Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*768d
if this polytope has a name.
Group : SmallGroup(768,1086333)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 64, 192, 64
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 12
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, {6,6}*192b
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {3,3}*24
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope