Overview
- Group
- SmallGroup(1620,140)
- Rank
- 3
- Schläfli Type
- {15,18}
- Vertices, edges, …
- 45, 405, 54
- Order of s0s1s2
- 30
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
15-fold
27-fold
45-fold
81-fold
135-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)( 5, 6)( 8, 9)( 10, 37)( 11, 39)( 12, 38)( 13, 40)( 14, 42)( 15, 41)( 16, 43)( 17, 45)( 18, 44)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,128)( 56,127)( 57,129)( 58,131)( 59,130)( 60,132)( 61,134)( 62,133)( 63,135)( 64,119)( 65,118)( 66,120)( 67,122)( 68,121)( 69,123)( 70,125)( 71,124)( 72,126)( 73,110)( 74,109)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108);; s1 := ( 1, 58)( 2, 60)( 3, 59)( 4, 63)( 5, 62)( 6, 61)( 7, 56)( 8, 55)( 9, 57)( 10, 49)( 11, 51)( 12, 50)( 13, 54)( 14, 53)( 15, 52)( 16, 47)( 17, 46)( 18, 48)( 19, 85)( 20, 87)( 21, 86)( 22, 90)( 23, 89)( 24, 88)( 25, 83)( 26, 82)( 27, 84)( 28, 76)( 29, 78)( 30, 77)( 31, 81)( 32, 80)( 33, 79)( 34, 74)( 35, 73)( 36, 75)( 37, 67)( 38, 69)( 39, 68)( 40, 72)( 41, 71)( 42, 70)( 43, 65)( 44, 64)( 45, 66)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,127)(110,129)(111,128)(112,132)(113,131)(114,130)(115,134)(116,133)(117,135)(119,120)(121,123)(124,125);; s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 46, 92)( 47, 91)( 48, 93)( 49, 98)( 50, 97)( 51, 99)( 52, 95)( 53, 94)( 54, 96)( 55,101)( 56,100)( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)( 64,110)( 65,109)( 66,111)( 67,116)( 68,115)( 69,117)( 70,113)( 71,112)( 72,114)( 73,119)( 74,118)( 75,120)( 76,125)( 77,124)( 78,126)( 79,122)( 80,121)( 81,123)( 82,128)( 83,127)( 84,129)( 85,134)( 86,133)( 87,135)( 88,131)( 89,130)( 90,132);; 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,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(135)!( 2, 3)( 5, 6)( 8, 9)( 10, 37)( 11, 39)( 12, 38)( 13, 40)( 14, 42)( 15, 41)( 16, 43)( 17, 45)( 18, 44)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,128)( 56,127)( 57,129)( 58,131)( 59,130)( 60,132)( 61,134)( 62,133)( 63,135)( 64,119)( 65,118)( 66,120)( 67,122)( 68,121)( 69,123)( 70,125)( 71,124)( 72,126)( 73,110)( 74,109)( 75,111)( 76,113)( 77,112)( 78,114)( 79,116)( 80,115)( 81,117)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108); s1 := Sym(135)!( 1, 58)( 2, 60)( 3, 59)( 4, 63)( 5, 62)( 6, 61)( 7, 56)( 8, 55)( 9, 57)( 10, 49)( 11, 51)( 12, 50)( 13, 54)( 14, 53)( 15, 52)( 16, 47)( 17, 46)( 18, 48)( 19, 85)( 20, 87)( 21, 86)( 22, 90)( 23, 89)( 24, 88)( 25, 83)( 26, 82)( 27, 84)( 28, 76)( 29, 78)( 30, 77)( 31, 81)( 32, 80)( 33, 79)( 34, 74)( 35, 73)( 36, 75)( 37, 67)( 38, 69)( 39, 68)( 40, 72)( 41, 71)( 42, 70)( 43, 65)( 44, 64)( 45, 66)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,127)(110,129)(111,128)(112,132)(113,131)(114,130)(115,134)(116,133)(117,135)(119,120)(121,123)(124,125); s2 := Sym(135)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 46, 92)( 47, 91)( 48, 93)( 49, 98)( 50, 97)( 51, 99)( 52, 95)( 53, 94)( 54, 96)( 55,101)( 56,100)( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)( 64,110)( 65,109)( 66,111)( 67,116)( 68,115)( 69,117)( 70,113)( 71,112)( 72,114)( 73,119)( 74,118)( 75,120)( 76,125)( 77,124)( 78,126)( 79,122)( 80,121)( 81,123)( 82,128)( 83,127)( 84,129)( 85,134)( 86,133)( 87,135)( 88,131)( 89,130)( 90,132); poly := sub<Sym(135)|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, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References
None.
to this polytope.