         24 of {5}*10
      20 vertex figures:
         20 of {6}*12
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 12.
      16 facets:
         16 of {5}*10
      16 vertex figures:
         4 of {2}*4
         12 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 16.
      12 facets:
         12 of {5}*10
      10 vertex figures:
         10 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2> of order 16.
      12 facets:
         12 of {5}*10
      10 vertex figures:
         10 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2, s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1> of order 16.
      12 facets:
         12 of {5}*10
      10 vertex figures:
         10 of {6}*12

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {5,6}

Twisty Puzzle