Polytope of Type {12,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768v
if this polytope has a name.
Group : SmallGroup(768,1087795)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s0s1s2 : 6
Order of s0s1s2s1 : 8
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 : {6,8}*384d
   4-fold quotients : {6,8}*192a, {12,4}*192c
   8-fold quotients : {6,4}*96
   16-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {3,4}*24, {6,2}*24
   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=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {12}*24
      32 vertex figures:
         16 of {8}*16
         16 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 2.
      16 facets:
         16 of {12}*24
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {12}*24
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 2.
      16 facets:
         16 of {12}*24
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1, s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         8 of {8}*16
         8 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1, s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         8 of {8}*16
         8 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         8 of {8}*16
         8 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 4.
      8 facets:
         8 of {12}*24
      24 vertex figures:
         8 of {8}*16
         16 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         8 of {8}*16
         8 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {12}*24
      16 vertex figures:
         8 of {8}*16
         8 of {4}*8

Permutation Representation (GAP) : 
s0 := (  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,101)(  6,102)(  7,104)(  8,103)(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)( 24,135)( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)( 32,137)( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)( 40,119)( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)( 48,121)( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)( 56,151)( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)( 64,153)( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)( 72,183)( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)( 80,185)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)( 96,169);;
s1 := (  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 44)(  6, 42)(  7, 43)(  8, 41)(  9, 40)( 10, 38)( 11, 39)( 12, 37)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 28)( 22, 26)( 23, 27)( 24, 25)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 92)( 54, 90)( 55, 91)( 56, 89)( 57, 88)( 58, 86)( 59, 87)( 60, 85)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 78, 79)( 97,177)( 98,179)( 99,178)(100,180)(101,188)(102,186)(103,187)(104,185)(105,184)(106,182)(107,183)(108,181)(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)(116,164)(117,172)(118,170)(119,171)(120,169)(121,168)(122,166)(123,167)(124,165)(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)(132,148)(133,156)(134,154)(135,155)(136,153)(137,152)(138,150)(139,151)(140,149)(141,157)(142,159)(143,158)(144,160);;
s2 := (  1,101)(  2,102)(  3,103)(  4,104)(  5, 97)(  6, 98)(  7, 99)(  8,100)(  9,111)( 10,112)( 11,109)( 12,110)( 13,107)( 14,108)( 15,105)( 16,106)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)( 25,127)( 26,128)( 27,125)( 28,126)( 29,123)( 30,124)( 31,121)( 32,122)( 33,133)( 34,134)( 35,135)( 36,136)( 37,129)( 38,130)( 39,131)( 40,132)( 41,143)( 42,144)( 43,141)( 44,142)( 45,139)( 46,140)( 47,137)( 48,138)( 49,149)( 50,150)( 51,151)( 52,152)( 53,145)( 54,146)( 55,147)( 56,148)( 57,159)( 58,160)( 59,157)( 60,158)( 61,155)( 62,156)( 63,153)( 64,154)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)( 73,175)( 74,176)( 75,173)( 76,174)( 77,171)( 78,172)( 79,169)( 80,170)( 81,181)( 82,182)( 83,183)( 84,184)( 85,177)( 86,178)( 87,179)( 88,180)( 89,191)( 90,192)( 91,189)( 92,190)( 93,187)( 94,188)( 95,185)( 96,186);;
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*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(192)!(  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,101)(  6,102)(  7,104)(  8,103)(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)( 17,129)( 18,130)( 19,132)( 20,131)( 21,133)( 22,134)( 23,136)( 24,135)( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)( 32,137)( 33,113)( 34,114)( 35,116)( 36,115)( 37,117)( 38,118)( 39,120)( 40,119)( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)( 48,121)( 49,145)( 50,146)( 51,148)( 52,147)( 53,149)( 54,150)( 55,152)( 56,151)( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)( 64,153)( 65,177)( 66,178)( 67,180)( 68,179)( 69,181)( 70,182)( 71,184)( 72,183)( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)( 80,185)( 81,161)( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)( 96,169);
s1 := Sym(192)!(  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 44)(  6, 42)(  7, 43)(  8, 41)(  9, 40)( 10, 38)( 11, 39)( 12, 37)( 13, 45)( 14, 47)( 15, 46)( 16, 48)( 18, 19)( 21, 28)( 22, 26)( 23, 27)( 24, 25)( 30, 31)( 49, 81)( 50, 83)( 51, 82)( 52, 84)( 53, 92)( 54, 90)( 55, 91)( 56, 89)( 57, 88)( 58, 86)( 59, 87)( 60, 85)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 76)( 70, 74)( 71, 75)( 72, 73)( 78, 79)( 97,177)( 98,179)( 99,178)(100,180)(101,188)(102,186)(103,187)(104,185)(105,184)(106,182)(107,183)(108,181)(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)(116,164)(117,172)(118,170)(119,171)(120,169)(121,168)(122,166)(123,167)(124,165)(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)(132,148)(133,156)(134,154)(135,155)(136,153)(137,152)(138,150)(139,151)(140,149)(141,157)(142,159)(143,158)(144,160);
s2 := Sym(192)!(  1,101)(  2,102)(  3,103)(  4,104)(  5, 97)(  6, 98)(  7, 99)(  8,100)(  9,111)( 10,112)( 11,109)( 12,110)( 13,107)( 14,108)( 15,105)( 16,106)( 17,117)( 18,118)( 19,119)( 20,120)( 21,113)( 22,114)( 23,115)( 24,116)( 25,127)( 26,128)( 27,125)( 28,126)( 29,123)( 30,124)( 31,121)( 32,122)( 33,133)( 34,134)( 35,135)( 36,136)( 37,129)( 38,130)( 39,131)( 40,132)( 41,143)( 42,144)( 43,141)( 44,142)( 45,139)( 46,140)( 47,137)( 48,138)( 49,149)( 50,150)( 51,151)( 52,152)( 53,145)( 54,146)( 55,147)( 56,148)( 57,159)( 58,160)( 59,157)( 60,158)( 61,155)( 62,156)( 63,153)( 64,154)( 65,165)( 66,166)( 67,167)( 68,168)( 69,161)( 70,162)( 71,163)( 72,164)( 73,175)( 74,176)( 75,173)( 76,174)( 77,171)( 78,172)( 79,169)( 80,170)( 81,181)( 82,182)( 83,183)( 84,184)( 85,177)( 86,178)( 87,179)( 88,180)( 89,191)( 90,192)( 91,189)( 92,190)( 93,187)( 94,188)( 95,185)( 96,186);
poly := sub<Sym(192)|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*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle