Overview
- Group
- SmallGroup(1440,1584)
- Rank
- 4
- Schläfli Type
- {2,20,18}
- Vertices, edges, …
- 2, 20, 180, 18
- Order of s0s1s2s3
- 180
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
9-fold
10-fold
15-fold
18-fold
20-fold
30-fold
36-fold
45-fold
60-fold
90-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 6, 15)( 7, 16)( 8, 17)( 9, 12)( 10, 13)( 11, 14)( 21, 30)( 22, 31)( 23, 32)( 24, 27)( 25, 28)( 26, 29)( 36, 45)( 37, 46)( 38, 47)( 39, 42)( 40, 43)( 41, 44)( 51, 60)( 52, 61)( 53, 62)( 54, 57)( 55, 58)( 56, 59)( 66, 75)( 67, 76)( 68, 77)( 69, 72)( 70, 73)( 71, 74)( 81, 90)( 82, 91)( 83, 92)( 84, 87)( 85, 88)( 86, 89)( 93,138)( 94,139)( 95,140)( 96,150)( 97,151)( 98,152)( 99,147)(100,148)(101,149)(102,144)(103,145)(104,146)(105,141)(106,142)(107,143)(108,153)(109,154)(110,155)(111,165)(112,166)(113,167)(114,162)(115,163)(116,164)(117,159)(118,160)(119,161)(120,156)(121,157)(122,158)(123,168)(124,169)(125,170)(126,180)(127,181)(128,182)(129,177)(130,178)(131,179)(132,174)(133,175)(134,176)(135,171)(136,172)(137,173);; s2 := ( 3, 96)( 4, 98)( 5, 97)( 6, 93)( 7, 95)( 8, 94)( 9,105)( 10,107)( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,137)( 25,136)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,130)( 32,129)( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,115)( 47,114)( 48,141)( 49,143)( 50,142)( 51,138)( 52,140)( 53,139)( 54,150)( 55,152)( 56,151)( 57,147)( 58,149)( 59,148)( 60,144)( 61,146)( 62,145)( 63,173)( 64,172)( 65,171)( 66,170)( 67,169)( 68,168)( 69,182)( 70,181)( 71,180)( 72,179)( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,158)( 79,157)( 80,156)( 81,155)( 82,154)( 83,153)( 84,167)( 85,166)( 86,165)( 87,164)( 88,163)( 89,162)( 90,161)( 91,160)( 92,159);; s3 := ( 3, 18)( 4, 20)( 5, 19)( 6, 21)( 7, 23)( 8, 22)( 9, 24)( 10, 26)( 11, 25)( 12, 27)( 13, 29)( 14, 28)( 15, 30)( 16, 32)( 17, 31)( 33, 35)( 36, 38)( 39, 41)( 42, 44)( 45, 47)( 48, 63)( 49, 65)( 50, 64)( 51, 66)( 52, 68)( 53, 67)( 54, 69)( 55, 71)( 56, 70)( 57, 72)( 58, 74)( 59, 73)( 60, 75)( 61, 77)( 62, 76)( 78, 80)( 81, 83)( 84, 86)( 87, 89)( 90, 92)( 93,108)( 94,110)( 95,109)( 96,111)( 97,113)( 98,112)( 99,114)(100,116)(101,115)(102,117)(103,119)(104,118)(105,120)(106,122)(107,121)(123,125)(126,128)(129,131)(132,134)(135,137)(138,153)(139,155)(140,154)(141,156)(142,158)(143,157)(144,159)(145,161)(146,160)(147,162)(148,164)(149,163)(150,165)(151,167)(152,166)(168,170)(171,173)(174,176)(177,179)(180,182);; 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(182)!(1,2); s1 := Sym(182)!( 6, 15)( 7, 16)( 8, 17)( 9, 12)( 10, 13)( 11, 14)( 21, 30)( 22, 31)( 23, 32)( 24, 27)( 25, 28)( 26, 29)( 36, 45)( 37, 46)( 38, 47)( 39, 42)( 40, 43)( 41, 44)( 51, 60)( 52, 61)( 53, 62)( 54, 57)( 55, 58)( 56, 59)( 66, 75)( 67, 76)( 68, 77)( 69, 72)( 70, 73)( 71, 74)( 81, 90)( 82, 91)( 83, 92)( 84, 87)( 85, 88)( 86, 89)( 93,138)( 94,139)( 95,140)( 96,150)( 97,151)( 98,152)( 99,147)(100,148)(101,149)(102,144)(103,145)(104,146)(105,141)(106,142)(107,143)(108,153)(109,154)(110,155)(111,165)(112,166)(113,167)(114,162)(115,163)(116,164)(117,159)(118,160)(119,161)(120,156)(121,157)(122,158)(123,168)(124,169)(125,170)(126,180)(127,181)(128,182)(129,177)(130,178)(131,179)(132,174)(133,175)(134,176)(135,171)(136,172)(137,173); s2 := Sym(182)!( 3, 96)( 4, 98)( 5, 97)( 6, 93)( 7, 95)( 8, 94)( 9,105)( 10,107)( 11,106)( 12,102)( 13,104)( 14,103)( 15, 99)( 16,101)( 17,100)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,137)( 25,136)( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,130)( 32,129)( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,122)( 40,121)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,115)( 47,114)( 48,141)( 49,143)( 50,142)( 51,138)( 52,140)( 53,139)( 54,150)( 55,152)( 56,151)( 57,147)( 58,149)( 59,148)( 60,144)( 61,146)( 62,145)( 63,173)( 64,172)( 65,171)( 66,170)( 67,169)( 68,168)( 69,182)( 70,181)( 71,180)( 72,179)( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,158)( 79,157)( 80,156)( 81,155)( 82,154)( 83,153)( 84,167)( 85,166)( 86,165)( 87,164)( 88,163)( 89,162)( 90,161)( 91,160)( 92,159); s3 := Sym(182)!( 3, 18)( 4, 20)( 5, 19)( 6, 21)( 7, 23)( 8, 22)( 9, 24)( 10, 26)( 11, 25)( 12, 27)( 13, 29)( 14, 28)( 15, 30)( 16, 32)( 17, 31)( 33, 35)( 36, 38)( 39, 41)( 42, 44)( 45, 47)( 48, 63)( 49, 65)( 50, 64)( 51, 66)( 52, 68)( 53, 67)( 54, 69)( 55, 71)( 56, 70)( 57, 72)( 58, 74)( 59, 73)( 60, 75)( 61, 77)( 62, 76)( 78, 80)( 81, 83)( 84, 86)( 87, 89)( 90, 92)( 93,108)( 94,110)( 95,109)( 96,111)( 97,113)( 98,112)( 99,114)(100,116)(101,115)(102,117)(103,119)(104,118)(105,120)(106,122)(107,121)(123,125)(126,128)(129,131)(132,134)(135,137)(138,153)(139,155)(140,154)(141,156)(142,158)(143,157)(144,159)(145,161)(146,160)(147,162)(148,164)(149,163)(150,165)(151,167)(152,166)(168,170)(171,173)(174,176)(177,179)(180,182); 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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 >;