Overview
- Group
- SmallGroup(1440,1665)
- Rank
- 4
- Schläfli Type
- {90,4,2}
- Vertices, edges, …
- 90, 180, 4, 2
- 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
4-fold
5-fold
6-fold
9-fold
10-fold
12-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 := ( 2, 3)( 4, 13)( 5, 15)( 6, 14)( 7, 10)( 8, 12)( 9, 11)( 16, 33)( 17, 32)( 18, 31)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 47, 48)( 49, 58)( 50, 60)( 51, 59)( 52, 55)( 53, 57)( 54, 56)( 61, 78)( 62, 77)( 63, 76)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 92, 93)( 94,103)( 95,105)( 96,104)( 97,100)( 98,102)( 99,101)(106,123)(107,122)(108,121)(109,135)(110,134)(111,133)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(137,138)(139,148)(140,150)(141,149)(142,145)(143,147)(144,146)(151,168)(152,167)(153,166)(154,180)(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169);; s1 := ( 1, 19)( 2, 21)( 3, 20)( 4, 16)( 5, 18)( 6, 17)( 7, 28)( 8, 30)( 9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 36)( 32, 35)( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 64)( 47, 66)( 48, 65)( 49, 61)( 50, 63)( 51, 62)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)( 76, 81)( 77, 80)( 78, 79)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,154)( 92,156)( 93,155)( 94,151)( 95,153)( 96,152)( 97,163)( 98,165)( 99,164)(100,160)(101,162)(102,161)(103,157)(104,159)(105,158)(106,139)(107,141)(108,140)(109,136)(110,138)(111,137)(112,148)(113,150)(114,149)(115,145)(116,147)(117,146)(118,142)(119,144)(120,143)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172);; s2 := ( 1, 91)( 2, 92)( 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);; s3 := (181,182);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(182)!( 2, 3)( 4, 13)( 5, 15)( 6, 14)( 7, 10)( 8, 12)( 9, 11)( 16, 33)( 17, 32)( 18, 31)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 47, 48)( 49, 58)( 50, 60)( 51, 59)( 52, 55)( 53, 57)( 54, 56)( 61, 78)( 62, 77)( 63, 76)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 92, 93)( 94,103)( 95,105)( 96,104)( 97,100)( 98,102)( 99,101)(106,123)(107,122)(108,121)(109,135)(110,134)(111,133)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(137,138)(139,148)(140,150)(141,149)(142,145)(143,147)(144,146)(151,168)(152,167)(153,166)(154,180)(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169); s1 := Sym(182)!( 1, 19)( 2, 21)( 3, 20)( 4, 16)( 5, 18)( 6, 17)( 7, 28)( 8, 30)( 9, 29)( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 31, 36)( 32, 35)( 33, 34)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 64)( 47, 66)( 48, 65)( 49, 61)( 50, 63)( 51, 62)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)( 76, 81)( 77, 80)( 78, 79)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,154)( 92,156)( 93,155)( 94,151)( 95,153)( 96,152)( 97,163)( 98,165)( 99,164)(100,160)(101,162)(102,161)(103,157)(104,159)(105,158)(106,139)(107,141)(108,140)(109,136)(110,138)(111,137)(112,148)(113,150)(114,149)(115,145)(116,147)(117,146)(118,142)(119,144)(120,143)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172); s2 := Sym(182)!( 1, 91)( 2, 92)( 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); s3 := Sym(182)!(181,182); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;