Polytope of Type {2,24,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,8}*768c
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}*384a
   3-fold quotients : {2,8,8}*256b
   4-fold quotients : {2,12,4}*192a, {2,24,2}*192, {2,6,8}*192
   6-fold quotients : {2,4,8}*128a, {2,8,4}*128a
   8-fold quotients : {2,12,2}*96, {2,6,4}*96a
   12-fold quotients : {2,4,4}*64, {2,2,8}*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 := (  3,147)(  4,149)(  5,148)(  6,150)(  7,152)(  8,151)(  9,153)( 10,155)
( 11,154)( 12,156)( 13,158)( 14,157)( 15,159)( 16,161)( 17,160)( 18,162)
( 19,164)( 20,163)( 21,165)( 22,167)( 23,166)( 24,168)( 25,170)( 26,169)
( 27,180)( 28,182)( 29,181)( 30,177)( 31,179)( 32,178)( 33,174)( 34,176)
( 35,175)( 36,171)( 37,173)( 38,172)( 39,192)( 40,194)( 41,193)( 42,189)
( 43,191)( 44,190)( 45,186)( 46,188)( 47,187)( 48,183)( 49,185)( 50,184)
( 51, 99)( 52,101)( 53,100)( 54,102)( 55,104)( 56,103)( 57,105)( 58,107)
( 59,106)( 60,108)( 61,110)( 62,109)( 63,111)( 64,113)( 65,112)( 66,114)
( 67,116)( 68,115)( 69,117)( 70,119)( 71,118)( 72,120)( 73,122)( 74,121)
( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)( 81,126)( 82,128)
( 83,127)( 84,123)( 85,125)( 86,124)( 87,144)( 88,146)( 89,145)( 90,141)
( 91,143)( 92,142)( 93,138)( 94,140)( 95,139)( 96,135)( 97,137)( 98,136);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(  3,147)(  4,149)(  5,148)(  6,150)(  7,152)(  8,151)(  9,153)
( 10,155)( 11,154)( 12,156)( 13,158)( 14,157)( 15,159)( 16,161)( 17,160)
( 18,162)( 19,164)( 20,163)( 21,165)( 22,167)( 23,166)( 24,168)( 25,170)
( 26,169)( 27,180)( 28,182)( 29,181)( 30,177)( 31,179)( 32,178)( 33,174)
( 34,176)( 35,175)( 36,171)( 37,173)( 38,172)( 39,192)( 40,194)( 41,193)
( 42,189)( 43,191)( 44,190)( 45,186)( 46,188)( 47,187)( 48,183)( 49,185)
( 50,184)( 51, 99)( 52,101)( 53,100)( 54,102)( 55,104)( 56,103)( 57,105)
( 58,107)( 59,106)( 60,108)( 61,110)( 62,109)( 63,111)( 64,113)( 65,112)
( 66,114)( 67,116)( 68,115)( 69,117)( 70,119)( 71,118)( 72,120)( 73,122)
( 74,121)( 75,132)( 76,134)( 77,133)( 78,129)( 79,131)( 80,130)( 81,126)
( 82,128)( 83,127)( 84,123)( 85,125)( 86,124)( 87,144)( 88,146)( 89,145)
( 90,141)( 91,143)( 92,142)( 93,138)( 94,140)( 95,139)( 96,135)( 97,137)
( 98,136);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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