Polytope of Type {12,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1087527)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 96, 192, 32
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*384b, {12,4}*384c, {6,4}*384a
   4-fold quotients : {6,4}*192a, {12,4}*192b
   8-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {3,2}*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*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 2.
      16 facets:
         16 of {12}*24
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {12}*24
      56 vertex figures:
         40 of {4}*8
         16 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   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.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 4.
      8 facets:
         8 of {12}*24
      32 vertex figures:
         16 of {4}*8
         16 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   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.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   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> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         8 of {2}*4
         20 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      36 vertex figures:
         12 of {4}*8
         24 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         24 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0> of order 4.
      8 facets:
         8 of {12}*24
      32 vertex figures:
         16 of {4}*8
         16 of {2}*4
   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.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 8.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   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.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      14 vertex figures:
         4 of {2}*4
         10 of {4}*8
   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.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0> of order 8.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      14 vertex figures:
         4 of {2}*4
         10 of {4}*8
   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*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      14 vertex figures:
         10 of {4}*8
         4 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 8.
      4 facets:
         4 of {12}*24
      16 vertex figures:
         8 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      14 vertex figures:
         10 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 8.
      4 facets:
         4 of {12}*24
      20 vertex figures:
         16 of {2}*4
         4 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 8.
      4 facets:
         4 of {12}*24
      12 vertex figures:
         12 of {4}*8

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

Twisty Puzzle