Overview
- Group
- SmallGroup(1440,5676)
- Rank
- 4
- Schläfli Type
- {6,60,2}
- Vertices, edges, …
- 6, 180, 60, 2
- Order of s0s1s2s3
- 60
- 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
12-fold
15-fold
18-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 := ( 16, 31)( 17, 32)( 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)( 61, 76)( 62, 77)( 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)(106,121)(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)(162,177)(163,178)(164,179)(165,180);; s1 := ( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 26)( 7, 30)( 8, 29)( 9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 71)( 52, 75)( 53, 74)( 54, 73)( 55, 72)( 56, 66)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,161)( 97,165)( 98,164)( 99,163)(100,162)(101,156)(102,160)(103,159)(104,158)(105,157)(106,136)(107,140)(108,139)(109,138)(110,137)(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)(118,144)(119,143)(120,142)(121,166)(122,170)(123,169)(124,168)(125,167)(126,176)(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)(134,173)(135,172);; s2 := ( 1, 97)( 2, 96)( 3,100)( 4, 99)( 5, 98)( 6, 92)( 7, 91)( 8, 95)( 9, 94)( 10, 93)( 11,102)( 12,101)( 13,105)( 14,104)( 15,103)( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)( 25,108)( 26,117)( 27,116)( 28,120)( 29,119)( 30,118)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,122)( 37,121)( 38,125)( 39,124)( 40,123)( 41,132)( 42,131)( 43,135)( 44,134)( 45,133)( 46,142)( 47,141)( 48,145)( 49,144)( 50,143)( 51,137)( 52,136)( 53,140)( 54,139)( 55,138)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,157)( 62,156)( 63,160)( 64,159)( 65,158)( 66,152)( 67,151)( 68,155)( 69,154)( 70,153)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,172)( 77,171)( 78,175)( 79,174)( 80,173)( 81,167)( 82,166)( 83,170)( 84,169)( 85,168)( 86,177)( 87,176)( 88,180)( 89,179)( 90,178);; 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)!( 16, 31)( 17, 32)( 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)( 61, 76)( 62, 77)( 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)(106,121)(107,122)(108,123)(109,124)(110,125)(111,126)(112,127)(113,128)(114,129)(115,130)(116,131)(117,132)(118,133)(119,134)(120,135)(151,166)(152,167)(153,168)(154,169)(155,170)(156,171)(157,172)(158,173)(159,174)(160,175)(161,176)(162,177)(163,178)(164,179)(165,180); s1 := Sym(182)!( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 26)( 7, 30)( 8, 29)( 9, 28)( 10, 27)( 11, 21)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 71)( 52, 75)( 53, 74)( 54, 73)( 55, 72)( 56, 66)( 57, 70)( 58, 69)( 59, 68)( 60, 67)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,161)( 97,165)( 98,164)( 99,163)(100,162)(101,156)(102,160)(103,159)(104,158)(105,157)(106,136)(107,140)(108,139)(109,138)(110,137)(111,146)(112,150)(113,149)(114,148)(115,147)(116,141)(117,145)(118,144)(119,143)(120,142)(121,166)(122,170)(123,169)(124,168)(125,167)(126,176)(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)(134,173)(135,172); s2 := Sym(182)!( 1, 97)( 2, 96)( 3,100)( 4, 99)( 5, 98)( 6, 92)( 7, 91)( 8, 95)( 9, 94)( 10, 93)( 11,102)( 12,101)( 13,105)( 14,104)( 15,103)( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)( 25,108)( 26,117)( 27,116)( 28,120)( 29,119)( 30,118)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,122)( 37,121)( 38,125)( 39,124)( 40,123)( 41,132)( 42,131)( 43,135)( 44,134)( 45,133)( 46,142)( 47,141)( 48,145)( 49,144)( 50,143)( 51,137)( 52,136)( 53,140)( 54,139)( 55,138)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,157)( 62,156)( 63,160)( 64,159)( 65,158)( 66,152)( 67,151)( 68,155)( 69,154)( 70,153)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,172)( 77,171)( 78,175)( 79,174)( 80,173)( 81,167)( 82,166)( 83,170)( 84,169)( 85,168)( 86,177)( 87,176)( 88,180)( 89,179)( 90,178); 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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 >;