Overview
- Group
- SmallGroup(864,4321)
- Rank
- 3
- Schläfli Type
- {12,12}
- Vertices, edges, …
- 36, 216, 36
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- 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
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s1*s2*s1*(s0*(s2*s1)^2)^2*s2> of order 2
18 facets
- 18 of {12}*24
18 vertex figures
- 18 of {12}*24
Representations
Permutation Representation (GAP)
s0 := ( 1, 55)( 2, 56)( 3, 57)( 4, 61)( 5, 62)( 6, 63)( 7, 58)( 8, 59)( 9, 60)( 10, 73)( 11, 74)( 12, 75)( 13, 79)( 14, 80)( 15, 81)( 16, 76)( 17, 77)( 18, 78)( 19, 64)( 20, 65)( 21, 66)( 22, 70)( 23, 71)( 24, 72)( 25, 67)( 26, 68)( 27, 69)( 28, 82)( 29, 83)( 30, 84)( 31, 88)( 32, 89)( 33, 90)( 34, 85)( 35, 86)( 36, 87)( 37,100)( 38,101)( 39,102)( 40,106)( 41,107)( 42,108)( 43,103)( 44,104)( 45,105)( 46, 91)( 47, 92)( 48, 93)( 49, 97)( 50, 98)( 51, 99)( 52, 94)( 53, 95)( 54, 96);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 16)( 11, 18)( 12, 17)( 14, 15)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 31)( 29, 33)( 30, 32)( 35, 36)( 37, 43)( 38, 45)( 39, 44)( 41, 42)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 85)( 56, 87)( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 88)( 62, 90)( 63, 89)( 64, 97)( 65, 99)( 66, 98)( 67, 94)( 68, 96)( 69, 95)( 70, 91)( 71, 93)( 72, 92)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104);; s2 := ( 1, 2)( 4, 23)( 5, 22)( 6, 24)( 7, 17)( 8, 16)( 9, 18)( 10, 20)( 11, 19)( 12, 21)( 13, 14)( 25, 26)( 28, 29)( 31, 50)( 32, 49)( 33, 51)( 34, 44)( 35, 43)( 36, 45)( 37, 47)( 38, 46)( 39, 48)( 40, 41)( 52, 53)( 55, 56)( 58, 77)( 59, 76)( 60, 78)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 66, 75)( 67, 68)( 79, 80)( 82, 83)( 85,104)( 86,103)( 87,105)( 88, 98)( 89, 97)( 90, 99)( 91,101)( 92,100)( 93,102)( 94, 95)(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*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 1, 55)( 2, 56)( 3, 57)( 4, 61)( 5, 62)( 6, 63)( 7, 58)( 8, 59)( 9, 60)( 10, 73)( 11, 74)( 12, 75)( 13, 79)( 14, 80)( 15, 81)( 16, 76)( 17, 77)( 18, 78)( 19, 64)( 20, 65)( 21, 66)( 22, 70)( 23, 71)( 24, 72)( 25, 67)( 26, 68)( 27, 69)( 28, 82)( 29, 83)( 30, 84)( 31, 88)( 32, 89)( 33, 90)( 34, 85)( 35, 86)( 36, 87)( 37,100)( 38,101)( 39,102)( 40,106)( 41,107)( 42,108)( 43,103)( 44,104)( 45,105)( 46, 91)( 47, 92)( 48, 93)( 49, 97)( 50, 98)( 51, 99)( 52, 94)( 53, 95)( 54, 96); s1 := Sym(108)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 16)( 11, 18)( 12, 17)( 14, 15)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 31)( 29, 33)( 30, 32)( 35, 36)( 37, 43)( 38, 45)( 39, 44)( 41, 42)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 85)( 56, 87)( 57, 86)( 58, 82)( 59, 84)( 60, 83)( 61, 88)( 62, 90)( 63, 89)( 64, 97)( 65, 99)( 66, 98)( 67, 94)( 68, 96)( 69, 95)( 70, 91)( 71, 93)( 72, 92)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104); s2 := Sym(108)!( 1, 2)( 4, 23)( 5, 22)( 6, 24)( 7, 17)( 8, 16)( 9, 18)( 10, 20)( 11, 19)( 12, 21)( 13, 14)( 25, 26)( 28, 29)( 31, 50)( 32, 49)( 33, 51)( 34, 44)( 35, 43)( 36, 45)( 37, 47)( 38, 46)( 39, 48)( 40, 41)( 52, 53)( 55, 56)( 58, 77)( 59, 76)( 60, 78)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 66, 75)( 67, 68)( 79, 80)( 82, 83)( 85,104)( 86,103)( 87,105)( 88, 98)( 89, 97)( 90, 99)( 91,101)( 92,100)( 93,102)( 94, 95)(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*s2*s1*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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 >;
References
None.
to this polytope.