Polytope of Type {2,60,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,6}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5676)
Rank : 4
Schlafli Type : {2,60,6}
Number of vertices, edges, etc : 2, 60, 180, 6
Order of s₀s₁s₂s₃ : 60
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 : {2,30,6}*720b
   3-fold quotients : {2,20,6}*480a, {2,60,2}*480
   5-fold quotients : {2,12,6}*288a
   6-fold quotients : {2,10,6}*240, {2,30,2}*240
   9-fold quotients : {2,20,2}*160
   10-fold quotients : {2,6,6}*144a
   12-fold quotients : {2,15,2}*120
   15-fold quotients : {2,12,2}*96, {2,4,6}*96a
   18-fold quotients : {2,10,2}*80
   30-fold quotients : {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {2,4,2}*32
   60-fold quotients : {2,2,3}*24, {2,3,2}*24
   90-fold quotients : {2,2,2}*16
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)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)( 69, 77)
( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)( 93,138)( 94,142)( 95,141)( 96,140)( 97,139)( 98,148)
( 99,152)(100,151)(101,150)(102,149)(103,143)(104,147)(105,146)(106,145)
(107,144)(108,153)(109,157)(110,156)(111,155)(112,154)(113,163)(114,167)
(115,166)(116,165)(117,164)(118,158)(119,162)(120,161)(121,160)(122,159)
(123,168)(124,172)(125,171)(126,170)(127,169)(128,178)(129,182)(130,181)
(131,180)(132,179)(133,173)(134,177)(135,176)(136,175)(137,174);;
s2 := (  3, 99)(  4, 98)(  5,102)(  6,101)(  7,100)(  8, 94)(  9, 93)( 10, 97)
( 11, 96)( 12, 95)( 13,104)( 14,103)( 15,107)( 16,106)( 17,105)( 18,129)
( 19,128)( 20,132)( 21,131)( 22,130)( 23,124)( 24,123)( 25,127)( 26,126)
( 27,125)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,114)( 34,113)
( 35,117)( 36,116)( 37,115)( 38,109)( 39,108)( 40,112)( 41,111)( 42,110)
( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)( 48,144)( 49,143)( 50,147)
( 51,146)( 52,145)( 53,139)( 54,138)( 55,142)( 56,141)( 57,140)( 58,149)
( 59,148)( 60,152)( 61,151)( 62,150)( 63,174)( 64,173)( 65,177)( 66,176)
( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,179)( 74,178)
( 75,182)( 76,181)( 77,180)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)
( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,164)( 89,163)( 90,167)
( 91,166)( 92,165);;
s3 := (  3, 18)(  4, 19)(  5, 20)(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)
( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 16, 31)( 17, 32)( 48, 63)
( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)( 54, 69)( 55, 70)( 56, 71)
( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 93,108)( 94,109)
( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)
(103,118)(104,119)(105,120)(106,121)(107,122)(138,153)(139,154)(140,155)
(141,156)(142,157)(143,158)(144,159)(145,160)(146,161)(147,162)(148,163)
(149,164)(150,165)(151,166)(152,167);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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*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)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 64, 67)( 65, 66)( 68, 73)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 82)( 80, 81)( 83, 88)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)( 93,138)( 94,142)( 95,141)( 96,140)( 97,139)
( 98,148)( 99,152)(100,151)(101,150)(102,149)(103,143)(104,147)(105,146)
(106,145)(107,144)(108,153)(109,157)(110,156)(111,155)(112,154)(113,163)
(114,167)(115,166)(116,165)(117,164)(118,158)(119,162)(120,161)(121,160)
(122,159)(123,168)(124,172)(125,171)(126,170)(127,169)(128,178)(129,182)
(130,181)(131,180)(132,179)(133,173)(134,177)(135,176)(136,175)(137,174);
s2 := Sym(182)!(  3, 99)(  4, 98)(  5,102)(  6,101)(  7,100)(  8, 94)(  9, 93)
( 10, 97)( 11, 96)( 12, 95)( 13,104)( 14,103)( 15,107)( 16,106)( 17,105)
( 18,129)( 19,128)( 20,132)( 21,131)( 22,130)( 23,124)( 24,123)( 25,127)
( 26,126)( 27,125)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,114)
( 34,113)( 35,117)( 36,116)( 37,115)( 38,109)( 39,108)( 40,112)( 41,111)
( 42,110)( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)( 48,144)( 49,143)
( 50,147)( 51,146)( 52,145)( 53,139)( 54,138)( 55,142)( 56,141)( 57,140)
( 58,149)( 59,148)( 60,152)( 61,151)( 62,150)( 63,174)( 64,173)( 65,177)
( 66,176)( 67,175)( 68,169)( 69,168)( 70,172)( 71,171)( 72,170)( 73,179)
( 74,178)( 75,182)( 76,181)( 77,180)( 78,159)( 79,158)( 80,162)( 81,161)
( 82,160)( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,164)( 89,163)
( 90,167)( 91,166)( 92,165);
s3 := Sym(182)!(  3, 18)(  4, 19)(  5, 20)(  6, 21)(  7, 22)(  8, 23)(  9, 24)
( 10, 25)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 16, 31)( 17, 32)
( 48, 63)( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)( 54, 69)( 55, 70)
( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 93,108)
( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)
(102,117)(103,118)(104,119)(105,120)(106,121)(107,122)(138,153)(139,154)
(140,155)(141,156)(142,157)(143,158)(144,159)(145,160)(146,161)(147,162)
(148,163)(149,164)(150,165)(151,166)(152,167);
poly := sub<Sym(182)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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*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