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}*768l
if this polytope has a name.
Group : SmallGroup(768,1086324)
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}*384e
   4-fold quotients : {3,8}*192
   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=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2> 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*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=<s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2> 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*s2*s1*s0*s2, s1*s0*s2*s1*s2*s1*s0*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*s2*s1*s2*s1*s0*s2, 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

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