Polytope of Type {2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,24}*768c
if this polytope has a name.
Group : SmallGroup(768,1089134)
Rank : 4
Schlafli Type : {2,4,24}
Number of vertices, edges, etc : 2, 8, 96, 48
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 : {2,4,24}*384c, {2,4,24}*384d, {2,4,12}*384b
   4-fold quotients : {2,2,24}*192, {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   8-fold quotients : {2,2,12}*96, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   12-fold quotients : {2,2,8}*64
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope