Overview
- Group
- SmallGroup(1296,1860)
- Rank
- 4
- Schläfli Type
- {18,6,2}
- Vertices, edges, …
- 54, 162, 18, 2
- Order of s0s1s2s3
- 6
- 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)( 4, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 55)( 29, 57)( 30, 56)( 31, 60)( 32, 59)( 33, 58)( 34, 62)( 35, 61)( 36, 63)( 37, 73)( 38, 75)( 39, 74)( 40, 78)( 41, 77)( 42, 76)( 43, 80)( 44, 79)( 45, 81)( 46, 64)( 47, 66)( 48, 65)( 49, 69)( 50, 68)( 51, 67)( 52, 71)( 53, 70)( 54, 72)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,136)(110,138)(111,137)(112,141)(113,140)(114,139)(115,143)(116,142)(117,144)(118,154)(119,156)(120,155)(121,159)(122,158)(123,157)(124,161)(125,160)(126,162)(127,145)(128,147)(129,146)(130,150)(131,149)(132,148)(133,152)(134,151)(135,153);; s1 := ( 1,148)( 2,150)( 3,149)( 4,151)( 5,153)( 6,152)( 7,145)( 8,147)( 9,146)( 10,142)( 11,144)( 12,143)( 13,136)( 14,138)( 15,137)( 16,139)( 17,141)( 18,140)( 19,156)( 20,155)( 21,154)( 22,159)( 23,158)( 24,157)( 25,162)( 26,161)( 27,160)( 28,121)( 29,123)( 30,122)( 31,124)( 32,126)( 33,125)( 34,118)( 35,120)( 36,119)( 37,115)( 38,117)( 39,116)( 40,109)( 41,111)( 42,110)( 43,112)( 44,114)( 45,113)( 46,129)( 47,128)( 48,127)( 49,132)( 50,131)( 51,130)( 52,135)( 53,134)( 54,133)( 55, 94)( 56, 96)( 57, 95)( 58, 97)( 59, 99)( 60, 98)( 61, 91)( 62, 93)( 63, 92)( 64, 88)( 65, 90)( 66, 89)( 67, 82)( 68, 84)( 69, 83)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)( 76,105)( 77,104)( 78,103)( 79,108)( 80,107)( 81,106);; s2 := ( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 85, 89)( 86, 90)( 87, 88)( 91,100)( 92,101)( 93,102)( 94,107)( 95,108)( 96,106)( 97,105)( 98,103)( 99,104)(112,116)(113,117)(114,115)(118,127)(119,128)(120,129)(121,134)(122,135)(123,133)(124,132)(125,130)(126,131)(139,143)(140,144)(141,142)(145,154)(146,155)(147,156)(148,161)(149,162)(150,160)(151,159)(152,157)(153,158);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(164)!( 2, 3)( 4, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 55)( 29, 57)( 30, 56)( 31, 60)( 32, 59)( 33, 58)( 34, 62)( 35, 61)( 36, 63)( 37, 73)( 38, 75)( 39, 74)( 40, 78)( 41, 77)( 42, 76)( 43, 80)( 44, 79)( 45, 81)( 46, 64)( 47, 66)( 48, 65)( 49, 69)( 50, 68)( 51, 67)( 52, 71)( 53, 70)( 54, 72)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,136)(110,138)(111,137)(112,141)(113,140)(114,139)(115,143)(116,142)(117,144)(118,154)(119,156)(120,155)(121,159)(122,158)(123,157)(124,161)(125,160)(126,162)(127,145)(128,147)(129,146)(130,150)(131,149)(132,148)(133,152)(134,151)(135,153); s1 := Sym(164)!( 1,148)( 2,150)( 3,149)( 4,151)( 5,153)( 6,152)( 7,145)( 8,147)( 9,146)( 10,142)( 11,144)( 12,143)( 13,136)( 14,138)( 15,137)( 16,139)( 17,141)( 18,140)( 19,156)( 20,155)( 21,154)( 22,159)( 23,158)( 24,157)( 25,162)( 26,161)( 27,160)( 28,121)( 29,123)( 30,122)( 31,124)( 32,126)( 33,125)( 34,118)( 35,120)( 36,119)( 37,115)( 38,117)( 39,116)( 40,109)( 41,111)( 42,110)( 43,112)( 44,114)( 45,113)( 46,129)( 47,128)( 48,127)( 49,132)( 50,131)( 51,130)( 52,135)( 53,134)( 54,133)( 55, 94)( 56, 96)( 57, 95)( 58, 97)( 59, 99)( 60, 98)( 61, 91)( 62, 93)( 63, 92)( 64, 88)( 65, 90)( 66, 89)( 67, 82)( 68, 84)( 69, 83)( 70, 85)( 71, 87)( 72, 86)( 73,102)( 74,101)( 75,100)( 76,105)( 77,104)( 78,103)( 79,108)( 80,107)( 81,106); s2 := Sym(164)!( 4, 8)( 5, 9)( 6, 7)( 10, 19)( 11, 20)( 12, 21)( 13, 26)( 14, 27)( 15, 25)( 16, 24)( 17, 22)( 18, 23)( 31, 35)( 32, 36)( 33, 34)( 37, 46)( 38, 47)( 39, 48)( 40, 53)( 41, 54)( 42, 52)( 43, 51)( 44, 49)( 45, 50)( 58, 62)( 59, 63)( 60, 61)( 64, 73)( 65, 74)( 66, 75)( 67, 80)( 68, 81)( 69, 79)( 70, 78)( 71, 76)( 72, 77)( 85, 89)( 86, 90)( 87, 88)( 91,100)( 92,101)( 93,102)( 94,107)( 95,108)( 96,106)( 97,105)( 98,103)( 99,104)(112,116)(113,117)(114,115)(118,127)(119,128)(120,129)(121,134)(122,135)(123,133)(124,132)(125,130)(126,131)(139,143)(140,144)(141,142)(145,154)(146,155)(147,156)(148,161)(149,162)(150,160)(151,159)(152,157)(153,158); 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;