Overview
- Group
- SmallGroup(1296,2976)
- Rank
- 3
- Schläfli Type
- {36,6}
- Vertices, edges, …
- 108, 324, 18
- Order of s0s1s2
- 36
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
9-fold
18-fold
27-fold
36-fold
54-fold
81-fold
108-fold
162-fold
Covers minimal covers in bold
None in this atlas.
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, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 55)( 29, 57)( 30, 56)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 73)( 47, 75)( 48, 74)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 90)( 86, 89)( 87, 88)( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)(103,108)(104,107)(105,106)(109,136)(110,138)(111,137)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,145)(119,147)(120,146)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,154)(128,156)(129,155)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)( 16, 63)( 17, 62)( 18, 61)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)( 27, 34)( 37, 76)( 38, 78)( 39, 77)( 40, 73)( 41, 75)( 42, 74)( 43, 81)( 44, 80)( 45, 79)( 46, 49)( 47, 51)( 48, 50)( 52, 54)( 64, 67)( 65, 69)( 66, 68)( 70, 72)( 82, 85)( 83, 87)( 84, 86)( 88, 90)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,112)(101,114)(102,113)(103,109)(104,111)(105,110)(106,117)(107,116)(108,115)(118,157)(119,159)(120,158)(121,154)(122,156)(123,155)(124,162)(125,161)(126,160)(127,130)(128,132)(129,131)(133,135)(145,148)(146,150)(147,149)(151,153);; s2 := ( 1, 91)( 2, 92)( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19,100)( 20,101)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)( 26,107)( 27,108)( 28,145)( 29,146)( 30,147)( 31,148)( 32,149)( 33,150)( 34,151)( 35,152)( 36,153)( 37,136)( 38,137)( 39,138)( 40,139)( 41,140)( 42,141)( 43,142)( 44,143)( 45,144)( 46,154)( 47,155)( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,118)( 56,119)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)( 72,117)( 73,127)( 74,128)( 75,129)( 76,130)( 77,131)( 78,132)( 79,133)( 80,134)( 81,135);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(162)!( 2, 3)( 4, 9)( 5, 8)( 6, 7)( 11, 12)( 13, 18)( 14, 17)( 15, 16)( 20, 21)( 22, 27)( 23, 26)( 24, 25)( 28, 55)( 29, 57)( 30, 56)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 64)( 38, 66)( 39, 65)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 73)( 47, 75)( 48, 74)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 90)( 86, 89)( 87, 88)( 92, 93)( 94, 99)( 95, 98)( 96, 97)(101,102)(103,108)(104,107)(105,106)(109,136)(110,138)(111,137)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,145)(119,147)(120,146)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,154)(128,156)(129,155)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157); s1 := Sym(162)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)( 16, 63)( 17, 62)( 18, 61)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)( 27, 34)( 37, 76)( 38, 78)( 39, 77)( 40, 73)( 41, 75)( 42, 74)( 43, 81)( 44, 80)( 45, 79)( 46, 49)( 47, 51)( 48, 50)( 52, 54)( 64, 67)( 65, 69)( 66, 68)( 70, 72)( 82, 85)( 83, 87)( 84, 86)( 88, 90)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,112)(101,114)(102,113)(103,109)(104,111)(105,110)(106,117)(107,116)(108,115)(118,157)(119,159)(120,158)(121,154)(122,156)(123,155)(124,162)(125,161)(126,160)(127,130)(128,132)(129,131)(133,135)(145,148)(146,150)(147,149)(151,153); s2 := Sym(162)!( 1, 91)( 2, 92)( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19,100)( 20,101)( 21,102)( 22,103)( 23,104)( 24,105)( 25,106)( 26,107)( 27,108)( 28,145)( 29,146)( 30,147)( 31,148)( 32,149)( 33,150)( 34,151)( 35,152)( 36,153)( 37,136)( 38,137)( 39,138)( 40,139)( 41,140)( 42,141)( 43,142)( 44,143)( 45,144)( 46,154)( 47,155)( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,118)( 56,119)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,109)( 65,110)( 66,111)( 67,112)( 68,113)( 69,114)( 70,115)( 71,116)( 72,117)( 73,127)( 74,128)( 75,129)( 76,130)( 77,131)( 78,132)( 79,133)( 80,134)( 81,135); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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*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 >;
References
None.
to this polytope.