Overview
- Group
- SmallGroup(1080,286)
- Rank
- 3
- Schläfli Type
- {18,30}
- Vertices, edges, …
- 18, 270, 30
- Order of s0s1s2
- 90
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
10-fold
15-fold
27-fold
30-fold
45-fold
54-fold
90-fold
135-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 16, 31)( 17, 33)( 18, 32)( 19, 34)( 20, 36)( 21, 35)( 22, 37)( 23, 39)( 24, 38)( 25, 40)( 26, 42)( 27, 41)( 28, 43)( 29, 45)( 30, 44)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,101)( 56,100)( 57,102)( 58,104)( 59,103)( 60,105)( 61,122)( 62,121)( 63,123)( 64,125)( 65,124)( 66,126)( 67,128)( 68,127)( 69,129)( 70,131)( 71,130)( 72,132)( 73,134)( 74,133)( 75,135)( 76,107)( 77,106)( 78,108)( 79,110)( 80,109)( 81,111)( 82,113)( 83,112)( 84,114)( 85,116)( 86,115)( 87,117)( 88,119)( 89,118)( 90,120);; s1 := ( 1, 61)( 2, 63)( 3, 62)( 4, 73)( 5, 75)( 6, 74)( 7, 70)( 8, 72)( 9, 71)( 10, 67)( 11, 69)( 12, 68)( 13, 64)( 14, 66)( 15, 65)( 16, 46)( 17, 48)( 18, 47)( 19, 58)( 20, 60)( 21, 59)( 22, 55)( 23, 57)( 24, 56)( 25, 52)( 26, 54)( 27, 53)( 28, 49)( 29, 51)( 30, 50)( 31, 76)( 32, 78)( 33, 77)( 34, 88)( 35, 90)( 36, 89)( 37, 85)( 38, 87)( 39, 86)( 40, 82)( 41, 84)( 42, 83)( 43, 79)( 44, 81)( 45, 80)( 91,107)( 92,106)( 93,108)( 94,119)( 95,118)( 96,120)( 97,116)( 98,115)( 99,117)(100,113)(101,112)(102,114)(103,110)(104,109)(105,111)(121,122)(124,134)(125,133)(126,135)(127,131)(128,130)(129,132);; s2 := ( 1, 4)( 2, 5)( 3, 6)( 7, 13)( 8, 14)( 9, 15)( 16, 34)( 17, 35)( 18, 36)( 19, 31)( 20, 32)( 21, 33)( 22, 43)( 23, 44)( 24, 45)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 61, 79)( 62, 80)( 63, 81)( 64, 76)( 65, 77)( 66, 78)( 67, 88)( 68, 89)( 69, 90)( 70, 85)( 71, 86)( 72, 87)( 73, 82)( 74, 83)( 75, 84)( 91, 94)( 92, 95)( 93, 96)( 97,103)( 98,104)( 99,105)(106,124)(107,125)(108,126)(109,121)(110,122)(111,123)(112,133)(113,134)(114,135)(115,130)(116,131)(117,132)(118,127)(119,128)(120,129);; 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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(135)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 16, 31)( 17, 33)( 18, 32)( 19, 34)( 20, 36)( 21, 35)( 22, 37)( 23, 39)( 24, 38)( 25, 40)( 26, 42)( 27, 41)( 28, 43)( 29, 45)( 30, 44)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,101)( 56,100)( 57,102)( 58,104)( 59,103)( 60,105)( 61,122)( 62,121)( 63,123)( 64,125)( 65,124)( 66,126)( 67,128)( 68,127)( 69,129)( 70,131)( 71,130)( 72,132)( 73,134)( 74,133)( 75,135)( 76,107)( 77,106)( 78,108)( 79,110)( 80,109)( 81,111)( 82,113)( 83,112)( 84,114)( 85,116)( 86,115)( 87,117)( 88,119)( 89,118)( 90,120); s1 := Sym(135)!( 1, 61)( 2, 63)( 3, 62)( 4, 73)( 5, 75)( 6, 74)( 7, 70)( 8, 72)( 9, 71)( 10, 67)( 11, 69)( 12, 68)( 13, 64)( 14, 66)( 15, 65)( 16, 46)( 17, 48)( 18, 47)( 19, 58)( 20, 60)( 21, 59)( 22, 55)( 23, 57)( 24, 56)( 25, 52)( 26, 54)( 27, 53)( 28, 49)( 29, 51)( 30, 50)( 31, 76)( 32, 78)( 33, 77)( 34, 88)( 35, 90)( 36, 89)( 37, 85)( 38, 87)( 39, 86)( 40, 82)( 41, 84)( 42, 83)( 43, 79)( 44, 81)( 45, 80)( 91,107)( 92,106)( 93,108)( 94,119)( 95,118)( 96,120)( 97,116)( 98,115)( 99,117)(100,113)(101,112)(102,114)(103,110)(104,109)(105,111)(121,122)(124,134)(125,133)(126,135)(127,131)(128,130)(129,132); s2 := Sym(135)!( 1, 4)( 2, 5)( 3, 6)( 7, 13)( 8, 14)( 9, 15)( 16, 34)( 17, 35)( 18, 36)( 19, 31)( 20, 32)( 21, 33)( 22, 43)( 23, 44)( 24, 45)( 25, 40)( 26, 41)( 27, 42)( 28, 37)( 29, 38)( 30, 39)( 46, 49)( 47, 50)( 48, 51)( 52, 58)( 53, 59)( 54, 60)( 61, 79)( 62, 80)( 63, 81)( 64, 76)( 65, 77)( 66, 78)( 67, 88)( 68, 89)( 69, 90)( 70, 85)( 71, 86)( 72, 87)( 73, 82)( 74, 83)( 75, 84)( 91, 94)( 92, 95)( 93, 96)( 97,103)( 98,104)( 99,105)(106,124)(107,125)(108,126)(109,121)(110,122)(111,123)(112,133)(113,134)(114,135)(115,130)(116,131)(117,132)(118,127)(119,128)(120,129); 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*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*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 >;
References
None.
to this polytope.