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}*768h
if this polytope has a name.
Group : SmallGroup(768,1088009)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 32, 192, 64
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
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 : {6,6}*384d
   4-fold quotients : {6,3}*192, {6,12}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*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=<s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 2.
      32 facets:
         32 of {6}*12
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      32 facets:
         32 of {6}*12
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s1*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
      16 facets:
         16 of {6}*12
      8 vertex figures:
         8 of {12}*24

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