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Polytope of Type {24,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8,2}*768d
if this polytope has a name.
Group : SmallGroup(768,150684)
Rank : 4
Schlafli Type : {24,8,2}
Number of vertices, edges, etc : 24, 96, 8, 2
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 : {24,4,2}*384b, {12,8,2}*384b
   3-fold quotients : {8,8,2}*256d
   4-fold quotients : {12,4,2}*192a
   6-fold quotients : {4,8,2}*128b, {8,4,2}*128b
   8-fold quotients : {12,2,2}*96, {6,4,2}*96a
   12-fold quotients : {4,4,2}*64
   16-fold quotients : {6,2,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)(  8,105)
(  9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)( 16,109)
( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)( 24,116)
( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)( 32,123)
( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)( 40,139)
( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)( 48,134)
( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)( 56,153)
( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)( 64,157)
( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)( 72,164)
( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)( 80,171)
( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)( 88,187)
( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)( 96,182);;
s1 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 23)( 14, 22)( 15, 24)( 16, 20)
( 17, 19)( 18, 21)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)
( 37, 41)( 38, 40)( 39, 42)( 43, 47)( 44, 46)( 45, 48)( 49, 62)( 50, 61)
( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)
( 59, 70)( 60, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)( 78, 96)
( 79, 86)( 80, 85)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)( 98,121)
( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)
(107,130)(108,132)(109,143)(110,142)(111,144)(112,140)(113,139)(114,141)
(115,137)(116,136)(117,138)(118,134)(119,133)(120,135)(145,185)(146,184)
(147,186)(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)
(155,187)(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)
(163,179)(164,178)(165,180)(166,176)(167,175)(168,177);;
s2 := (  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)(  8, 56)
(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 70)( 14, 71)( 15, 72)( 16, 67)
( 17, 68)( 18, 69)( 19, 64)( 20, 65)( 21, 66)( 22, 61)( 23, 62)( 24, 63)
( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)
( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 91)( 38, 92)( 39, 93)( 40, 94)
( 41, 95)( 42, 96)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)( 48, 90)
( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)
(105,153)(106,154)(107,155)(108,156)(109,166)(110,167)(111,168)(112,163)
(113,164)(114,165)(115,160)(116,161)(117,162)(118,157)(119,158)(120,159)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(133,187)(134,188)(135,189)(136,190)
(137,191)(138,192)(139,181)(140,182)(141,183)(142,184)(143,185)(144,186);;
s3 := (193,194);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(194)!(  1, 97)(  2, 99)(  3, 98)(  4,100)(  5,102)(  6,101)(  7,103)
(  8,105)(  9,104)( 10,106)( 11,108)( 12,107)( 13,112)( 14,114)( 15,113)
( 16,109)( 17,111)( 18,110)( 19,118)( 20,120)( 21,119)( 22,115)( 23,117)
( 24,116)( 25,127)( 26,129)( 27,128)( 28,130)( 29,132)( 30,131)( 31,121)
( 32,123)( 33,122)( 34,124)( 35,126)( 36,125)( 37,142)( 38,144)( 39,143)
( 40,139)( 41,141)( 42,140)( 43,136)( 44,138)( 45,137)( 46,133)( 47,135)
( 48,134)( 49,145)( 50,147)( 51,146)( 52,148)( 53,150)( 54,149)( 55,151)
( 56,153)( 57,152)( 58,154)( 59,156)( 60,155)( 61,160)( 62,162)( 63,161)
( 64,157)( 65,159)( 66,158)( 67,166)( 68,168)( 69,167)( 70,163)( 71,165)
( 72,164)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,169)
( 80,171)( 81,170)( 82,172)( 83,174)( 84,173)( 85,190)( 86,192)( 87,191)
( 88,187)( 89,189)( 90,188)( 91,184)( 92,186)( 93,185)( 94,181)( 95,183)
( 96,182);
s1 := Sym(194)!(  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 23)( 14, 22)( 15, 24)
( 16, 20)( 17, 19)( 18, 21)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)
( 30, 36)( 37, 41)( 38, 40)( 39, 42)( 43, 47)( 44, 46)( 45, 48)( 49, 62)
( 50, 61)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)
( 58, 71)( 59, 70)( 60, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 95)( 77, 94)
( 78, 96)( 79, 86)( 80, 85)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 97,122)
( 98,121)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)
(106,131)(107,130)(108,132)(109,143)(110,142)(111,144)(112,140)(113,139)
(114,141)(115,137)(116,136)(117,138)(118,134)(119,133)(120,135)(145,185)
(146,184)(147,186)(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)
(154,188)(155,187)(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)
(162,171)(163,179)(164,178)(165,180)(166,176)(167,175)(168,177);
s2 := Sym(194)!(  1, 49)(  2, 50)(  3, 51)(  4, 52)(  5, 53)(  6, 54)(  7, 55)
(  8, 56)(  9, 57)( 10, 58)( 11, 59)( 12, 60)( 13, 70)( 14, 71)( 15, 72)
( 16, 67)( 17, 68)( 18, 69)( 19, 64)( 20, 65)( 21, 66)( 22, 61)( 23, 62)
( 24, 63)( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)
( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 91)( 38, 92)( 39, 93)
( 40, 94)( 41, 95)( 42, 96)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)
( 48, 90)( 97,145)( 98,146)( 99,147)(100,148)(101,149)(102,150)(103,151)
(104,152)(105,153)(106,154)(107,155)(108,156)(109,166)(110,167)(111,168)
(112,163)(113,164)(114,165)(115,160)(116,161)(117,162)(118,157)(119,158)
(120,159)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)
(128,179)(129,180)(130,175)(131,176)(132,177)(133,187)(134,188)(135,189)
(136,190)(137,191)(138,192)(139,181)(140,182)(141,183)(142,184)(143,185)
(144,186);
s3 := Sym(194)!(193,194);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0 >; 
 

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