Overview
- Group
- SmallGroup(1296,1862)
- Rank
- 4
- Schläfli Type
- {2,6,6}
- Vertices, edges, …
- 2, 54, 162, 54
- 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 := (1,2);; s1 := ( 6, 10)( 7, 11)( 8, 9)( 12, 21)( 13, 22)( 14, 23)( 15, 28)( 16, 29)( 17, 27)( 18, 26)( 19, 24)( 20, 25)( 33, 37)( 34, 38)( 35, 36)( 39, 48)( 40, 49)( 41, 50)( 42, 55)( 43, 56)( 44, 54)( 45, 53)( 46, 51)( 47, 52)( 60, 64)( 61, 65)( 62, 63)( 66, 75)( 67, 76)( 68, 77)( 69, 82)( 70, 83)( 71, 81)( 72, 80)( 73, 78)( 74, 79)( 87, 91)( 88, 92)( 89, 90)( 93,102)( 94,103)( 95,104)( 96,109)( 97,110)( 98,108)( 99,107)(100,105)(101,106)(114,118)(115,119)(116,117)(120,129)(121,130)(122,131)(123,136)(124,137)(125,135)(126,134)(127,132)(128,133)(141,145)(142,146)(143,144)(147,156)(148,157)(149,158)(150,163)(151,164)(152,162)(153,161)(154,159)(155,160);; s2 := ( 3, 12)( 4, 14)( 5, 13)( 6, 15)( 7, 17)( 8, 16)( 9, 18)( 10, 20)( 11, 19)( 22, 23)( 25, 26)( 28, 29)( 30, 68)( 31, 67)( 32, 66)( 33, 71)( 34, 70)( 35, 69)( 36, 74)( 37, 73)( 38, 72)( 39, 59)( 40, 58)( 41, 57)( 42, 62)( 43, 61)( 44, 60)( 45, 65)( 46, 64)( 47, 63)( 48, 77)( 49, 76)( 50, 75)( 51, 80)( 52, 79)( 53, 78)( 54, 83)( 55, 82)( 56, 81)( 84, 93)( 85, 95)( 86, 94)( 87, 96)( 88, 98)( 89, 97)( 90, 99)( 91,101)( 92,100)(103,104)(106,107)(109,110)(111,149)(112,148)(113,147)(114,152)(115,151)(116,150)(117,155)(118,154)(119,153)(120,140)(121,139)(122,138)(123,143)(124,142)(125,141)(126,146)(127,145)(128,144)(129,158)(130,157)(131,156)(132,161)(133,160)(134,159)(135,164)(136,163)(137,162);; s3 := ( 3,111)( 4,113)( 5,112)( 6,116)( 7,115)( 8,114)( 9,118)( 10,117)( 11,119)( 12,136)( 13,135)( 14,137)( 15,129)( 16,131)( 17,130)( 18,134)( 19,133)( 20,132)( 21,123)( 22,125)( 23,124)( 24,128)( 25,127)( 26,126)( 27,121)( 28,120)( 29,122)( 30, 84)( 31, 86)( 32, 85)( 33, 89)( 34, 88)( 35, 87)( 36, 91)( 37, 90)( 38, 92)( 39,109)( 40,108)( 41,110)( 42,102)( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48, 96)( 49, 98)( 50, 97)( 51,101)( 52,100)( 53, 99)( 54, 94)( 55, 93)( 56, 95)( 57,140)( 58,139)( 59,138)( 60,142)( 61,141)( 62,143)( 63,144)( 64,146)( 65,145)( 66,162)( 67,164)( 68,163)( 69,158)( 70,157)( 71,156)( 72,160)( 73,159)( 74,161)( 75,152)( 76,151)( 77,150)( 78,154)( 79,153)( 80,155)( 81,147)( 82,149)( 83,148);; 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(164)!(1,2); s1 := Sym(164)!( 6, 10)( 7, 11)( 8, 9)( 12, 21)( 13, 22)( 14, 23)( 15, 28)( 16, 29)( 17, 27)( 18, 26)( 19, 24)( 20, 25)( 33, 37)( 34, 38)( 35, 36)( 39, 48)( 40, 49)( 41, 50)( 42, 55)( 43, 56)( 44, 54)( 45, 53)( 46, 51)( 47, 52)( 60, 64)( 61, 65)( 62, 63)( 66, 75)( 67, 76)( 68, 77)( 69, 82)( 70, 83)( 71, 81)( 72, 80)( 73, 78)( 74, 79)( 87, 91)( 88, 92)( 89, 90)( 93,102)( 94,103)( 95,104)( 96,109)( 97,110)( 98,108)( 99,107)(100,105)(101,106)(114,118)(115,119)(116,117)(120,129)(121,130)(122,131)(123,136)(124,137)(125,135)(126,134)(127,132)(128,133)(141,145)(142,146)(143,144)(147,156)(148,157)(149,158)(150,163)(151,164)(152,162)(153,161)(154,159)(155,160); s2 := Sym(164)!( 3, 12)( 4, 14)( 5, 13)( 6, 15)( 7, 17)( 8, 16)( 9, 18)( 10, 20)( 11, 19)( 22, 23)( 25, 26)( 28, 29)( 30, 68)( 31, 67)( 32, 66)( 33, 71)( 34, 70)( 35, 69)( 36, 74)( 37, 73)( 38, 72)( 39, 59)( 40, 58)( 41, 57)( 42, 62)( 43, 61)( 44, 60)( 45, 65)( 46, 64)( 47, 63)( 48, 77)( 49, 76)( 50, 75)( 51, 80)( 52, 79)( 53, 78)( 54, 83)( 55, 82)( 56, 81)( 84, 93)( 85, 95)( 86, 94)( 87, 96)( 88, 98)( 89, 97)( 90, 99)( 91,101)( 92,100)(103,104)(106,107)(109,110)(111,149)(112,148)(113,147)(114,152)(115,151)(116,150)(117,155)(118,154)(119,153)(120,140)(121,139)(122,138)(123,143)(124,142)(125,141)(126,146)(127,145)(128,144)(129,158)(130,157)(131,156)(132,161)(133,160)(134,159)(135,164)(136,163)(137,162); s3 := Sym(164)!( 3,111)( 4,113)( 5,112)( 6,116)( 7,115)( 8,114)( 9,118)( 10,117)( 11,119)( 12,136)( 13,135)( 14,137)( 15,129)( 16,131)( 17,130)( 18,134)( 19,133)( 20,132)( 21,123)( 22,125)( 23,124)( 24,128)( 25,127)( 26,126)( 27,121)( 28,120)( 29,122)( 30, 84)( 31, 86)( 32, 85)( 33, 89)( 34, 88)( 35, 87)( 36, 91)( 37, 90)( 38, 92)( 39,109)( 40,108)( 41,110)( 42,102)( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48, 96)( 49, 98)( 50, 97)( 51,101)( 52,100)( 53, 99)( 54, 94)( 55, 93)( 56, 95)( 57,140)( 58,139)( 59,138)( 60,142)( 61,141)( 62,143)( 63,144)( 64,146)( 65,145)( 66,162)( 67,164)( 68,163)( 69,158)( 70,157)( 71,156)( 72,160)( 73,159)( 74,161)( 75,152)( 76,151)( 77,150)( 78,154)( 79,153)( 80,155)( 81,147)( 82,149)( 83,148); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;