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