Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*768c
if this polytope has a name.
Group : SmallGroup(768,1087581)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 32, 192, 96
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
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 : {4,6}*384a
   4-fold quotients : {4,6}*192a, {4,12}*192c
   8-fold quotients : {4,6}*96
   16-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {4,3}*24, {2,6}*24
   64-fold quotients : {2,3}*12
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5,  9)(  6, 10)(  7, 11)(  8, 12)
( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)
( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)
( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)
( 97,157)( 98,158)( 99,159)(100,160)(101,153)(102,154)(103,155)(104,156)
(105,149)(106,150)(107,151)(108,152)(109,145)(110,146)(111,147)(112,148)
(113,173)(114,174)(115,175)(116,176)(117,169)(118,170)(119,171)(120,172)
(121,165)(122,166)(123,167)(124,168)(125,161)(126,162)(127,163)(128,164)
(129,189)(130,190)(131,191)(132,192)(133,185)(134,186)(135,187)(136,188)
(137,181)(138,182)(139,183)(140,184)(141,177)(142,178)(143,179)(144,180);;
s1 := (  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,102)(  6,101)(  7,103)(  8,104)
(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)
( 17,129)( 18,130)( 19,132)( 20,131)( 21,134)( 22,133)( 23,135)( 24,136)
( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)( 32,137)
( 33,113)( 34,114)( 35,116)( 36,115)( 37,118)( 38,117)( 39,119)( 40,120)
( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)( 48,121)
( 49,145)( 50,146)( 51,148)( 52,147)( 53,150)( 54,149)( 55,151)( 56,152)
( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)( 64,153)
( 65,177)( 66,178)( 67,180)( 68,179)( 69,182)( 70,181)( 71,183)( 72,184)
( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)( 80,185)
( 81,161)( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)
( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)( 96,169);;
s2 := (  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 41)(  6, 43)(  7, 42)(  8, 44)
(  9, 37)( 10, 39)( 11, 38)( 12, 40)( 13, 45)( 14, 47)( 15, 46)( 16, 48)
( 18, 19)( 21, 25)( 22, 27)( 23, 26)( 24, 28)( 30, 31)( 49, 81)( 50, 83)
( 51, 82)( 52, 84)( 53, 89)( 54, 91)( 55, 90)( 56, 92)( 57, 85)( 58, 87)
( 59, 86)( 60, 88)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)( 69, 73)
( 70, 75)( 71, 74)( 72, 76)( 78, 79)( 97,177)( 98,179)( 99,178)(100,180)
(101,185)(102,187)(103,186)(104,188)(105,181)(106,183)(107,182)(108,184)
(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)(116,164)
(117,169)(118,171)(119,170)(120,172)(121,165)(122,167)(123,166)(124,168)
(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)(132,148)
(133,153)(134,155)(135,154)(136,156)(137,149)(138,151)(139,150)(140,152)
(141,157)(142,159)(143,158)(144,160);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(192)!(  1, 13)(  2, 14)(  3, 15)(  4, 16)(  5,  9)(  6, 10)(  7, 11)
(  8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)
( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)
( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)
( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)
( 88, 92)( 97,157)( 98,158)( 99,159)(100,160)(101,153)(102,154)(103,155)
(104,156)(105,149)(106,150)(107,151)(108,152)(109,145)(110,146)(111,147)
(112,148)(113,173)(114,174)(115,175)(116,176)(117,169)(118,170)(119,171)
(120,172)(121,165)(122,166)(123,167)(124,168)(125,161)(126,162)(127,163)
(128,164)(129,189)(130,190)(131,191)(132,192)(133,185)(134,186)(135,187)
(136,188)(137,181)(138,182)(139,183)(140,184)(141,177)(142,178)(143,179)
(144,180);
s1 := Sym(192)!(  1, 97)(  2, 98)(  3,100)(  4, 99)(  5,102)(  6,101)(  7,103)
(  8,104)(  9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)
( 16,105)( 17,129)( 18,130)( 19,132)( 20,131)( 21,134)( 22,133)( 23,135)
( 24,136)( 25,144)( 26,143)( 27,141)( 28,142)( 29,139)( 30,140)( 31,138)
( 32,137)( 33,113)( 34,114)( 35,116)( 36,115)( 37,118)( 38,117)( 39,119)
( 40,120)( 41,128)( 42,127)( 43,125)( 44,126)( 45,123)( 46,124)( 47,122)
( 48,121)( 49,145)( 50,146)( 51,148)( 52,147)( 53,150)( 54,149)( 55,151)
( 56,152)( 57,160)( 58,159)( 59,157)( 60,158)( 61,155)( 62,156)( 63,154)
( 64,153)( 65,177)( 66,178)( 67,180)( 68,179)( 69,182)( 70,181)( 71,183)
( 72,184)( 73,192)( 74,191)( 75,189)( 76,190)( 77,187)( 78,188)( 79,186)
( 80,185)( 81,161)( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)
( 88,168)( 89,176)( 90,175)( 91,173)( 92,174)( 93,171)( 94,172)( 95,170)
( 96,169);
s2 := Sym(192)!(  1, 33)(  2, 35)(  3, 34)(  4, 36)(  5, 41)(  6, 43)(  7, 42)
(  8, 44)(  9, 37)( 10, 39)( 11, 38)( 12, 40)( 13, 45)( 14, 47)( 15, 46)
( 16, 48)( 18, 19)( 21, 25)( 22, 27)( 23, 26)( 24, 28)( 30, 31)( 49, 81)
( 50, 83)( 51, 82)( 52, 84)( 53, 89)( 54, 91)( 55, 90)( 56, 92)( 57, 85)
( 58, 87)( 59, 86)( 60, 88)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 66, 67)
( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 78, 79)( 97,177)( 98,179)( 99,178)
(100,180)(101,185)(102,187)(103,186)(104,188)(105,181)(106,183)(107,182)
(108,184)(109,189)(110,191)(111,190)(112,192)(113,161)(114,163)(115,162)
(116,164)(117,169)(118,171)(119,170)(120,172)(121,165)(122,167)(123,166)
(124,168)(125,173)(126,175)(127,174)(128,176)(129,145)(130,147)(131,146)
(132,148)(133,153)(134,155)(135,154)(136,156)(137,149)(138,151)(139,150)
(140,152)(141,157)(142,159)(143,158)(144,160);
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope