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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}*768f
if this polytope has a name.
Group : SmallGroup(768,1089367)
Rank : 4
Schlafli Type : {2,24,4}
Number of vertices, edges, etc : 2, 48, 96, 8
Order of s0s1s2s3 : 12
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 : {2,12,4}*384c
   4-fold quotients : {2,6,4}*192
   8-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,3,4}*48, {2,6,2}*48
   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)(  4,100)(  5,104)(  6,103)(  7,102)(  8,101)(  9,106)( 10,105)
( 11,115)( 12,116)( 13,120)( 14,119)( 15,118)( 16,117)( 17,122)( 18,121)
( 19,107)( 20,108)( 21,112)( 22,111)( 23,110)( 24,109)( 25,114)( 26,113)
( 27,124)( 28,123)( 29,127)( 30,128)( 31,125)( 32,126)( 33,129)( 34,130)
( 35,140)( 36,139)( 37,143)( 38,144)( 39,141)( 40,142)( 41,145)( 42,146)
( 43,132)( 44,131)( 45,135)( 46,136)( 47,133)( 48,134)( 49,137)( 50,138)
( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)( 56,174)( 57,177)( 58,178)
( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)( 64,190)( 65,193)( 66,194)
( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)( 72,182)( 73,185)( 74,186)
( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,153)( 82,154)
( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)( 88,166)( 89,169)( 90,170)
( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)( 96,158)( 97,161)( 98,162);;
s2 := (  3, 59)(  4, 60)(  5, 62)(  6, 61)(  7, 65)(  8, 66)(  9, 63)( 10, 64)
( 11, 51)( 12, 52)( 13, 54)( 14, 53)( 15, 57)( 16, 58)( 17, 55)( 18, 56)
( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 73)( 24, 74)( 25, 71)( 26, 72)
( 27, 84)( 28, 83)( 29, 85)( 30, 86)( 31, 90)( 32, 89)( 33, 88)( 34, 87)
( 35, 76)( 36, 75)( 37, 77)( 38, 78)( 39, 82)( 40, 81)( 41, 80)( 42, 79)
( 43, 92)( 44, 91)( 45, 93)( 46, 94)( 47, 98)( 48, 97)( 49, 96)( 50, 95)
( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)(106,159)
(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)(114,151)
(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)(122,167)
(123,179)(124,180)(125,182)(126,181)(127,185)(128,186)(129,183)(130,184)
(131,171)(132,172)(133,174)(134,173)(135,177)(136,178)(137,175)(138,176)
(139,187)(140,188)(141,190)(142,189)(143,193)(144,194)(145,191)(146,192);;
s3 := (  3,105)(  4,106)(  5,103)(  6,104)(  7,102)(  8,101)(  9,100)( 10, 99)
( 11,113)( 12,114)( 13,111)( 14,112)( 15,110)( 16,109)( 17,108)( 18,107)
( 19,121)( 20,122)( 21,119)( 22,120)( 23,118)( 24,117)( 25,116)( 26,115)
( 27,130)( 28,129)( 29,128)( 30,127)( 31,125)( 32,126)( 33,123)( 34,124)
( 35,138)( 36,137)( 37,136)( 38,135)( 39,133)( 40,134)( 41,131)( 42,132)
( 43,146)( 44,145)( 45,144)( 46,143)( 47,141)( 48,142)( 49,139)( 50,140)
( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)( 58,171)
( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)( 66,179)
( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)( 74,187)
( 75,153)( 76,154)( 77,151)( 78,152)( 79,150)( 80,149)( 81,148)( 82,147)
( 83,161)( 84,162)( 85,159)( 86,160)( 87,158)( 88,157)( 89,156)( 90,155)
( 91,169)( 92,170)( 93,167)( 94,168)( 95,166)( 96,165)( 97,164)( 98,163);;
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, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!(  3, 99)(  4,100)(  5,104)(  6,103)(  7,102)(  8,101)(  9,106)
( 10,105)( 11,115)( 12,116)( 13,120)( 14,119)( 15,118)( 16,117)( 17,122)
( 18,121)( 19,107)( 20,108)( 21,112)( 22,111)( 23,110)( 24,109)( 25,114)
( 26,113)( 27,124)( 28,123)( 29,127)( 30,128)( 31,125)( 32,126)( 33,129)
( 34,130)( 35,140)( 36,139)( 37,143)( 38,144)( 39,141)( 40,142)( 41,145)
( 42,146)( 43,132)( 44,131)( 45,135)( 46,136)( 47,133)( 48,134)( 49,137)
( 50,138)( 51,172)( 52,171)( 53,175)( 54,176)( 55,173)( 56,174)( 57,177)
( 58,178)( 59,188)( 60,187)( 61,191)( 62,192)( 63,189)( 64,190)( 65,193)
( 66,194)( 67,180)( 68,179)( 69,183)( 70,184)( 71,181)( 72,182)( 73,185)
( 74,186)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)( 80,150)( 81,153)
( 82,154)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)( 88,166)( 89,169)
( 90,170)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)( 96,158)( 97,161)
( 98,162);
s2 := Sym(194)!(  3, 59)(  4, 60)(  5, 62)(  6, 61)(  7, 65)(  8, 66)(  9, 63)
( 10, 64)( 11, 51)( 12, 52)( 13, 54)( 14, 53)( 15, 57)( 16, 58)( 17, 55)
( 18, 56)( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 73)( 24, 74)( 25, 71)
( 26, 72)( 27, 84)( 28, 83)( 29, 85)( 30, 86)( 31, 90)( 32, 89)( 33, 88)
( 34, 87)( 35, 76)( 36, 75)( 37, 77)( 38, 78)( 39, 82)( 40, 81)( 41, 80)
( 42, 79)( 43, 92)( 44, 91)( 45, 93)( 46, 94)( 47, 98)( 48, 97)( 49, 96)
( 50, 95)( 99,156)(100,155)(101,157)(102,158)(103,162)(104,161)(105,160)
(106,159)(107,148)(108,147)(109,149)(110,150)(111,154)(112,153)(113,152)
(114,151)(115,164)(116,163)(117,165)(118,166)(119,170)(120,169)(121,168)
(122,167)(123,179)(124,180)(125,182)(126,181)(127,185)(128,186)(129,183)
(130,184)(131,171)(132,172)(133,174)(134,173)(135,177)(136,178)(137,175)
(138,176)(139,187)(140,188)(141,190)(142,189)(143,193)(144,194)(145,191)
(146,192);
s3 := Sym(194)!(  3,105)(  4,106)(  5,103)(  6,104)(  7,102)(  8,101)(  9,100)
( 10, 99)( 11,113)( 12,114)( 13,111)( 14,112)( 15,110)( 16,109)( 17,108)
( 18,107)( 19,121)( 20,122)( 21,119)( 22,120)( 23,118)( 24,117)( 25,116)
( 26,115)( 27,130)( 28,129)( 29,128)( 30,127)( 31,125)( 32,126)( 33,123)
( 34,124)( 35,138)( 36,137)( 37,136)( 38,135)( 39,133)( 40,134)( 41,131)
( 42,132)( 43,146)( 44,145)( 45,144)( 46,143)( 47,141)( 48,142)( 49,139)
( 50,140)( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)
( 58,171)( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)
( 66,179)( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)
( 74,187)( 75,153)( 76,154)( 77,151)( 78,152)( 79,150)( 80,149)( 81,148)
( 82,147)( 83,161)( 84,162)( 85,159)( 86,160)( 87,158)( 88,157)( 89,156)
( 90,155)( 91,169)( 92,170)( 93,167)( 94,168)( 95,166)( 96,165)( 97,164)
( 98,163);
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, 
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2 >; 
 

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