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