Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*768e
if this polytope has a name.
Group : SmallGroup(768,1086320)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 64, 192, 48
Order of s₀s₁s₂ : 12
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 : {4,6}*384a
   4-fold quotients : {4,6}*192a, {8,6}*192b
   8-fold quotients : {8,3}*96, {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 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)
(  9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)( 16,120)
( 17,106)( 18,105)( 19,108)( 20,107)( 21,110)( 22,109)( 23,112)( 24,111)
( 25, 98)( 26, 97)( 27,100)( 28, 99)( 29,102)( 30,101)( 31,104)( 32,103)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)
( 41,145)( 42,146)( 43,147)( 44,148)( 45,149)( 46,150)( 47,151)( 48,152)
( 49,138)( 50,137)( 51,140)( 52,139)( 53,142)( 54,141)( 55,144)( 56,143)
( 57,130)( 58,129)( 59,132)( 60,131)( 61,134)( 62,133)( 63,136)( 64,135)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,177)( 74,178)( 75,179)( 76,180)( 77,181)( 78,182)( 79,183)( 80,184)
( 81,170)( 82,169)( 83,172)( 84,171)( 85,174)( 86,173)( 87,176)( 88,175)
( 89,162)( 90,161)( 91,164)( 92,163)( 93,166)( 94,165)( 95,168)( 96,167);;
s1 := (  5,  7)(  6,  8)(  9, 12)( 10, 11)( 13, 14)( 15, 16)( 17, 31)( 18, 32)
( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 76)( 42, 75)
( 43, 74)( 44, 73)( 45, 78)( 46, 77)( 47, 80)( 48, 79)( 49, 95)( 50, 96)
( 51, 93)( 52, 94)( 53, 89)( 54, 90)( 55, 91)( 56, 92)( 57, 85)( 58, 86)
( 59, 87)( 60, 88)( 61, 83)( 62, 84)( 63, 81)( 64, 82)( 97, 98)( 99,100)
(101,104)(102,103)(105,107)(106,108)(113,128)(114,127)(115,126)(116,125)
(117,122)(118,121)(119,124)(120,123)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,171)(138,172)(139,169)(140,170)
(141,173)(142,174)(143,175)(144,176)(145,192)(146,191)(147,190)(148,189)
(149,186)(150,185)(151,188)(152,187)(153,182)(154,181)(155,184)(156,183)
(157,180)(158,179)(159,178)(160,177);;
s2 := (  1, 65)(  2, 66)(  3, 69)(  4, 70)(  5, 67)(  6, 68)(  7, 71)(  8, 72)
(  9, 82)( 10, 81)( 11, 86)( 12, 85)( 13, 84)( 14, 83)( 15, 88)( 16, 87)
( 17, 74)( 18, 73)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 80)( 24, 79)
( 25, 90)( 26, 89)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 96)( 32, 95)
( 35, 37)( 36, 38)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 46, 51)
( 47, 56)( 48, 55)( 57, 58)( 59, 62)( 60, 61)( 63, 64)( 97,162)( 98,161)
( 99,166)(100,165)(101,164)(102,163)(103,168)(104,167)(105,177)(106,178)
(107,181)(108,182)(109,179)(110,180)(111,183)(112,184)(113,169)(114,170)
(115,173)(116,174)(117,171)(118,172)(119,175)(120,176)(121,185)(122,186)
(123,189)(124,190)(125,187)(126,188)(127,191)(128,192)(129,130)(131,134)
(132,133)(135,136)(137,145)(138,146)(139,149)(140,150)(141,147)(142,148)
(143,151)(144,152)(155,157)(156,158);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope