Overview
- Group
- SmallGroup(648,301)
- Rank
- 3
- Schläfli Type
- {6,6}
- Vertices, edges, …
- 54, 162, 54
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 6
- 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 := ( 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);; s1 := ( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)( 8, 18)( 9, 17)( 20, 21)( 23, 24)( 26, 27)( 28, 66)( 29, 65)( 30, 64)( 31, 69)( 32, 68)( 33, 67)( 34, 72)( 35, 71)( 36, 70)( 37, 57)( 38, 56)( 39, 55)( 40, 60)( 41, 59)( 42, 58)( 43, 63)( 44, 62)( 45, 61)( 46, 75)( 47, 74)( 48, 73)( 49, 78)( 50, 77)( 51, 76)( 52, 81)( 53, 80)( 54, 79)( 82, 91)( 83, 93)( 84, 92)( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(101,102)(104,105)(107,108)(109,147)(110,146)(111,145)(112,150)(113,149)(114,148)(115,153)(116,152)(117,151)(118,138)(119,137)(120,136)(121,141)(122,140)(123,139)(124,144)(125,143)(126,142)(127,156)(128,155)(129,154)(130,159)(131,158)(132,157)(133,162)(134,161)(135,160);; s2 := ( 1,109)( 2,111)( 3,110)( 4,114)( 5,113)( 6,112)( 7,116)( 8,115)( 9,117)( 10,134)( 11,133)( 12,135)( 13,127)( 14,129)( 15,128)( 16,132)( 17,131)( 18,130)( 19,121)( 20,123)( 21,122)( 22,126)( 23,125)( 24,124)( 25,119)( 26,118)( 27,120)( 28, 82)( 29, 84)( 30, 83)( 31, 87)( 32, 86)( 33, 85)( 34, 89)( 35, 88)( 36, 90)( 37,107)( 38,106)( 39,108)( 40,100)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46, 94)( 47, 96)( 48, 95)( 49, 99)( 50, 98)( 51, 97)( 52, 92)( 53, 91)( 54, 93)( 55,138)( 56,137)( 57,136)( 58,140)( 59,139)( 60,141)( 61,142)( 62,144)( 63,143)( 64,160)( 65,162)( 66,161)( 67,156)( 68,155)( 69,154)( 70,158)( 71,157)( 72,159)( 73,150)( 74,149)( 75,148)( 76,152)( 77,151)( 78,153)( 79,145)( 80,147)( 81,146);; 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(162)!( 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); s1 := Sym(162)!( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)( 8, 18)( 9, 17)( 20, 21)( 23, 24)( 26, 27)( 28, 66)( 29, 65)( 30, 64)( 31, 69)( 32, 68)( 33, 67)( 34, 72)( 35, 71)( 36, 70)( 37, 57)( 38, 56)( 39, 55)( 40, 60)( 41, 59)( 42, 58)( 43, 63)( 44, 62)( 45, 61)( 46, 75)( 47, 74)( 48, 73)( 49, 78)( 50, 77)( 51, 76)( 52, 81)( 53, 80)( 54, 79)( 82, 91)( 83, 93)( 84, 92)( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(101,102)(104,105)(107,108)(109,147)(110,146)(111,145)(112,150)(113,149)(114,148)(115,153)(116,152)(117,151)(118,138)(119,137)(120,136)(121,141)(122,140)(123,139)(124,144)(125,143)(126,142)(127,156)(128,155)(129,154)(130,159)(131,158)(132,157)(133,162)(134,161)(135,160); s2 := Sym(162)!( 1,109)( 2,111)( 3,110)( 4,114)( 5,113)( 6,112)( 7,116)( 8,115)( 9,117)( 10,134)( 11,133)( 12,135)( 13,127)( 14,129)( 15,128)( 16,132)( 17,131)( 18,130)( 19,121)( 20,123)( 21,122)( 22,126)( 23,125)( 24,124)( 25,119)( 26,118)( 27,120)( 28, 82)( 29, 84)( 30, 83)( 31, 87)( 32, 86)( 33, 85)( 34, 89)( 35, 88)( 36, 90)( 37,107)( 38,106)( 39,108)( 40,100)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46, 94)( 47, 96)( 48, 95)( 49, 99)( 50, 98)( 51, 97)( 52, 92)( 53, 91)( 54, 93)( 55,138)( 56,137)( 57,136)( 58,140)( 59,139)( 60,141)( 61,142)( 62,144)( 63,143)( 64,160)( 65,162)( 66,161)( 67,156)( 68,155)( 69,154)( 70,158)( 71,157)( 72,159)( 73,150)( 74,149)( 75,148)( 76,152)( 77,151)( 78,153)( 79,145)( 80,147)( 81,146); 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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.