Polytope of Type {6,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240996)
Rank : 3
Schlafli Type : {6,8}
Number of vertices, edges, etc : 120, 480, 160
Order of s0s1s2 : 5
Order of s0s1s2s1 : 6
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 : {6,4}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      72 vertex figures:
         48 of {8}*16
         24 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 2.
      80 facets:
         80 of {6}*12
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s0*s1> of order 3.
      56 facets:
         4 of {2}*4
         52 of {6}*12
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 4.
      40 facets:
         40 of {6}*12
      42 vertex figures:
         24 of {4}*8
         18 of {8}*16
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
      40 facets:
         40 of {6}*12
      36 vertex figures:
         24 of {8}*16
         12 of {4}*8
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      40 facets:
         40 of {6}*12
      30 vertex figures:
         30 of {8}*16
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0> of order 4.
      40 facets:
         40 of {6}*12
      38 vertex figures:
         24 of {8}*16
         4 of {2}*4
         10 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 8.
      20 facets:
         20 of {6}*12
      18 vertex figures:
         12 of {8}*16
         6 of {4}*8
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 8.
      20 facets:
         20 of {6}*12
      24 vertex figures:
         18 of {4}*8
         6 of {8}*16
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0> of order 8.
      20 facets:
         20 of {6}*12
      21 vertex figures:
         12 of {8}*16
         6 of {2}*4
         3 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0> of order 8.
      20 facets:
         20 of {6}*12
      20 vertex figures:
         12 of {8}*16
         4 of {2}*4
         4 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2, s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      20 facets:
         20 of {6}*12
      18 vertex figures:
         12 of {8}*16
         6 of {4}*8
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 12.
      16 facets:
         4 of {2}*4
         12 of {6}*12
      10 vertex figures:
         10 of {8}*16

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