Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*768c
if this polytope has a name.
Group : SmallGroup(768,1087745)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 32, 192, 32
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {12,12}*384a
   4-fold quotients : {6,12}*192a, {12,6}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {4,4}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16, {4,2}*16
   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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 2.
      24 facets:
         16 of {6}*12
         8 of {12}*24
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 2.
      16 facets:
         16 of {12}*24
      24 vertex figures:
         16 of {6}*12
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      16 facets:
         8 of {4}*8
         8 of {12}*24
      16 vertex figures:
         8 of {12}*24
         8 of {4}*8

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