Polytope of Type {2,24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,8}*768a
if this polytope has a name.
Group : SmallGroup(768,145173)
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}*384b, {2,12,8}*384a
3-fold quotients : {2,8,8}*256a
4-fold quotients : {2,12,4}*192a, {2,6,8}*192
6-fold quotients : {2,4,8}*128a, {2,8,4}*128b
8-fold quotients : {2,12,2}*96, {2,6,4}*96a
12-fold quotients : {2,4,4}*64, {2,2,8}*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, 51)( 4, 53)( 5, 52)( 6, 54)( 7, 56)( 8, 55)( 9, 57)( 10, 59)
( 11, 58)( 12, 60)( 13, 62)( 14, 61)( 15, 66)( 16, 68)( 17, 67)( 18, 63)
( 19, 65)( 20, 64)( 21, 72)( 22, 74)( 23, 73)( 24, 69)( 25, 71)( 26, 70)
( 27, 78)( 28, 80)( 29, 79)( 30, 75)( 31, 77)( 32, 76)( 33, 84)( 34, 86)
( 35, 85)( 36, 81)( 37, 83)( 38, 82)( 39, 87)( 40, 89)( 41, 88)( 42, 90)
( 43, 92)( 44, 91)( 45, 93)( 46, 95)( 47, 94)( 48, 96)( 49, 98)( 50, 97)
( 99,147)(100,149)(101,148)(102,150)(103,152)(104,151)(105,153)(106,155)
(107,154)(108,156)(109,158)(110,157)(111,162)(112,164)(113,163)(114,159)
(115,161)(116,160)(117,168)(118,170)(119,169)(120,165)(121,167)(122,166)
(123,174)(124,176)(125,175)(126,171)(127,173)(128,172)(129,180)(130,182)
(131,181)(132,177)(133,179)(134,178)(135,183)(136,185)(137,184)(138,186)
(139,188)(140,187)(141,189)(142,191)(143,190)(144,192)(145,194)(146,193);;
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, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)( 10,106)
( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)( 18,111)
( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)
( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)( 42,141)
( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)( 50,137)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)
( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)( 66,159)
( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)
( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)( 90,189)
( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)( 98,185);;
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,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 51)( 4, 53)( 5, 52)( 6, 54)( 7, 56)( 8, 55)( 9, 57)
( 10, 59)( 11, 58)( 12, 60)( 13, 62)( 14, 61)( 15, 66)( 16, 68)( 17, 67)
( 18, 63)( 19, 65)( 20, 64)( 21, 72)( 22, 74)( 23, 73)( 24, 69)( 25, 71)
( 26, 70)( 27, 78)( 28, 80)( 29, 79)( 30, 75)( 31, 77)( 32, 76)( 33, 84)
( 34, 86)( 35, 85)( 36, 81)( 37, 83)( 38, 82)( 39, 87)( 40, 89)( 41, 88)
( 42, 90)( 43, 92)( 44, 91)( 45, 93)( 46, 95)( 47, 94)( 48, 96)( 49, 98)
( 50, 97)( 99,147)(100,149)(101,148)(102,150)(103,152)(104,151)(105,153)
(106,155)(107,154)(108,156)(109,158)(110,157)(111,162)(112,164)(113,163)
(114,159)(115,161)(116,160)(117,168)(118,170)(119,169)(120,165)(121,167)
(122,166)(123,174)(124,176)(125,175)(126,171)(127,173)(128,172)(129,180)
(130,182)(131,181)(132,177)(133,179)(134,178)(135,183)(136,185)(137,184)
(138,186)(139,188)(140,187)(141,189)(142,191)(143,190)(144,192)(145,194)
(146,193);
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, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)
( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)
( 18,111)( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)
( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)
( 42,141)( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)
( 50,137)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)
( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)
( 66,159)( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)
( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)
( 90,189)( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)
( 98,185);
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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
to this polytope