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Polytope of Type {2,24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1089134)
Rank : 4
Schlafli Type : {2,24,4}
Number of vertices, edges, etc : 2, 48, 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}*384c, {2,24,4}*384d, {2,12,4}*384b
   4-fold quotients : {2,24,2}*192, {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
   8-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   12-fold quotients : {2,8,2}*64
   16-fold quotients : {2,3,4}*48, {2,6,2}*48
   24-fold quotients : {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 := (  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);;
s2 := (  3, 55)(  4, 56)(  5, 58)(  6, 57)(  7, 51)(  8, 52)(  9, 54)( 10, 53)
( 11, 59)( 12, 60)( 13, 62)( 14, 61)( 15, 67)( 16, 68)( 17, 70)( 18, 69)
( 19, 63)( 20, 64)( 21, 66)( 22, 65)( 23, 71)( 24, 72)( 25, 74)( 26, 73)
( 27, 91)( 28, 92)( 29, 94)( 30, 93)( 31, 87)( 32, 88)( 33, 90)( 34, 89)
( 35, 95)( 36, 96)( 37, 98)( 38, 97)( 39, 79)( 40, 80)( 41, 82)( 42, 81)
( 43, 75)( 44, 76)( 45, 78)( 46, 77)( 47, 83)( 48, 84)( 49, 86)( 50, 85)
( 99,151)(100,152)(101,154)(102,153)(103,147)(104,148)(105,150)(106,149)
(107,155)(108,156)(109,158)(110,157)(111,163)(112,164)(113,166)(114,165)
(115,159)(116,160)(117,162)(118,161)(119,167)(120,168)(121,170)(122,169)
(123,187)(124,188)(125,190)(126,189)(127,183)(128,184)(129,186)(130,185)
(131,191)(132,192)(133,194)(134,193)(135,175)(136,176)(137,178)(138,177)
(139,171)(140,172)(141,174)(142,173)(143,179)(144,180)(145,182)(146,181);;
s3 := (  3,102)(  4,101)(  5,100)(  6, 99)(  7,106)(  8,105)(  9,104)( 10,103)
( 11,110)( 12,109)( 13,108)( 14,107)( 15,114)( 16,113)( 17,112)( 18,111)
( 19,118)( 20,117)( 21,116)( 22,115)( 23,122)( 24,121)( 25,120)( 26,119)
( 27,126)( 28,125)( 29,124)( 30,123)( 31,130)( 32,129)( 33,128)( 34,127)
( 35,134)( 36,133)( 37,132)( 38,131)( 39,138)( 40,137)( 41,136)( 42,135)
( 43,142)( 44,141)( 45,140)( 46,139)( 47,146)( 48,145)( 49,144)( 50,143)
( 51,150)( 52,149)( 53,148)( 54,147)( 55,154)( 56,153)( 57,152)( 58,151)
( 59,158)( 60,157)( 61,156)( 62,155)( 63,162)( 64,161)( 65,160)( 66,159)
( 67,166)( 68,165)( 69,164)( 70,163)( 71,170)( 72,169)( 73,168)( 74,167)
( 75,174)( 76,173)( 77,172)( 78,171)( 79,178)( 80,177)( 81,176)( 82,175)
( 83,182)( 84,181)( 85,180)( 86,179)( 87,186)( 88,185)( 89,184)( 90,183)
( 91,190)( 92,189)( 93,188)( 94,187)( 95,194)( 96,193)( 97,192)( 98,191);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := 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);
s2 := Sym(194)!(  3, 55)(  4, 56)(  5, 58)(  6, 57)(  7, 51)(  8, 52)(  9, 54)
( 10, 53)( 11, 59)( 12, 60)( 13, 62)( 14, 61)( 15, 67)( 16, 68)( 17, 70)
( 18, 69)( 19, 63)( 20, 64)( 21, 66)( 22, 65)( 23, 71)( 24, 72)( 25, 74)
( 26, 73)( 27, 91)( 28, 92)( 29, 94)( 30, 93)( 31, 87)( 32, 88)( 33, 90)
( 34, 89)( 35, 95)( 36, 96)( 37, 98)( 38, 97)( 39, 79)( 40, 80)( 41, 82)
( 42, 81)( 43, 75)( 44, 76)( 45, 78)( 46, 77)( 47, 83)( 48, 84)( 49, 86)
( 50, 85)( 99,151)(100,152)(101,154)(102,153)(103,147)(104,148)(105,150)
(106,149)(107,155)(108,156)(109,158)(110,157)(111,163)(112,164)(113,166)
(114,165)(115,159)(116,160)(117,162)(118,161)(119,167)(120,168)(121,170)
(122,169)(123,187)(124,188)(125,190)(126,189)(127,183)(128,184)(129,186)
(130,185)(131,191)(132,192)(133,194)(134,193)(135,175)(136,176)(137,178)
(138,177)(139,171)(140,172)(141,174)(142,173)(143,179)(144,180)(145,182)
(146,181);
s3 := Sym(194)!(  3,102)(  4,101)(  5,100)(  6, 99)(  7,106)(  8,105)(  9,104)
( 10,103)( 11,110)( 12,109)( 13,108)( 14,107)( 15,114)( 16,113)( 17,112)
( 18,111)( 19,118)( 20,117)( 21,116)( 22,115)( 23,122)( 24,121)( 25,120)
( 26,119)( 27,126)( 28,125)( 29,124)( 30,123)( 31,130)( 32,129)( 33,128)
( 34,127)( 35,134)( 36,133)( 37,132)( 38,131)( 39,138)( 40,137)( 41,136)
( 42,135)( 43,142)( 44,141)( 45,140)( 46,139)( 47,146)( 48,145)( 49,144)
( 50,143)( 51,150)( 52,149)( 53,148)( 54,147)( 55,154)( 56,153)( 57,152)
( 58,151)( 59,158)( 60,157)( 61,156)( 62,155)( 63,162)( 64,161)( 65,160)
( 66,159)( 67,166)( 68,165)( 69,164)( 70,163)( 71,170)( 72,169)( 73,168)
( 74,167)( 75,174)( 76,173)( 77,172)( 78,171)( 79,178)( 80,177)( 81,176)
( 82,175)( 83,182)( 84,181)( 85,180)( 86,179)( 87,186)( 88,185)( 89,184)
( 90,183)( 91,190)( 92,189)( 93,188)( 94,187)( 95,194)( 96,193)( 97,192)
( 98,191);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*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 >; 
 

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