Polytope of Type {2,24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,8}*768b
if this polytope has a name.
Group : SmallGroup(768,145174)
Rank : 4
Schlafli Type : {2,24,8}
Number of vertices, edges, etc : 2, 24, 96, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,24,4}*384a, {2,12,8}*384b
   3-fold quotients : {2,8,8}*256c
   4-fold quotients : {2,12,4}*192a, {2,24,2}*192
   6-fold quotients : {2,8,4}*128a, {2,4,8}*128b
   8-fold quotients : {2,12,2}*96, {2,6,4}*96a
   12-fold quotients : {2,4,4}*64, {2,8,2}*64
   16-fold quotients : {2,6,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3, 99)(  4,101)(  5,100)(  6,102)(  7,104)(  8,103)(  9,105)( 10,107)
( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)( 18,111)
( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)( 26,118)
( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)( 34,125)
( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)( 42,141)
( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)( 50,136)
( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)( 58,155)
( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)( 66,159)
( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)( 74,166)
( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)( 82,173)
( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)( 90,189)
( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)( 98,184);;
s2 := (  3,  4)(  6,  7)(  9, 10)( 12, 13)( 15, 19)( 16, 18)( 17, 20)( 21, 25)
( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)
( 39, 49)( 40, 48)( 41, 50)( 42, 46)( 43, 45)( 44, 47)( 51, 64)( 52, 63)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 73)
( 61, 72)( 62, 74)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)
( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)
(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)(107,131)(108,133)
(109,132)(110,134)(111,139)(112,138)(113,140)(114,136)(115,135)(116,137)
(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)(148,186)
(149,188)(150,184)(151,183)(152,185)(153,193)(154,192)(155,194)(156,190)
(157,189)(158,191)(159,175)(160,174)(161,176)(162,172)(163,171)(164,173)
(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);;
s3 := (  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)(  8, 56)(  9, 57)( 10, 58)
( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)( 18, 63)
( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)( 26, 71)
( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)( 34, 85)
( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 87)( 40, 88)( 41, 89)( 42, 90)
( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)( 50, 98)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)(114,159)
(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)(122,167)
(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)
(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)(138,186)
(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(194)!(1,2);
s1 := Sym(194)!(  3, 99)(  4,101)(  5,100)(  6,102)(  7,104)(  8,103)(  9,105)
( 10,107)( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)
( 18,111)( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)
( 26,118)( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)
( 34,125)( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)
( 42,141)( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)
( 50,136)( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)
( 58,155)( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)
( 66,159)( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)
( 74,166)( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)
( 82,173)( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)
( 90,189)( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)
( 98,184);
s2 := Sym(194)!(  3,  4)(  6,  7)(  9, 10)( 12, 13)( 15, 19)( 16, 18)( 17, 20)
( 21, 25)( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)
( 32, 38)( 39, 49)( 40, 48)( 41, 50)( 42, 46)( 43, 45)( 44, 47)( 51, 64)
( 52, 63)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 70)( 58, 69)( 59, 71)
( 60, 73)( 61, 72)( 62, 74)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)
( 80, 98)( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)
(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)(107,131)
(108,133)(109,132)(110,134)(111,139)(112,138)(113,140)(114,136)(115,135)
(116,137)(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)
(148,186)(149,188)(150,184)(151,183)(152,185)(153,193)(154,192)(155,194)
(156,190)(157,189)(158,191)(159,175)(160,174)(161,176)(162,172)(163,171)
(164,173)(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);
s3 := Sym(194)!(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)(  8, 56)(  9, 57)
( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)
( 18, 63)( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)
( 26, 71)( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)
( 34, 85)( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 87)( 40, 88)( 41, 89)
( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)
( 50, 98)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)
(114,159)(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)
(122,167)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)
(130,181)(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)
(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)
(146,194);
poly := sub<Sym(194)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope