Overview
- Group
- SmallGroup(1440,1584)
- Rank
- 4
- Schläfli Type
- {2,18,20}
- Vertices, edges, …
- 2, 18, 180, 20
- 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 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 18, 35)( 19, 34)( 20, 33)( 21, 38)( 22, 37)( 23, 36)( 24, 41)( 25, 40)( 26, 39)( 27, 44)( 28, 43)( 29, 42)( 30, 47)( 31, 46)( 32, 45)( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 63, 80)( 64, 79)( 65, 78)( 66, 83)( 67, 82)( 68, 81)( 69, 86)( 70, 85)( 71, 84)( 72, 89)( 73, 88)( 74, 87)( 75, 92)( 76, 91)( 77, 90)( 94, 95)( 97, 98)(100,101)(103,104)(106,107)(108,125)(109,124)(110,123)(111,128)(112,127)(113,126)(114,131)(115,130)(116,129)(117,134)(118,133)(119,132)(120,137)(121,136)(122,135)(139,140)(142,143)(145,146)(148,149)(151,152)(153,170)(154,169)(155,168)(156,173)(157,172)(158,171)(159,176)(160,175)(161,174)(162,179)(163,178)(164,177)(165,182)(166,181)(167,180);; s2 := ( 3, 18)( 4, 20)( 5, 19)( 6, 30)( 7, 32)( 8, 31)( 9, 27)( 10, 29)( 11, 28)( 12, 24)( 13, 26)( 14, 25)( 15, 21)( 16, 23)( 17, 22)( 33, 35)( 36, 47)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 63)( 49, 65)( 50, 64)( 51, 75)( 52, 77)( 53, 76)( 54, 72)( 55, 74)( 56, 73)( 57, 69)( 58, 71)( 59, 70)( 60, 66)( 61, 68)( 62, 67)( 78, 80)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 93,153)( 94,155)( 95,154)( 96,165)( 97,167)( 98,166)( 99,162)(100,164)(101,163)(102,159)(103,161)(104,160)(105,156)(106,158)(107,157)(108,138)(109,140)(110,139)(111,150)(112,152)(113,151)(114,147)(115,149)(116,148)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(123,170)(124,169)(125,168)(126,182)(127,181)(128,180)(129,179)(130,178)(131,177)(132,176)(133,175)(134,174)(135,173)(136,172)(137,171);; s3 := ( 3, 96)( 4, 97)( 5, 98)( 6, 93)( 7, 94)( 8, 95)( 9,105)( 10,106)( 11,107)( 12,102)( 13,103)( 14,104)( 15, 99)( 16,100)( 17,101)( 18,111)( 19,112)( 20,113)( 21,108)( 22,109)( 23,110)( 24,120)( 25,121)( 26,122)( 27,117)( 28,118)( 29,119)( 30,114)( 31,115)( 32,116)( 33,126)( 34,127)( 35,128)( 36,123)( 37,124)( 38,125)( 39,135)( 40,136)( 41,137)( 42,132)( 43,133)( 44,134)( 45,129)( 46,130)( 47,131)( 48,141)( 49,142)( 50,143)( 51,138)( 52,139)( 53,140)( 54,150)( 55,151)( 56,152)( 57,147)( 58,148)( 59,149)( 60,144)( 61,145)( 62,146)( 63,156)( 64,157)( 65,158)( 66,153)( 67,154)( 68,155)( 69,165)( 70,166)( 71,167)( 72,162)( 73,163)( 74,164)( 75,159)( 76,160)( 77,161)( 78,171)( 79,172)( 80,173)( 81,168)( 82,169)( 83,170)( 84,180)( 85,181)( 86,182)( 87,177)( 88,178)( 89,179)( 90,174)( 91,175)( 92,176);; 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*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,
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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(182)!(1,2); s1 := Sym(182)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 18, 35)( 19, 34)( 20, 33)( 21, 38)( 22, 37)( 23, 36)( 24, 41)( 25, 40)( 26, 39)( 27, 44)( 28, 43)( 29, 42)( 30, 47)( 31, 46)( 32, 45)( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 63, 80)( 64, 79)( 65, 78)( 66, 83)( 67, 82)( 68, 81)( 69, 86)( 70, 85)( 71, 84)( 72, 89)( 73, 88)( 74, 87)( 75, 92)( 76, 91)( 77, 90)( 94, 95)( 97, 98)(100,101)(103,104)(106,107)(108,125)(109,124)(110,123)(111,128)(112,127)(113,126)(114,131)(115,130)(116,129)(117,134)(118,133)(119,132)(120,137)(121,136)(122,135)(139,140)(142,143)(145,146)(148,149)(151,152)(153,170)(154,169)(155,168)(156,173)(157,172)(158,171)(159,176)(160,175)(161,174)(162,179)(163,178)(164,177)(165,182)(166,181)(167,180); s2 := Sym(182)!( 3, 18)( 4, 20)( 5, 19)( 6, 30)( 7, 32)( 8, 31)( 9, 27)( 10, 29)( 11, 28)( 12, 24)( 13, 26)( 14, 25)( 15, 21)( 16, 23)( 17, 22)( 33, 35)( 36, 47)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 63)( 49, 65)( 50, 64)( 51, 75)( 52, 77)( 53, 76)( 54, 72)( 55, 74)( 56, 73)( 57, 69)( 58, 71)( 59, 70)( 60, 66)( 61, 68)( 62, 67)( 78, 80)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 93,153)( 94,155)( 95,154)( 96,165)( 97,167)( 98,166)( 99,162)(100,164)(101,163)(102,159)(103,161)(104,160)(105,156)(106,158)(107,157)(108,138)(109,140)(110,139)(111,150)(112,152)(113,151)(114,147)(115,149)(116,148)(117,144)(118,146)(119,145)(120,141)(121,143)(122,142)(123,170)(124,169)(125,168)(126,182)(127,181)(128,180)(129,179)(130,178)(131,177)(132,176)(133,175)(134,174)(135,173)(136,172)(137,171); s3 := Sym(182)!( 3, 96)( 4, 97)( 5, 98)( 6, 93)( 7, 94)( 8, 95)( 9,105)( 10,106)( 11,107)( 12,102)( 13,103)( 14,104)( 15, 99)( 16,100)( 17,101)( 18,111)( 19,112)( 20,113)( 21,108)( 22,109)( 23,110)( 24,120)( 25,121)( 26,122)( 27,117)( 28,118)( 29,119)( 30,114)( 31,115)( 32,116)( 33,126)( 34,127)( 35,128)( 36,123)( 37,124)( 38,125)( 39,135)( 40,136)( 41,137)( 42,132)( 43,133)( 44,134)( 45,129)( 46,130)( 47,131)( 48,141)( 49,142)( 50,143)( 51,138)( 52,139)( 53,140)( 54,150)( 55,151)( 56,152)( 57,147)( 58,148)( 59,149)( 60,144)( 61,145)( 62,146)( 63,156)( 64,157)( 65,158)( 66,153)( 67,154)( 68,155)( 69,165)( 70,166)( 71,167)( 72,162)( 73,163)( 74,164)( 75,159)( 76,160)( 77,161)( 78,171)( 79,172)( 80,173)( 81,168)( 82,169)( 83,170)( 84,180)( 85,181)( 86,182)( 87,177)( 88,178)( 89,179)( 90,174)( 91,175)( 92,176); 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*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, 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*s2*s3*s2*s3 >;