Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1152j
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 48, 288, 96
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {3,12}*576
   4-fold quotients : {6,6}*288b, {6,12}*288b
   8-fold quotients : {3,6}*144, {3,12}*144
   12-fold quotients : {6,4}*96, {6,6}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {3,4}*48, {3,6}*48, {6,3}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,3}*24, {3,4}*24, {6,2}*24
   96-fold quotients : {3,2}*12
   144-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*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      32 vertex figures:
         16 of {12}*24
         16 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 3.
      32 facets:
         32 of {6}*12
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3.
      32 facets:
         32 of {6}*12
      24 vertex figures:
         12 of {12}*24
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      24 vertex figures:
         8 of {12}*24
         16 of {3}*6
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 4.
      24 facets:
         24 of {6}*12
      16 vertex figures:
         8 of {12}*24
         8 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         6 of {12}*24
         6 of {4}*8
   P/N, where N=<s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         6 of {12}*24
         6 of {4}*8
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      16 vertex figures:
         4 of {12}*24
         4 of {4}*8
         4 of {6}*12
         4 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1, s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      12 facets:
         12 of {6}*12
      8 vertex figures:
         4 of {12}*24
         4 of {6}*12

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)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);;
s1 := (  1,209)(  2,212)(  3,211)(  4,210)(  5,221)(  6,224)(  7,223)(  8,222)(  9,217)( 10,220)( 11,219)( 12,218)( 13,213)( 14,216)( 15,215)( 16,214)( 17,193)( 18,196)( 19,195)( 20,194)( 21,205)( 22,208)( 23,207)( 24,206)( 25,201)( 26,204)( 27,203)( 28,202)( 29,197)( 30,200)( 31,199)( 32,198)( 33,225)( 34,228)( 35,227)( 36,226)( 37,237)( 38,240)( 39,239)( 40,238)( 41,233)( 42,236)( 43,235)( 44,234)( 45,229)( 46,232)( 47,231)( 48,230)( 49,161)( 50,164)( 51,163)( 52,162)( 53,173)( 54,176)( 55,175)( 56,174)( 57,169)( 58,172)( 59,171)( 60,170)( 61,165)( 62,168)( 63,167)( 64,166)( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)( 72,158)( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)( 80,150)( 81,177)( 82,180)( 83,179)( 84,178)( 85,189)( 86,192)( 87,191)( 88,190)( 89,185)( 90,188)( 91,187)( 92,186)( 93,181)( 94,184)( 95,183)( 96,182)( 97,257)( 98,260)( 99,259)(100,258)(101,269)(102,272)(103,271)(104,270)(105,265)(106,268)(107,267)(108,266)(109,261)(110,264)(111,263)(112,262)(113,241)(114,244)(115,243)(116,242)(117,253)(118,256)(119,255)(120,254)(121,249)(122,252)(123,251)(124,250)(125,245)(126,248)(127,247)(128,246)(129,273)(130,276)(131,275)(132,274)(133,285)(134,288)(135,287)(136,286)(137,281)(138,284)(139,283)(140,282)(141,277)(142,280)(143,279)(144,278);;
s2 := (  1,  6)(  2,  5)(  3,  7)(  4,  8)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 30)( 26, 29)( 27, 31)( 28, 32)( 33, 38)( 34, 37)( 35, 39)( 36, 40)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,102)( 50,101)( 51,103)( 52,104)( 53, 98)( 54, 97)( 55, 99)( 56,100)( 57,110)( 58,109)( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,118)( 66,117)( 67,119)( 68,120)( 69,114)( 70,113)( 71,115)( 72,116)( 73,126)( 74,125)( 75,127)( 76,128)( 77,122)( 78,121)( 79,123)( 80,124)( 81,134)( 82,133)( 83,135)( 84,136)( 85,130)( 86,129)( 87,131)( 88,132)( 89,142)( 90,141)( 91,143)( 92,144)( 93,138)( 94,137)( 95,139)( 96,140)(145,150)(146,149)(147,151)(148,152)(153,158)(154,157)(155,159)(156,160)(161,166)(162,165)(163,167)(164,168)(169,174)(170,173)(171,175)(172,176)(177,182)(178,181)(179,183)(180,184)(185,190)(186,189)(187,191)(188,192)(193,246)(194,245)(195,247)(196,248)(197,242)(198,241)(199,243)(200,244)(201,254)(202,253)(203,255)(204,256)(205,250)(206,249)(207,251)(208,252)(209,262)(210,261)(211,263)(212,264)(213,258)(214,257)(215,259)(216,260)(217,270)(218,269)(219,271)(220,272)(221,266)(222,265)(223,267)(224,268)(225,278)(226,277)(227,279)(228,280)(229,274)(230,273)(231,275)(232,276)(233,286)(234,285)(235,287)(236,288)(237,282)(238,281)(239,283)(240,284);;
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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(288)!(  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)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)(237,265)(238,266)(239,268)(240,267);
s1 := Sym(288)!(  1,209)(  2,212)(  3,211)(  4,210)(  5,221)(  6,224)(  7,223)(  8,222)(  9,217)( 10,220)( 11,219)( 12,218)( 13,213)( 14,216)( 15,215)( 16,214)( 17,193)( 18,196)( 19,195)( 20,194)( 21,205)( 22,208)( 23,207)( 24,206)( 25,201)( 26,204)( 27,203)( 28,202)( 29,197)( 30,200)( 31,199)( 32,198)( 33,225)( 34,228)( 35,227)( 36,226)( 37,237)( 38,240)( 39,239)( 40,238)( 41,233)( 42,236)( 43,235)( 44,234)( 45,229)( 46,232)( 47,231)( 48,230)( 49,161)( 50,164)( 51,163)( 52,162)( 53,173)( 54,176)( 55,175)( 56,174)( 57,169)( 58,172)( 59,171)( 60,170)( 61,165)( 62,168)( 63,167)( 64,166)( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)( 72,158)( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)( 80,150)( 81,177)( 82,180)( 83,179)( 84,178)( 85,189)( 86,192)( 87,191)( 88,190)( 89,185)( 90,188)( 91,187)( 92,186)( 93,181)( 94,184)( 95,183)( 96,182)( 97,257)( 98,260)( 99,259)(100,258)(101,269)(102,272)(103,271)(104,270)(105,265)(106,268)(107,267)(108,266)(109,261)(110,264)(111,263)(112,262)(113,241)(114,244)(115,243)(116,242)(117,253)(118,256)(119,255)(120,254)(121,249)(122,252)(123,251)(124,250)(125,245)(126,248)(127,247)(128,246)(129,273)(130,276)(131,275)(132,274)(133,285)(134,288)(135,287)(136,286)(137,281)(138,284)(139,283)(140,282)(141,277)(142,280)(143,279)(144,278);
s2 := Sym(288)!(  1,  6)(  2,  5)(  3,  7)(  4,  8)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 22)( 18, 21)( 19, 23)( 20, 24)( 25, 30)( 26, 29)( 27, 31)( 28, 32)( 33, 38)( 34, 37)( 35, 39)( 36, 40)( 41, 46)( 42, 45)( 43, 47)( 44, 48)( 49,102)( 50,101)( 51,103)( 52,104)( 53, 98)( 54, 97)( 55, 99)( 56,100)( 57,110)( 58,109)( 59,111)( 60,112)( 61,106)( 62,105)( 63,107)( 64,108)( 65,118)( 66,117)( 67,119)( 68,120)( 69,114)( 70,113)( 71,115)( 72,116)( 73,126)( 74,125)( 75,127)( 76,128)( 77,122)( 78,121)( 79,123)( 80,124)( 81,134)( 82,133)( 83,135)( 84,136)( 85,130)( 86,129)( 87,131)( 88,132)( 89,142)( 90,141)( 91,143)( 92,144)( 93,138)( 94,137)( 95,139)( 96,140)(145,150)(146,149)(147,151)(148,152)(153,158)(154,157)(155,159)(156,160)(161,166)(162,165)(163,167)(164,168)(169,174)(170,173)(171,175)(172,176)(177,182)(178,181)(179,183)(180,184)(185,190)(186,189)(187,191)(188,192)(193,246)(194,245)(195,247)(196,248)(197,242)(198,241)(199,243)(200,244)(201,254)(202,253)(203,255)(204,256)(205,250)(206,249)(207,251)(208,252)(209,262)(210,261)(211,263)(212,264)(213,258)(214,257)(215,259)(216,260)(217,270)(218,269)(219,271)(220,272)(221,266)(222,265)(223,267)(224,268)(225,278)(226,277)(227,279)(228,280)(229,274)(230,273)(231,275)(232,276)(233,286)(234,285)(235,287)(236,288)(237,282)(238,281)(239,283)(240,284);
poly := sub<Sym(288)|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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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