Overview
- Group
- SmallGroup(1296,2978)
- Rank
- 3
- Schläfli Type
- {6,36}
- Vertices, edges, …
- 18, 324, 108
- 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
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
9-fold
18-fold
27-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 := ( 1, 82)( 2, 83)( 3, 84)( 4, 85)( 5, 86)( 6, 87)( 7, 88)( 8, 89)( 9, 90)( 10,102)( 11,100)( 12,101)( 13,105)( 14,103)( 15,104)( 16,108)( 17,106)( 18,107)( 19, 92)( 20, 93)( 21, 91)( 22, 95)( 23, 96)( 24, 94)( 25, 98)( 26, 99)( 27, 97)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,156)( 38,154)( 39,155)( 40,159)( 41,157)( 42,158)( 43,162)( 44,160)( 45,161)( 46,146)( 47,147)( 48,145)( 49,149)( 50,150)( 51,148)( 52,152)( 53,153)( 54,151)( 55,109)( 56,110)( 57,111)( 58,112)( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,129)( 65,127)( 66,128)( 67,132)( 68,130)( 69,131)( 70,135)( 71,133)( 72,134)( 73,119)( 74,120)( 75,118)( 76,122)( 77,123)( 78,121)( 79,125)( 80,126)( 81,124);; s1 := ( 1, 28)( 2, 30)( 3, 29)( 4, 36)( 5, 35)( 6, 34)( 7, 33)( 8, 32)( 9, 31)( 10, 39)( 11, 38)( 12, 37)( 13, 44)( 14, 43)( 15, 45)( 16, 41)( 17, 40)( 18, 42)( 19, 47)( 20, 46)( 21, 48)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)( 27, 50)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 64, 66)( 67, 71)( 68, 70)( 69, 72)( 73, 74)( 76, 79)( 77, 81)( 78, 80)( 82,109)( 83,111)( 84,110)( 85,117)( 86,116)( 87,115)( 88,114)( 89,113)( 90,112)( 91,120)( 92,119)( 93,118)( 94,125)( 95,124)( 96,126)( 97,122)( 98,121)( 99,123)(100,128)(101,127)(102,129)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131)(137,138)(139,144)(140,143)(141,142)(145,147)(148,152)(149,151)(150,153)(154,155)(157,160)(158,162)(159,161);; s2 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 35)( 17, 34)( 18, 36)( 19, 59)( 20, 58)( 21, 60)( 22, 56)( 23, 55)( 24, 57)( 25, 61)( 26, 63)( 27, 62)( 37, 42)( 38, 41)( 39, 40)( 43, 44)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 71)( 53, 70)( 54, 72)( 73, 76)( 74, 78)( 75, 77)( 79, 81)( 82, 85)( 83, 87)( 84, 86)( 88, 90)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)( 96,109)( 97,116)( 98,115)( 99,117)(100,140)(101,139)(102,141)(103,137)(104,136)(105,138)(106,142)(107,144)(108,143)(118,123)(119,122)(120,121)(124,125)(127,150)(128,149)(129,148)(130,147)(131,146)(132,145)(133,152)(134,151)(135,153)(154,157)(155,159)(156,158)(160,162);; 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*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(162)!( 1, 82)( 2, 83)( 3, 84)( 4, 85)( 5, 86)( 6, 87)( 7, 88)( 8, 89)( 9, 90)( 10,102)( 11,100)( 12,101)( 13,105)( 14,103)( 15,104)( 16,108)( 17,106)( 18,107)( 19, 92)( 20, 93)( 21, 91)( 22, 95)( 23, 96)( 24, 94)( 25, 98)( 26, 99)( 27, 97)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,156)( 38,154)( 39,155)( 40,159)( 41,157)( 42,158)( 43,162)( 44,160)( 45,161)( 46,146)( 47,147)( 48,145)( 49,149)( 50,150)( 51,148)( 52,152)( 53,153)( 54,151)( 55,109)( 56,110)( 57,111)( 58,112)( 59,113)( 60,114)( 61,115)( 62,116)( 63,117)( 64,129)( 65,127)( 66,128)( 67,132)( 68,130)( 69,131)( 70,135)( 71,133)( 72,134)( 73,119)( 74,120)( 75,118)( 76,122)( 77,123)( 78,121)( 79,125)( 80,126)( 81,124); s1 := Sym(162)!( 1, 28)( 2, 30)( 3, 29)( 4, 36)( 5, 35)( 6, 34)( 7, 33)( 8, 32)( 9, 31)( 10, 39)( 11, 38)( 12, 37)( 13, 44)( 14, 43)( 15, 45)( 16, 41)( 17, 40)( 18, 42)( 19, 47)( 20, 46)( 21, 48)( 22, 52)( 23, 54)( 24, 53)( 25, 49)( 26, 51)( 27, 50)( 56, 57)( 58, 63)( 59, 62)( 60, 61)( 64, 66)( 67, 71)( 68, 70)( 69, 72)( 73, 74)( 76, 79)( 77, 81)( 78, 80)( 82,109)( 83,111)( 84,110)( 85,117)( 86,116)( 87,115)( 88,114)( 89,113)( 90,112)( 91,120)( 92,119)( 93,118)( 94,125)( 95,124)( 96,126)( 97,122)( 98,121)( 99,123)(100,128)(101,127)(102,129)(103,133)(104,135)(105,134)(106,130)(107,132)(108,131)(137,138)(139,144)(140,143)(141,142)(145,147)(148,152)(149,151)(150,153)(154,155)(157,160)(158,162)(159,161); s2 := Sym(162)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 35)( 17, 34)( 18, 36)( 19, 59)( 20, 58)( 21, 60)( 22, 56)( 23, 55)( 24, 57)( 25, 61)( 26, 63)( 27, 62)( 37, 42)( 38, 41)( 39, 40)( 43, 44)( 46, 69)( 47, 68)( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 71)( 53, 70)( 54, 72)( 73, 76)( 74, 78)( 75, 77)( 79, 81)( 82, 85)( 83, 87)( 84, 86)( 88, 90)( 91,114)( 92,113)( 93,112)( 94,111)( 95,110)( 96,109)( 97,116)( 98,115)( 99,117)(100,140)(101,139)(102,141)(103,137)(104,136)(105,138)(106,142)(107,144)(108,143)(118,123)(119,122)(120,121)(124,125)(127,150)(128,149)(129,148)(130,147)(131,146)(132,145)(133,152)(134,151)(135,153)(154,157)(155,159)(156,158)(160,162); 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*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1, s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0 >;
References
None.
to this polytope.