Polytope of Type {4,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*768b
if this polytope has a name.
Group : SmallGroup(768,1087527)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 32, 192, 96
Order of s0s1s2 : 12
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 : {4,12}*384b, {4,12}*384c, {4,6}*384a
   4-fold quotients : {4,6}*192a, {4,12}*192b
   8-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
   16-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,4}*16
   64-fold quotients : {2,3}*12
   96-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=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s1> of order 2.
      56 facets:
         16 of {2}*4
         40 of {4}*8
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      32 facets:
         16 of {2}*4
         16 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      28 facets:
         20 of {4}*8
         8 of {2}*4
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      28 facets:
         20 of {4}*8
         8 of {2}*4
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      36 facets:
         24 of {2}*4
         12 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 4.
      28 facets:
         8 of {2}*4
         20 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {4}*8
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      32 facets:
         16 of {4}*8
         16 of {2}*4
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1, s0*s2*s1*s0*s2*s1*s2*s1*s0*s1> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      16 facets:
         8 of {2}*4
         8 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      16 facets:
         8 of {2}*4
         8 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      14 facets:
         10 of {4}*8
         4 of {2}*4
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      16 facets:
         8 of {4}*8
         8 of {2}*4
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      16 facets:
         8 of {4}*8
         8 of {2}*4
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      14 facets:
         10 of {4}*8
         4 of {2}*4
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      14 facets:
         4 of {2}*4
         10 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      16 facets:
         8 of {2}*4
         8 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      14 facets:
         4 of {2}*4
         10 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1> of order 8.
      20 facets:
         16 of {2}*4
         4 of {4}*8
      4 vertex figures:
         4 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {4}*8
      4 vertex figures:
         4 of {12}*24

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

Twisty Puzzle