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