Overview
- Group
- SmallGroup(648,301)
- Rank
- 3
- Schläfli Type
- {6,18}
- Vertices, edges, …
- 18, 162, 54
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
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
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
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, 57)( 29, 56)( 30, 55)( 31, 59)( 32, 58)( 33, 60)( 34, 61)( 35, 63)( 36, 62)( 37, 75)( 38, 74)( 39, 73)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 66)( 47, 65)( 48, 64)( 49, 68)( 50, 67)( 51, 69)( 52, 70)( 53, 72)( 54, 71)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,138)(110,137)(111,136)(112,140)(113,139)(114,141)(115,142)(116,144)(117,143)(118,156)(119,155)(120,154)(121,158)(122,157)(123,159)(124,160)(125,162)(126,161)(127,147)(128,146)(129,145)(130,149)(131,148)(132,150)(133,151)(134,153)(135,152);; 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 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 57)( 29, 56)( 30, 55)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 66)( 38, 65)( 39, 64)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 75)( 47, 74)( 48, 73)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,138)(110,137)(111,136)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,147)(119,146)(120,145)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(162)!( 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, 57)( 29, 56)( 30, 55)( 31, 59)( 32, 58)( 33, 60)( 34, 61)( 35, 63)( 36, 62)( 37, 75)( 38, 74)( 39, 73)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 66)( 47, 65)( 48, 64)( 49, 68)( 50, 67)( 51, 69)( 52, 70)( 53, 72)( 54, 71)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,138)(110,137)(111,136)(112,140)(113,139)(114,141)(115,142)(116,144)(117,143)(118,156)(119,155)(120,154)(121,158)(122,157)(123,159)(124,160)(125,162)(126,161)(127,147)(128,146)(129,145)(130,149)(131,148)(132,150)(133,151)(134,153)(135,152); s1 := Sym(162)!( 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(162)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 57)( 29, 56)( 30, 55)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 66)( 38, 65)( 39, 64)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 75)( 47, 74)( 48, 73)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,138)(110,137)(111,136)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,147)(119,146)(120,145)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157); poly := sub<Sym(162)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.