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