Polytope of Type {2,24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,8}*768d
if this polytope has a name.
Group : SmallGroup(768,150684)
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}*384b
3-fold quotients : {2,8,8}*256d
4-fold quotients : {2,12,4}*192a
6-fold quotients : {2,4,8}*128b, {2,8,4}*128b
8-fold quotients : {2,12,2}*96, {2,6,4}*96a
12-fold quotients : {2,4,4}*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, 99)( 4,101)( 5,100)( 6,102)( 7,104)( 8,103)( 9,105)( 10,107)
( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)( 18,111)
( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)( 26,118)
( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)( 34,125)
( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)( 42,141)
( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)( 50,136)
( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)( 58,155)
( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)( 66,159)
( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)( 74,166)
( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)( 82,173)
( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)( 90,189)
( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)( 98,184);;
s2 := ( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 25)( 16, 24)( 17, 26)( 18, 22)
( 19, 21)( 20, 23)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)
( 39, 43)( 40, 42)( 41, 44)( 45, 49)( 46, 48)( 47, 50)( 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)(111,145)(112,144)(113,146)(114,142)(115,141)(116,143)
(117,139)(118,138)(119,140)(120,136)(121,135)(122,137)(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, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)
( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 72)( 16, 73)( 17, 74)( 18, 69)
( 19, 70)( 20, 71)( 21, 66)( 22, 67)( 23, 68)( 24, 63)( 25, 64)( 26, 65)
( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)( 34, 85)
( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 93)( 40, 94)( 41, 95)( 42, 96)
( 43, 97)( 44, 98)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 92)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,168)(112,169)(113,170)(114,165)
(115,166)(116,167)(117,162)(118,163)(119,164)(120,159)(121,160)(122,161)
(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)
(131,182)(132,177)(133,178)(134,179)(135,189)(136,190)(137,191)(138,192)
(139,193)(140,194)(141,183)(142,184)(143,185)(144,186)(145,187)(146,188);;
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*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 99)( 4,101)( 5,100)( 6,102)( 7,104)( 8,103)( 9,105)
( 10,107)( 11,106)( 12,108)( 13,110)( 14,109)( 15,114)( 16,116)( 17,115)
( 18,111)( 19,113)( 20,112)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)
( 26,118)( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)
( 34,125)( 35,124)( 36,126)( 37,128)( 38,127)( 39,144)( 40,146)( 41,145)
( 42,141)( 43,143)( 44,142)( 45,138)( 46,140)( 47,139)( 48,135)( 49,137)
( 50,136)( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,153)
( 58,155)( 59,154)( 60,156)( 61,158)( 62,157)( 63,162)( 64,164)( 65,163)
( 66,159)( 67,161)( 68,160)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)
( 74,166)( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)
( 82,173)( 83,172)( 84,174)( 85,176)( 86,175)( 87,192)( 88,194)( 89,193)
( 90,189)( 91,191)( 92,190)( 93,186)( 94,188)( 95,187)( 96,183)( 97,185)
( 98,184);
s2 := Sym(194)!( 3, 4)( 6, 7)( 9, 10)( 12, 13)( 15, 25)( 16, 24)( 17, 26)
( 18, 22)( 19, 21)( 20, 23)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)
( 32, 38)( 39, 43)( 40, 42)( 41, 44)( 45, 49)( 46, 48)( 47, 50)( 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)(111,145)(112,144)(113,146)(114,142)(115,141)
(116,143)(117,139)(118,138)(119,140)(120,136)(121,135)(122,137)(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, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)
( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 72)( 16, 73)( 17, 74)
( 18, 69)( 19, 70)( 20, 71)( 21, 66)( 22, 67)( 23, 68)( 24, 63)( 25, 64)
( 26, 65)( 27, 78)( 28, 79)( 29, 80)( 30, 75)( 31, 76)( 32, 77)( 33, 84)
( 34, 85)( 35, 86)( 36, 81)( 37, 82)( 38, 83)( 39, 93)( 40, 94)( 41, 95)
( 42, 96)( 43, 97)( 44, 98)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)
( 50, 92)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,168)(112,169)(113,170)
(114,165)(115,166)(116,167)(117,162)(118,163)(119,164)(120,159)(121,160)
(122,161)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)
(130,181)(131,182)(132,177)(133,178)(134,179)(135,189)(136,190)(137,191)
(138,192)(139,193)(140,194)(141,183)(142,184)(143,185)(144,186)(145,187)
(146,188);
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*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1 >;
to this polytope