Polytope of Type {2,4,6,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,15}*1440
if this polytope has a name.
Group : SmallGroup(1440,5712)
Rank : 5
Schlafli Type : {2,4,6,15}
Number of vertices, edges, etc : 2, 4, 12, 45, 15
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,6,15}*720
3-fold quotients : {2,4,2,15}*480
5-fold quotients : {2,4,6,3}*288
6-fold quotients : {2,2,2,15}*240
9-fold quotients : {2,4,2,5}*160
10-fold quotients : {2,2,6,3}*144
15-fold quotients : {2,4,2,3}*96
18-fold quotients : {2,2,2,5}*80
30-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)( 10,100)
( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,106)( 17,107)( 18,108)
( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)( 25,115)( 26,116)
( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)( 32,122)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)
( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)
( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,147)( 58,148)
( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)( 64,154)( 65,155)( 66,156)
( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)( 73,163)( 74,164)
( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180)
( 91,181)( 92,182);;
s2 := ( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)( 24, 39)( 25, 40)
( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 31, 46)( 32, 47)( 63, 78)
( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,138)( 94,139)
( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,147)
(103,148)(104,149)(105,150)(106,151)(107,152)(108,168)(109,169)(110,170)
(111,171)(112,172)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)
(119,179)(120,180)(121,181)(122,182)(123,153)(124,154)(125,155)(126,156)
(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)
(135,165)(136,166)(137,167);;
s3 := ( 3, 18)( 4, 22)( 5, 21)( 6, 20)( 7, 19)( 8, 28)( 9, 32)( 10, 31)
( 11, 30)( 12, 29)( 13, 23)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 48, 63)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 73)( 54, 77)( 55, 76)( 56, 75)( 57, 74)
( 58, 68)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 79, 82)( 80, 81)( 83, 88)
( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 93,108)( 94,112)( 95,111)( 96,110)
( 97,109)( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)(104,117)
(105,116)(106,115)(107,114)(124,127)(125,126)(128,133)(129,137)(130,136)
(131,135)(132,134)(138,153)(139,157)(140,156)(141,155)(142,154)(143,163)
(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)(151,160)
(152,159)(169,172)(170,171)(173,178)(174,182)(175,181)(176,180)(177,179);;
s4 := ( 3, 9)( 4, 8)( 5, 12)( 6, 11)( 7, 10)( 13, 14)( 15, 17)( 18, 39)
( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)( 26, 36)
( 27, 35)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 48, 54)( 49, 53)
( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 84)( 64, 83)( 65, 87)
( 66, 86)( 67, 85)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)( 73, 89)
( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93, 99)( 94, 98)( 95,102)( 96,101)
( 97,100)(103,104)(105,107)(108,129)(109,128)(110,132)(111,131)(112,130)
(113,124)(114,123)(115,127)(116,126)(117,125)(118,134)(119,133)(120,137)
(121,136)(122,135)(138,144)(139,143)(140,147)(141,146)(142,145)(148,149)
(150,152)(153,174)(154,173)(155,177)(156,176)(157,175)(158,169)(159,168)
(160,172)(161,171)(162,170)(163,179)(164,178)(165,182)(166,181)(167,180);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(182)!(1,2);
s1 := Sym(182)!( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)
( 10,100)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,106)( 17,107)
( 18,108)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)( 25,115)
( 26,116)( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)( 32,122)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)
( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)
( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,147)
( 58,148)( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)( 64,154)( 65,155)
( 66,156)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)( 73,163)
( 74,164)( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)
( 90,180)( 91,181)( 92,182);
s2 := Sym(182)!( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)( 24, 39)
( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 31, 46)( 32, 47)
( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)
( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,138)
( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)
(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,168)(109,169)
(110,170)(111,171)(112,172)(113,173)(114,174)(115,175)(116,176)(117,177)
(118,178)(119,179)(120,180)(121,181)(122,182)(123,153)(124,154)(125,155)
(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)
(134,164)(135,165)(136,166)(137,167);
s3 := Sym(182)!( 3, 18)( 4, 22)( 5, 21)( 6, 20)( 7, 19)( 8, 28)( 9, 32)
( 10, 31)( 11, 30)( 12, 29)( 13, 23)( 14, 27)( 15, 26)( 16, 25)( 17, 24)
( 34, 37)( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 48, 63)
( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 73)( 54, 77)( 55, 76)( 56, 75)
( 57, 74)( 58, 68)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 79, 82)( 80, 81)
( 83, 88)( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 93,108)( 94,112)( 95,111)
( 96,110)( 97,109)( 98,118)( 99,122)(100,121)(101,120)(102,119)(103,113)
(104,117)(105,116)(106,115)(107,114)(124,127)(125,126)(128,133)(129,137)
(130,136)(131,135)(132,134)(138,153)(139,157)(140,156)(141,155)(142,154)
(143,163)(144,167)(145,166)(146,165)(147,164)(148,158)(149,162)(150,161)
(151,160)(152,159)(169,172)(170,171)(173,178)(174,182)(175,181)(176,180)
(177,179);
s4 := Sym(182)!( 3, 9)( 4, 8)( 5, 12)( 6, 11)( 7, 10)( 13, 14)( 15, 17)
( 18, 39)( 19, 38)( 20, 42)( 21, 41)( 22, 40)( 23, 34)( 24, 33)( 25, 37)
( 26, 36)( 27, 35)( 28, 44)( 29, 43)( 30, 47)( 31, 46)( 32, 45)( 48, 54)
( 49, 53)( 50, 57)( 51, 56)( 52, 55)( 58, 59)( 60, 62)( 63, 84)( 64, 83)
( 65, 87)( 66, 86)( 67, 85)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)
( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93, 99)( 94, 98)( 95,102)
( 96,101)( 97,100)(103,104)(105,107)(108,129)(109,128)(110,132)(111,131)
(112,130)(113,124)(114,123)(115,127)(116,126)(117,125)(118,134)(119,133)
(120,137)(121,136)(122,135)(138,144)(139,143)(140,147)(141,146)(142,145)
(148,149)(150,152)(153,174)(154,173)(155,177)(156,176)(157,175)(158,169)
(159,168)(160,172)(161,171)(162,170)(163,179)(164,178)(165,182)(166,181)
(167,180);
poly := sub<Sym(182)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope