Polytope of Type {2,8,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,24}*768c
if this polytope has a name.
Group : SmallGroup(768,145174)
Rank : 4
Schlafli Type : {2,8,24}
Number of vertices, edges, etc : 2, 8, 96, 24
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 : {2,4,24}*384a, {2,8,12}*384a
3-fold quotients : {2,8,8}*256b
4-fold quotients : {2,4,12}*192a, {2,2,24}*192, {2,8,6}*192
6-fold quotients : {2,4,8}*128a, {2,8,4}*128a
8-fold quotients : {2,2,12}*96, {2,4,6}*96a
12-fold quotients : {2,4,4}*64, {2,2,8}*64, {2,8,2}*64
16-fold quotients : {2,2,6}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {2,2,3}*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, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)
( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 66)( 16, 67)( 17, 68)( 18, 63)
( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)( 26, 71)
( 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, 87)( 40, 88)( 41, 89)( 42, 90)
( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)( 50, 98)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)(114,159)
(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)(122,167)
(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)(130,181)
(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)(138,186)
(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194);;
s2 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 24)
( 22, 26)( 23, 25)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)( 32, 37)
( 39, 48)( 40, 50)( 41, 49)( 42, 45)( 43, 47)( 44, 46)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)( 60, 72)
( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)
( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)(100,125)
(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)(108,132)
(109,134)(110,133)(111,138)(112,140)(113,139)(114,135)(115,137)(116,136)
(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,186)(148,188)
(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)(156,189)
(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)(164,172)
(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);;
s3 := ( 3,148)( 4,147)( 5,149)( 6,151)( 7,150)( 8,152)( 9,154)( 10,153)
( 11,155)( 12,157)( 13,156)( 14,158)( 15,160)( 16,159)( 17,161)( 18,163)
( 19,162)( 20,164)( 21,166)( 22,165)( 23,167)( 24,169)( 25,168)( 26,170)
( 27,181)( 28,180)( 29,182)( 30,178)( 31,177)( 32,179)( 33,175)( 34,174)
( 35,176)( 36,172)( 37,171)( 38,173)( 39,193)( 40,192)( 41,194)( 42,190)
( 43,189)( 44,191)( 45,187)( 46,186)( 47,188)( 48,184)( 49,183)( 50,185)
( 51,100)( 52, 99)( 53,101)( 54,103)( 55,102)( 56,104)( 57,106)( 58,105)
( 59,107)( 60,109)( 61,108)( 62,110)( 63,112)( 64,111)( 65,113)( 66,115)
( 67,114)( 68,116)( 69,118)( 70,117)( 71,119)( 72,121)( 73,120)( 74,122)
( 75,133)( 76,132)( 77,134)( 78,130)( 79,129)( 80,131)( 81,127)( 82,126)
( 83,128)( 84,124)( 85,123)( 86,125)( 87,145)( 88,144)( 89,146)( 90,142)
( 91,141)( 92,143)( 93,139)( 94,138)( 95,140)( 96,136)( 97,135)( 98,137);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := 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, 66)( 16, 67)( 17, 68)
( 18, 63)( 19, 64)( 20, 65)( 21, 72)( 22, 73)( 23, 74)( 24, 69)( 25, 70)
( 26, 71)( 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, 87)( 40, 88)( 41, 89)
( 42, 90)( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)
( 50, 98)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,162)(112,163)(113,164)
(114,159)(115,160)(116,161)(117,168)(118,169)(119,170)(120,165)(121,166)
(122,167)(123,174)(124,175)(125,176)(126,171)(127,172)(128,173)(129,180)
(130,181)(131,182)(132,177)(133,178)(134,179)(135,183)(136,184)(137,185)
(138,186)(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)
(146,194);
s2 := Sym(194)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 15, 18)( 16, 20)( 17, 19)
( 21, 24)( 22, 26)( 23, 25)( 27, 33)( 28, 35)( 29, 34)( 30, 36)( 31, 38)
( 32, 37)( 39, 48)( 40, 50)( 41, 49)( 42, 45)( 43, 47)( 44, 46)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)( 59, 70)
( 60, 72)( 61, 74)( 62, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)
( 80, 97)( 81, 87)( 82, 89)( 83, 88)( 84, 90)( 85, 92)( 86, 91)( 99,123)
(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)(107,130)
(108,132)(109,134)(110,133)(111,138)(112,140)(113,139)(114,135)(115,137)
(116,136)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(147,186)
(148,188)(149,187)(150,183)(151,185)(152,184)(153,192)(154,194)(155,193)
(156,189)(157,191)(158,190)(159,174)(160,176)(161,175)(162,171)(163,173)
(164,172)(165,180)(166,182)(167,181)(168,177)(169,179)(170,178);
s3 := Sym(194)!( 3,148)( 4,147)( 5,149)( 6,151)( 7,150)( 8,152)( 9,154)
( 10,153)( 11,155)( 12,157)( 13,156)( 14,158)( 15,160)( 16,159)( 17,161)
( 18,163)( 19,162)( 20,164)( 21,166)( 22,165)( 23,167)( 24,169)( 25,168)
( 26,170)( 27,181)( 28,180)( 29,182)( 30,178)( 31,177)( 32,179)( 33,175)
( 34,174)( 35,176)( 36,172)( 37,171)( 38,173)( 39,193)( 40,192)( 41,194)
( 42,190)( 43,189)( 44,191)( 45,187)( 46,186)( 47,188)( 48,184)( 49,183)
( 50,185)( 51,100)( 52, 99)( 53,101)( 54,103)( 55,102)( 56,104)( 57,106)
( 58,105)( 59,107)( 60,109)( 61,108)( 62,110)( 63,112)( 64,111)( 65,113)
( 66,115)( 67,114)( 68,116)( 69,118)( 70,117)( 71,119)( 72,121)( 73,120)
( 74,122)( 75,133)( 76,132)( 77,134)( 78,130)( 79,129)( 80,131)( 81,127)
( 82,126)( 83,128)( 84,124)( 85,123)( 86,125)( 87,145)( 88,144)( 89,146)
( 90,142)( 91,141)( 92,143)( 93,139)( 94,138)( 95,140)( 96,136)( 97,135)
( 98,137);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope