Overview
- Group
- SmallGroup(1296,1857)
- Rank
- 4
- Schläfli Type
- {18,18,2}
- Vertices, edges, …
- 18, 162, 18, 2
- Order of s0s1s2s3
- 18
- 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
6-fold
9-fold
18-fold
27-fold
54-fold
81-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)( 10, 21)( 11, 20)( 12, 19)( 13, 24)( 14, 23)( 15, 22)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 32, 33)( 35, 36)( 37, 48)( 38, 47)( 39, 46)( 40, 51)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)( 68, 77)( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 86, 87)( 89, 90)( 91,102)( 92,101)( 93,100)( 94,105)( 95,104)( 96,103)( 97,108)( 98,107)( 99,106)(110,111)(113,114)(116,117)(118,129)(119,128)(120,127)(121,132)(122,131)(123,130)(124,135)(125,134)(126,133)(137,138)(140,141)(143,144)(145,156)(146,155)(147,154)(148,159)(149,158)(150,157)(151,162)(152,161)(153,160);; s1 := ( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 70)( 29, 72)( 30, 71)( 31, 67)( 32, 69)( 33, 68)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 58)( 41, 60)( 42, 59)( 43, 55)( 44, 57)( 45, 56)( 46, 81)( 47, 80)( 48, 79)( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 82, 91)( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)( 90, 95)(100,102)(103,108)(104,107)(105,106)(109,151)(110,153)(111,152)(112,148)(113,150)(114,149)(115,145)(116,147)(117,146)(118,142)(119,144)(120,143)(121,139)(122,141)(123,140)(124,136)(125,138)(126,137)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154);; s2 := ( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)( 8,114)( 9,113)( 10,129)( 11,128)( 12,127)( 13,135)( 14,134)( 15,133)( 16,132)( 17,131)( 18,130)( 19,120)( 20,119)( 21,118)( 22,126)( 23,125)( 24,124)( 25,123)( 26,122)( 27,121)( 28, 82)( 29, 84)( 30, 83)( 31, 88)( 32, 90)( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)( 40,108)( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46, 93)( 47, 92)( 48, 91)( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55,142)( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)( 64,162)( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)( 72,154)( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)( 80,146)( 81,145);; s3 := (163,164);; 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*s0*s1*s0*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,
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(164)!( 2, 3)( 5, 6)( 8, 9)( 10, 21)( 11, 20)( 12, 19)( 13, 24)( 14, 23)( 15, 22)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 32, 33)( 35, 36)( 37, 48)( 38, 47)( 39, 46)( 40, 51)( 41, 50)( 42, 49)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 59, 60)( 62, 63)( 64, 75)( 65, 74)( 66, 73)( 67, 78)( 68, 77)( 69, 76)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 86, 87)( 89, 90)( 91,102)( 92,101)( 93,100)( 94,105)( 95,104)( 96,103)( 97,108)( 98,107)( 99,106)(110,111)(113,114)(116,117)(118,129)(119,128)(120,127)(121,132)(122,131)(123,130)(124,135)(125,134)(126,133)(137,138)(140,141)(143,144)(145,156)(146,155)(147,154)(148,159)(149,158)(150,157)(151,162)(152,161)(153,160); s1 := Sym(164)!( 1, 10)( 2, 12)( 3, 11)( 4, 16)( 5, 18)( 6, 17)( 7, 13)( 8, 15)( 9, 14)( 19, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 70)( 29, 72)( 30, 71)( 31, 67)( 32, 69)( 33, 68)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 58)( 41, 60)( 42, 59)( 43, 55)( 44, 57)( 45, 56)( 46, 81)( 47, 80)( 48, 79)( 49, 78)( 50, 77)( 51, 76)( 52, 75)( 53, 74)( 54, 73)( 82, 91)( 83, 93)( 84, 92)( 85, 97)( 86, 99)( 87, 98)( 88, 94)( 89, 96)( 90, 95)(100,102)(103,108)(104,107)(105,106)(109,151)(110,153)(111,152)(112,148)(113,150)(114,149)(115,145)(116,147)(117,146)(118,142)(119,144)(120,143)(121,139)(122,141)(123,140)(124,136)(125,138)(126,137)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154); s2 := Sym(164)!( 1,109)( 2,111)( 3,110)( 4,115)( 5,117)( 6,116)( 7,112)( 8,114)( 9,113)( 10,129)( 11,128)( 12,127)( 13,135)( 14,134)( 15,133)( 16,132)( 17,131)( 18,130)( 19,120)( 20,119)( 21,118)( 22,126)( 23,125)( 24,124)( 25,123)( 26,122)( 27,121)( 28, 82)( 29, 84)( 30, 83)( 31, 88)( 32, 90)( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37,102)( 38,101)( 39,100)( 40,108)( 41,107)( 42,106)( 43,105)( 44,104)( 45,103)( 46, 93)( 47, 92)( 48, 91)( 49, 99)( 50, 98)( 51, 97)( 52, 96)( 53, 95)( 54, 94)( 55,142)( 56,144)( 57,143)( 58,139)( 59,141)( 60,140)( 61,136)( 62,138)( 63,137)( 64,162)( 65,161)( 66,160)( 67,159)( 68,158)( 69,157)( 70,156)( 71,155)( 72,154)( 73,153)( 74,152)( 75,151)( 76,150)( 77,149)( 78,148)( 79,147)( 80,146)( 81,145); s3 := Sym(164)!(163,164); poly := sub<Sym(164)|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*s0*s1*s0*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, 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 >;