Polytope of Type {10,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 80, 480, 96
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12}*960e
   3-fold quotients : {10,4}*640b
   6-fold quotients : {5,4}*320, {10,4}*320a, {10,4}*320b
   12-fold quotients : {5,4}*160
   16-fold quotients : {10,6}*120
   48-fold quotients : {10,2}*40
   80-fold quotients : {2,6}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
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> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 2.
      48 facets:
         48 of {10}*20
      48 vertex figures:
         32 of {12}*24
         16 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 2.
      48 facets:
         48 of {10}*20
      40 vertex figures:
         40 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      28 vertex figures:
         12 of {12}*24
         16 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      28 vertex figures:
         16 of {6}*12
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      24 vertex figures:
         16 of {12}*24
         8 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {10}*20
      20 vertex figures:
         20 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      14 vertex figures:
         8 of {6}*12
         6 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 8.
      12 facets:
         12 of {10}*20
      14 vertex figures:
         6 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {10}*20
      14 vertex figures:
         8 of {6}*12
         6 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {10}*20
      16 vertex figures:
         12 of {6}*12
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {10}*20
      16 vertex figures:
         12 of {6}*12
         4 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 8.
      12 facets:
         12 of {10}*20
      12 vertex figures:
         8 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 8.
      12 facets:
         12 of {10}*20
      10 vertex figures:
         10 of {12}*24

Permutation Representation (GAP) : 
s0 := (  3,  4)(  7,  8)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)( 26, 77)( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)( 42, 61)( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 83, 84)( 87, 88)( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,145)( 98,146)( 99,148)(100,147)(101,149)(102,150)(103,152)(104,151)(105,158)(106,157)(107,159)(108,160)(109,154)(110,153)(111,155)(112,156)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,142)(122,141)(123,143)(124,144)(125,138)(126,137)(127,139)(128,140)(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)(178,226)(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)(186,237)(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)(202,221)(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(243,244)(247,248)(249,254)(250,253)(251,255)(252,256)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,318)(266,317)(267,319)(268,320)(269,314)(270,313)(271,315)(272,316)(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,302)(282,301)(283,303)(284,304)(285,298)(286,297)(287,299)(288,300)(323,324)(327,328)(329,334)(330,333)(331,335)(332,336)(337,385)(338,386)(339,388)(340,387)(341,389)(342,390)(343,392)(344,391)(345,398)(346,397)(347,399)(348,400)(349,394)(350,393)(351,395)(352,396)(353,369)(354,370)(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)(361,382)(362,381)(363,383)(364,384)(365,378)(366,377)(367,379)(368,380)(403,404)(407,408)(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)(445,458)(446,457)(447,459)(448,460);;
s1 := (  1, 17)(  2, 32)(  3, 22)(  4, 27)(  5, 30)(  6, 19)(  7, 25)(  8, 24)(  9, 23)( 10, 26)( 11, 20)( 12, 29)( 13, 28)( 14, 21)( 15, 31)( 16, 18)( 33, 65)( 34, 80)( 35, 70)( 36, 75)( 37, 78)( 38, 67)( 39, 73)( 40, 72)( 41, 71)( 42, 74)( 43, 68)( 44, 77)( 45, 76)( 46, 69)( 47, 79)( 48, 66)( 50, 64)( 51, 54)( 52, 59)( 53, 62)( 55, 57)( 60, 61)( 81,177)( 82,192)( 83,182)( 84,187)( 85,190)( 86,179)( 87,185)( 88,184)( 89,183)( 90,186)( 91,180)( 92,189)( 93,188)( 94,181)( 95,191)( 96,178)( 97,161)( 98,176)( 99,166)(100,171)(101,174)(102,163)(103,169)(104,168)(105,167)(106,170)(107,164)(108,173)(109,172)(110,165)(111,175)(112,162)(113,225)(114,240)(115,230)(116,235)(117,238)(118,227)(119,233)(120,232)(121,231)(122,234)(123,228)(124,237)(125,236)(126,229)(127,239)(128,226)(129,209)(130,224)(131,214)(132,219)(133,222)(134,211)(135,217)(136,216)(137,215)(138,218)(139,212)(140,221)(141,220)(142,213)(143,223)(144,210)(145,193)(146,208)(147,198)(148,203)(149,206)(150,195)(151,201)(152,200)(153,199)(154,202)(155,196)(156,205)(157,204)(158,197)(159,207)(160,194)(241,257)(242,272)(243,262)(244,267)(245,270)(246,259)(247,265)(248,264)(249,263)(250,266)(251,260)(252,269)(253,268)(254,261)(255,271)(256,258)(273,305)(274,320)(275,310)(276,315)(277,318)(278,307)(279,313)(280,312)(281,311)(282,314)(283,308)(284,317)(285,316)(286,309)(287,319)(288,306)(290,304)(291,294)(292,299)(293,302)(295,297)(300,301)(321,417)(322,432)(323,422)(324,427)(325,430)(326,419)(327,425)(328,424)(329,423)(330,426)(331,420)(332,429)(333,428)(334,421)(335,431)(336,418)(337,401)(338,416)(339,406)(340,411)(341,414)(342,403)(343,409)(344,408)(345,407)(346,410)(347,404)(348,413)(349,412)(350,405)(351,415)(352,402)(353,465)(354,480)(355,470)(356,475)(357,478)(358,467)(359,473)(360,472)(361,471)(362,474)(363,468)(364,477)(365,476)(366,469)(367,479)(368,466)(369,449)(370,464)(371,454)(372,459)(373,462)(374,451)(375,457)(376,456)(377,455)(378,458)(379,452)(380,461)(381,460)(382,453)(383,463)(384,450)(385,433)(386,448)(387,438)(388,443)(389,446)(390,435)(391,441)(392,440)(393,439)(394,442)(395,436)(396,445)(397,444)(398,437)(399,447)(400,434);;
s2 := (  1,325)(  2,326)(  3,327)(  4,328)(  5,321)(  6,322)(  7,323)(  8,324)(  9,333)( 10,334)( 11,335)( 12,336)( 13,329)( 14,330)( 15,331)( 16,332)( 17,341)( 18,342)( 19,343)( 20,344)( 21,337)( 22,338)( 23,339)( 24,340)( 25,349)( 26,350)( 27,351)( 28,352)( 29,345)( 30,346)( 31,347)( 32,348)( 33,357)( 34,358)( 35,359)( 36,360)( 37,353)( 38,354)( 39,355)( 40,356)( 41,365)( 42,366)( 43,367)( 44,368)( 45,361)( 46,362)( 47,363)( 48,364)( 49,373)( 50,374)( 51,375)( 52,376)( 53,369)( 54,370)( 55,371)( 56,372)( 57,381)( 58,382)( 59,383)( 60,384)( 61,377)( 62,378)( 63,379)( 64,380)( 65,389)( 66,390)( 67,391)( 68,392)( 69,385)( 70,386)( 71,387)( 72,388)( 73,397)( 74,398)( 75,399)( 76,400)( 77,393)( 78,394)( 79,395)( 80,396)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)( 96,252)( 97,261)( 98,262)( 99,263)(100,264)(101,257)(102,258)(103,259)(104,260)(105,269)(106,270)(107,271)(108,272)(109,265)(110,266)(111,267)(112,268)(113,277)(114,278)(115,279)(116,280)(117,273)(118,274)(119,275)(120,276)(121,285)(122,286)(123,287)(124,288)(125,281)(126,282)(127,283)(128,284)(129,293)(130,294)(131,295)(132,296)(133,289)(134,290)(135,291)(136,292)(137,301)(138,302)(139,303)(140,304)(141,297)(142,298)(143,299)(144,300)(145,309)(146,310)(147,311)(148,312)(149,305)(150,306)(151,307)(152,308)(153,317)(154,318)(155,319)(156,320)(157,313)(158,314)(159,315)(160,316)(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)(168,404)(169,413)(170,414)(171,415)(172,416)(173,409)(174,410)(175,411)(176,412)(177,421)(178,422)(179,423)(180,424)(181,417)(182,418)(183,419)(184,420)(185,429)(186,430)(187,431)(188,432)(189,425)(190,426)(191,427)(192,428)(193,437)(194,438)(195,439)(196,440)(197,433)(198,434)(199,435)(200,436)(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)(208,444)(209,453)(210,454)(211,455)(212,456)(213,449)(214,450)(215,451)(216,452)(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)(224,460)(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)(232,468)(233,477)(234,478)(235,479)(236,480)(237,473)(238,474)(239,475)(240,476);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(480)!(  3,  4)(  7,  8)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 78)( 26, 77)( 27, 79)( 28, 80)( 29, 74)( 30, 73)( 31, 75)( 32, 76)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 62)( 42, 61)( 43, 63)( 44, 64)( 45, 58)( 46, 57)( 47, 59)( 48, 60)( 83, 84)( 87, 88)( 89, 94)( 90, 93)( 91, 95)( 92, 96)( 97,145)( 98,146)( 99,148)(100,147)(101,149)(102,150)(103,152)(104,151)(105,158)(106,157)(107,159)(108,160)(109,154)(110,153)(111,155)(112,156)(113,129)(114,130)(115,132)(116,131)(117,133)(118,134)(119,136)(120,135)(121,142)(122,141)(123,143)(124,144)(125,138)(126,137)(127,139)(128,140)(163,164)(167,168)(169,174)(170,173)(171,175)(172,176)(177,225)(178,226)(179,228)(180,227)(181,229)(182,230)(183,232)(184,231)(185,238)(186,237)(187,239)(188,240)(189,234)(190,233)(191,235)(192,236)(193,209)(194,210)(195,212)(196,211)(197,213)(198,214)(199,216)(200,215)(201,222)(202,221)(203,223)(204,224)(205,218)(206,217)(207,219)(208,220)(243,244)(247,248)(249,254)(250,253)(251,255)(252,256)(257,305)(258,306)(259,308)(260,307)(261,309)(262,310)(263,312)(264,311)(265,318)(266,317)(267,319)(268,320)(269,314)(270,313)(271,315)(272,316)(273,289)(274,290)(275,292)(276,291)(277,293)(278,294)(279,296)(280,295)(281,302)(282,301)(283,303)(284,304)(285,298)(286,297)(287,299)(288,300)(323,324)(327,328)(329,334)(330,333)(331,335)(332,336)(337,385)(338,386)(339,388)(340,387)(341,389)(342,390)(343,392)(344,391)(345,398)(346,397)(347,399)(348,400)(349,394)(350,393)(351,395)(352,396)(353,369)(354,370)(355,372)(356,371)(357,373)(358,374)(359,376)(360,375)(361,382)(362,381)(363,383)(364,384)(365,378)(366,377)(367,379)(368,380)(403,404)(407,408)(409,414)(410,413)(411,415)(412,416)(417,465)(418,466)(419,468)(420,467)(421,469)(422,470)(423,472)(424,471)(425,478)(426,477)(427,479)(428,480)(429,474)(430,473)(431,475)(432,476)(433,449)(434,450)(435,452)(436,451)(437,453)(438,454)(439,456)(440,455)(441,462)(442,461)(443,463)(444,464)(445,458)(446,457)(447,459)(448,460);
s1 := Sym(480)!(  1, 17)(  2, 32)(  3, 22)(  4, 27)(  5, 30)(  6, 19)(  7, 25)(  8, 24)(  9, 23)( 10, 26)( 11, 20)( 12, 29)( 13, 28)( 14, 21)( 15, 31)( 16, 18)( 33, 65)( 34, 80)( 35, 70)( 36, 75)( 37, 78)( 38, 67)( 39, 73)( 40, 72)( 41, 71)( 42, 74)( 43, 68)( 44, 77)( 45, 76)( 46, 69)( 47, 79)( 48, 66)( 50, 64)( 51, 54)( 52, 59)( 53, 62)( 55, 57)( 60, 61)( 81,177)( 82,192)( 83,182)( 84,187)( 85,190)( 86,179)( 87,185)( 88,184)( 89,183)( 90,186)( 91,180)( 92,189)( 93,188)( 94,181)( 95,191)( 96,178)( 97,161)( 98,176)( 99,166)(100,171)(101,174)(102,163)(103,169)(104,168)(105,167)(106,170)(107,164)(108,173)(109,172)(110,165)(111,175)(112,162)(113,225)(114,240)(115,230)(116,235)(117,238)(118,227)(119,233)(120,232)(121,231)(122,234)(123,228)(124,237)(125,236)(126,229)(127,239)(128,226)(129,209)(130,224)(131,214)(132,219)(133,222)(134,211)(135,217)(136,216)(137,215)(138,218)(139,212)(140,221)(141,220)(142,213)(143,223)(144,210)(145,193)(146,208)(147,198)(148,203)(149,206)(150,195)(151,201)(152,200)(153,199)(154,202)(155,196)(156,205)(157,204)(158,197)(159,207)(160,194)(241,257)(242,272)(243,262)(244,267)(245,270)(246,259)(247,265)(248,264)(249,263)(250,266)(251,260)(252,269)(253,268)(254,261)(255,271)(256,258)(273,305)(274,320)(275,310)(276,315)(277,318)(278,307)(279,313)(280,312)(281,311)(282,314)(283,308)(284,317)(285,316)(286,309)(287,319)(288,306)(290,304)(291,294)(292,299)(293,302)(295,297)(300,301)(321,417)(322,432)(323,422)(324,427)(325,430)(326,419)(327,425)(328,424)(329,423)(330,426)(331,420)(332,429)(333,428)(334,421)(335,431)(336,418)(337,401)(338,416)(339,406)(340,411)(341,414)(342,403)(343,409)(344,408)(345,407)(346,410)(347,404)(348,413)(349,412)(350,405)(351,415)(352,402)(353,465)(354,480)(355,470)(356,475)(357,478)(358,467)(359,473)(360,472)(361,471)(362,474)(363,468)(364,477)(365,476)(366,469)(367,479)(368,466)(369,449)(370,464)(371,454)(372,459)(373,462)(374,451)(375,457)(376,456)(377,455)(378,458)(379,452)(380,461)(381,460)(382,453)(383,463)(384,450)(385,433)(386,448)(387,438)(388,443)(389,446)(390,435)(391,441)(392,440)(393,439)(394,442)(395,436)(396,445)(397,444)(398,437)(399,447)(400,434);
s2 := Sym(480)!(  1,325)(  2,326)(  3,327)(  4,328)(  5,321)(  6,322)(  7,323)(  8,324)(  9,333)( 10,334)( 11,335)( 12,336)( 13,329)( 14,330)( 15,331)( 16,332)( 17,341)( 18,342)( 19,343)( 20,344)( 21,337)( 22,338)( 23,339)( 24,340)( 25,349)( 26,350)( 27,351)( 28,352)( 29,345)( 30,346)( 31,347)( 32,348)( 33,357)( 34,358)( 35,359)( 36,360)( 37,353)( 38,354)( 39,355)( 40,356)( 41,365)( 42,366)( 43,367)( 44,368)( 45,361)( 46,362)( 47,363)( 48,364)( 49,373)( 50,374)( 51,375)( 52,376)( 53,369)( 54,370)( 55,371)( 56,372)( 57,381)( 58,382)( 59,383)( 60,384)( 61,377)( 62,378)( 63,379)( 64,380)( 65,389)( 66,390)( 67,391)( 68,392)( 69,385)( 70,386)( 71,387)( 72,388)( 73,397)( 74,398)( 75,399)( 76,400)( 77,393)( 78,394)( 79,395)( 80,396)( 81,245)( 82,246)( 83,247)( 84,248)( 85,241)( 86,242)( 87,243)( 88,244)( 89,253)( 90,254)( 91,255)( 92,256)( 93,249)( 94,250)( 95,251)( 96,252)( 97,261)( 98,262)( 99,263)(100,264)(101,257)(102,258)(103,259)(104,260)(105,269)(106,270)(107,271)(108,272)(109,265)(110,266)(111,267)(112,268)(113,277)(114,278)(115,279)(116,280)(117,273)(118,274)(119,275)(120,276)(121,285)(122,286)(123,287)(124,288)(125,281)(126,282)(127,283)(128,284)(129,293)(130,294)(131,295)(132,296)(133,289)(134,290)(135,291)(136,292)(137,301)(138,302)(139,303)(140,304)(141,297)(142,298)(143,299)(144,300)(145,309)(146,310)(147,311)(148,312)(149,305)(150,306)(151,307)(152,308)(153,317)(154,318)(155,319)(156,320)(157,313)(158,314)(159,315)(160,316)(161,405)(162,406)(163,407)(164,408)(165,401)(166,402)(167,403)(168,404)(169,413)(170,414)(171,415)(172,416)(173,409)(174,410)(175,411)(176,412)(177,421)(178,422)(179,423)(180,424)(181,417)(182,418)(183,419)(184,420)(185,429)(186,430)(187,431)(188,432)(189,425)(190,426)(191,427)(192,428)(193,437)(194,438)(195,439)(196,440)(197,433)(198,434)(199,435)(200,436)(201,445)(202,446)(203,447)(204,448)(205,441)(206,442)(207,443)(208,444)(209,453)(210,454)(211,455)(212,456)(213,449)(214,450)(215,451)(216,452)(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)(224,460)(225,469)(226,470)(227,471)(228,472)(229,465)(230,466)(231,467)(232,468)(233,477)(234,478)(235,479)(236,480)(237,473)(238,474)(239,475)(240,476);
poly := sub<Sym(480)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle