Overview
- Group
- SmallGroup(432,292)
- Rank
- 3
- Schläfli Type
- {12,18}
- Vertices, edges, …
- 12, 108, 18
- Order of s0s1s2
- 36
- Order of s0s1s2s1
- 2
- Also known as
- {12,18|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105);; s1 := ( 1, 58)( 2, 60)( 3, 59)( 4, 55)( 5, 57)( 6, 56)( 7, 61)( 8, 63)( 9, 62)( 10, 77)( 11, 76)( 12, 78)( 13, 74)( 14, 73)( 15, 75)( 16, 80)( 17, 79)( 18, 81)( 19, 68)( 20, 67)( 21, 69)( 22, 65)( 23, 64)( 24, 66)( 25, 71)( 26, 70)( 27, 72)( 28, 85)( 29, 87)( 30, 86)( 31, 82)( 32, 84)( 33, 83)( 34, 88)( 35, 90)( 36, 89)( 37,104)( 38,103)( 39,105)( 40,101)( 41,100)( 42,102)( 43,107)( 44,106)( 45,108)( 46, 95)( 47, 94)( 48, 96)( 49, 92)( 50, 91)( 51, 93)( 52, 98)( 53, 97)( 54, 99);; s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)( 8, 18)( 9, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 37)( 29, 39)( 30, 38)( 31, 40)( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 91)( 83, 93)( 84, 92)( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,101)(103,104)(106,107);; 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*s0*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,
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(108)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 55, 82)( 56, 83)( 57, 84)( 58, 88)( 59, 89)( 60, 90)( 61, 85)( 62, 86)( 63, 87)( 64, 91)( 65, 92)( 66, 93)( 67, 97)( 68, 98)( 69, 99)( 70, 94)( 71, 95)( 72, 96)( 73,100)( 74,101)( 75,102)( 76,106)( 77,107)( 78,108)( 79,103)( 80,104)( 81,105); s1 := Sym(108)!( 1, 58)( 2, 60)( 3, 59)( 4, 55)( 5, 57)( 6, 56)( 7, 61)( 8, 63)( 9, 62)( 10, 77)( 11, 76)( 12, 78)( 13, 74)( 14, 73)( 15, 75)( 16, 80)( 17, 79)( 18, 81)( 19, 68)( 20, 67)( 21, 69)( 22, 65)( 23, 64)( 24, 66)( 25, 71)( 26, 70)( 27, 72)( 28, 85)( 29, 87)( 30, 86)( 31, 82)( 32, 84)( 33, 83)( 34, 88)( 35, 90)( 36, 89)( 37,104)( 38,103)( 39,105)( 40,101)( 41,100)( 42,102)( 43,107)( 44,106)( 45,108)( 46, 95)( 47, 94)( 48, 96)( 49, 92)( 50, 91)( 51, 93)( 52, 98)( 53, 97)( 54, 99); s2 := Sym(108)!( 1, 10)( 2, 12)( 3, 11)( 4, 13)( 5, 15)( 6, 14)( 7, 16)( 8, 18)( 9, 17)( 19, 20)( 22, 23)( 25, 26)( 28, 37)( 29, 39)( 30, 38)( 31, 40)( 32, 42)( 33, 41)( 34, 43)( 35, 45)( 36, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 91)( 83, 93)( 84, 92)( 85, 94)( 86, 96)( 87, 95)( 88, 97)( 89, 99)( 90, 98)(100,101)(103,104)(106,107); poly := sub<Sym(108)|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*s0*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, 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.