Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*768
if this polytope has a name.
Group : SmallGroup(768,1086649)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 64, 192, 16
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 : {12,6}*384, {24,6}*384a, {24,6}*384b
   4-fold quotients : {12,6}*192a, {12,6}*192b, {6,6}*192b
   8-fold quotients : {12,3}*96, {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope