Overview
- Group
- SmallGroup(1440,4569)
- Rank
- 4
- Schläfli Type
- {2,18,20}
- Vertices, edges, …
- 2, 18, 180, 20
- Order of s0s1s2s3
- 90
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
10-fold
15-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)( 57, 60)( 58, 62)( 63,127)( 64,129)( 65,128)( 66,130)( 67,123)( 68,125)( 69,124)( 70,126)( 71,131)( 72,133)( 73,132)( 74,134)( 75,139)( 76,141)( 77,140)( 78,142)( 79,135)( 80,137)( 81,136)( 82,138)( 83,143)( 84,145)( 85,144)( 86,146)( 87,151)( 88,153)( 89,152)( 90,154)( 91,147)( 92,149)( 93,148)( 94,150)( 95,155)( 96,157)( 97,156)( 98,158)( 99,163)(100,165)(101,164)(102,166)(103,159)(104,161)(105,160)(106,162)(107,167)(108,169)(109,168)(110,170)(111,175)(112,177)(113,176)(114,178)(115,171)(116,173)(117,172)(118,174)(119,179)(120,181)(121,180)(122,182);; s2 := ( 3, 63)( 4, 64)( 5, 66)( 6, 65)( 7, 71)( 8, 72)( 9, 74)( 10, 73)( 11, 67)( 12, 68)( 13, 70)( 14, 69)( 15,111)( 16,112)( 17,114)( 18,113)( 19,119)( 20,120)( 21,122)( 22,121)( 23,115)( 24,116)( 25,118)( 26,117)( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)( 34,109)( 35,103)( 36,104)( 37,106)( 38,105)( 39, 87)( 40, 88)( 41, 90)( 42, 89)( 43, 95)( 44, 96)( 45, 98)( 46, 97)( 47, 91)( 48, 92)( 49, 94)( 50, 93)( 51, 75)( 52, 76)( 53, 78)( 54, 77)( 55, 83)( 56, 84)( 57, 86)( 58, 85)( 59, 79)( 60, 80)( 61, 82)( 62, 81)(123,127)(124,128)(125,130)(126,129)(133,134)(135,175)(136,176)(137,178)(138,177)(139,171)(140,172)(141,174)(142,173)(143,179)(144,180)(145,182)(146,181)(147,163)(148,164)(149,166)(150,165)(151,159)(152,160)(153,162)(154,161)(155,167)(156,168)(157,170)(158,169);; s3 := ( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 22)( 8, 21)( 9, 20)( 10, 19)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 27, 54)( 28, 53)( 29, 52)( 30, 51)( 31, 58)( 32, 57)( 33, 56)( 34, 55)( 35, 62)( 36, 61)( 37, 60)( 38, 59)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)( 63, 78)( 64, 77)( 65, 76)( 66, 75)( 67, 82)( 68, 81)( 69, 80)( 70, 79)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 87,114)( 88,113)( 89,112)( 90,111)( 91,118)( 92,117)( 93,116)( 94,115)( 95,122)( 96,121)( 97,120)( 98,119)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(123,138)(124,137)(125,136)(126,135)(127,142)(128,141)(129,140)(130,139)(131,146)(132,145)(133,144)(134,143)(147,174)(148,173)(149,172)(150,171)(151,178)(152,177)(153,176)(154,175)(155,182)(156,181)(157,180)(158,179)(159,162)(160,161)(163,166)(164,165)(167,170)(168,169);; 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*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(182)!(1,2); s1 := Sym(182)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)( 57, 60)( 58, 62)( 63,127)( 64,129)( 65,128)( 66,130)( 67,123)( 68,125)( 69,124)( 70,126)( 71,131)( 72,133)( 73,132)( 74,134)( 75,139)( 76,141)( 77,140)( 78,142)( 79,135)( 80,137)( 81,136)( 82,138)( 83,143)( 84,145)( 85,144)( 86,146)( 87,151)( 88,153)( 89,152)( 90,154)( 91,147)( 92,149)( 93,148)( 94,150)( 95,155)( 96,157)( 97,156)( 98,158)( 99,163)(100,165)(101,164)(102,166)(103,159)(104,161)(105,160)(106,162)(107,167)(108,169)(109,168)(110,170)(111,175)(112,177)(113,176)(114,178)(115,171)(116,173)(117,172)(118,174)(119,179)(120,181)(121,180)(122,182); s2 := Sym(182)!( 3, 63)( 4, 64)( 5, 66)( 6, 65)( 7, 71)( 8, 72)( 9, 74)( 10, 73)( 11, 67)( 12, 68)( 13, 70)( 14, 69)( 15,111)( 16,112)( 17,114)( 18,113)( 19,119)( 20,120)( 21,122)( 22,121)( 23,115)( 24,116)( 25,118)( 26,117)( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)( 34,109)( 35,103)( 36,104)( 37,106)( 38,105)( 39, 87)( 40, 88)( 41, 90)( 42, 89)( 43, 95)( 44, 96)( 45, 98)( 46, 97)( 47, 91)( 48, 92)( 49, 94)( 50, 93)( 51, 75)( 52, 76)( 53, 78)( 54, 77)( 55, 83)( 56, 84)( 57, 86)( 58, 85)( 59, 79)( 60, 80)( 61, 82)( 62, 81)(123,127)(124,128)(125,130)(126,129)(133,134)(135,175)(136,176)(137,178)(138,177)(139,171)(140,172)(141,174)(142,173)(143,179)(144,180)(145,182)(146,181)(147,163)(148,164)(149,166)(150,165)(151,159)(152,160)(153,162)(154,161)(155,167)(156,168)(157,170)(158,169); s3 := Sym(182)!( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 22)( 8, 21)( 9, 20)( 10, 19)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 27, 54)( 28, 53)( 29, 52)( 30, 51)( 31, 58)( 32, 57)( 33, 56)( 34, 55)( 35, 62)( 36, 61)( 37, 60)( 38, 59)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)( 63, 78)( 64, 77)( 65, 76)( 66, 75)( 67, 82)( 68, 81)( 69, 80)( 70, 79)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 87,114)( 88,113)( 89,112)( 90,111)( 91,118)( 92,117)( 93,116)( 94,115)( 95,122)( 96,121)( 97,120)( 98,119)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(123,138)(124,137)(125,136)(126,135)(127,142)(128,141)(129,140)(130,139)(131,146)(132,145)(133,144)(134,143)(147,174)(148,173)(149,172)(150,171)(151,178)(152,177)(153,176)(154,175)(155,182)(156,181)(157,180)(158,179)(159,162)(160,161)(163,166)(164,165)(167,170)(168,169); 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*s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s1*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;