Overview
- Group
- SmallGroup(288,340)
- Rank
- 3
- Schläfli Type
- {9,8}
- Vertices, edges, …
- 18, 72, 16
- Order of s0s1s2
- 36
- Order of s0s1s2s1
- 8
- 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
4-fold
6-fold
8-fold
12-fold
24-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9, 17)( 10, 18)( 11, 21)( 12, 22)( 13, 19)( 14, 20)( 15, 24)( 16, 23)( 25, 57)( 26, 58)( 27, 61)( 28, 62)( 29, 59)( 30, 60)( 31, 64)( 32, 63)( 33, 49)( 34, 50)( 35, 53)( 36, 54)( 37, 51)( 38, 52)( 39, 56)( 40, 55)( 41, 65)( 42, 66)( 43, 69)( 44, 70)( 45, 67)( 46, 68)( 47, 72)( 48, 71)( 73, 74)( 75, 78)( 76, 77)( 81, 90)( 82, 89)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 95)( 88, 96)( 97,130)( 98,129)( 99,134)(100,133)(101,132)(102,131)(103,135)(104,136)(105,122)(106,121)(107,126)(108,125)(109,124)(110,123)(111,127)(112,128)(113,138)(114,137)(115,142)(116,141)(117,140)(118,139)(119,143)(120,144);; s1 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 67, 68)( 69, 71)( 70, 72)( 73, 98)( 74, 97)( 75, 99)( 76,100)( 77,104)( 78,103)( 79,102)( 80,101)( 81,114)( 82,113)( 83,115)( 84,116)( 85,120)( 86,119)( 87,118)( 88,117)( 89,106)( 90,105)( 91,107)( 92,108)( 93,112)( 94,111)( 95,110)( 96,109)(121,130)(122,129)(123,131)(124,132)(125,136)(126,135)(127,134)(128,133)(137,138)(141,144)(142,143);; s2 := ( 1, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 87)( 10, 88)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 82)( 16, 81)( 17, 95)( 18, 96)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 90)( 24, 89)( 25,103)( 26,104)( 27,101)( 28,102)( 29,100)( 30, 99)( 31, 98)( 32, 97)( 33,111)( 34,112)( 35,109)( 36,110)( 37,108)( 38,107)( 39,106)( 40,105)( 41,119)( 42,120)( 43,117)( 44,118)( 45,116)( 46,115)( 47,114)( 48,113)( 49,127)( 50,128)( 51,125)( 52,126)( 53,124)( 54,123)( 55,122)( 56,121)( 57,135)( 58,136)( 59,133)( 60,134)( 61,132)( 62,131)( 63,130)( 64,129)( 65,143)( 66,144)( 67,141)( 68,142)( 69,140)( 70,139)( 71,138)( 72,137);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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(144)!( 3, 5)( 4, 6)( 7, 8)( 9, 17)( 10, 18)( 11, 21)( 12, 22)( 13, 19)( 14, 20)( 15, 24)( 16, 23)( 25, 57)( 26, 58)( 27, 61)( 28, 62)( 29, 59)( 30, 60)( 31, 64)( 32, 63)( 33, 49)( 34, 50)( 35, 53)( 36, 54)( 37, 51)( 38, 52)( 39, 56)( 40, 55)( 41, 65)( 42, 66)( 43, 69)( 44, 70)( 45, 67)( 46, 68)( 47, 72)( 48, 71)( 73, 74)( 75, 78)( 76, 77)( 81, 90)( 82, 89)( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 95)( 88, 96)( 97,130)( 98,129)( 99,134)(100,133)(101,132)(102,131)(103,135)(104,136)(105,122)(106,121)(107,126)(108,125)(109,124)(110,123)(111,127)(112,128)(113,138)(114,137)(115,142)(116,141)(117,140)(118,139)(119,143)(120,144); s1 := Sym(144)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 67, 68)( 69, 71)( 70, 72)( 73, 98)( 74, 97)( 75, 99)( 76,100)( 77,104)( 78,103)( 79,102)( 80,101)( 81,114)( 82,113)( 83,115)( 84,116)( 85,120)( 86,119)( 87,118)( 88,117)( 89,106)( 90,105)( 91,107)( 92,108)( 93,112)( 94,111)( 95,110)( 96,109)(121,130)(122,129)(123,131)(124,132)(125,136)(126,135)(127,134)(128,133)(137,138)(141,144)(142,143); s2 := Sym(144)!( 1, 79)( 2, 80)( 3, 77)( 4, 78)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 87)( 10, 88)( 11, 85)( 12, 86)( 13, 84)( 14, 83)( 15, 82)( 16, 81)( 17, 95)( 18, 96)( 19, 93)( 20, 94)( 21, 92)( 22, 91)( 23, 90)( 24, 89)( 25,103)( 26,104)( 27,101)( 28,102)( 29,100)( 30, 99)( 31, 98)( 32, 97)( 33,111)( 34,112)( 35,109)( 36,110)( 37,108)( 38,107)( 39,106)( 40,105)( 41,119)( 42,120)( 43,117)( 44,118)( 45,116)( 46,115)( 47,114)( 48,113)( 49,127)( 50,128)( 51,125)( 52,126)( 53,124)( 54,123)( 55,122)( 56,121)( 57,135)( 58,136)( 59,133)( 60,134)( 61,132)( 62,131)( 63,130)( 64,129)( 65,143)( 66,144)( 67,141)( 68,142)( 69,140)( 70,139)( 71,138)( 72,137); poly := sub<Sym(144)|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*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*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.