Overview
- Group
- SmallGroup(864,2282)
- Rank
- 3
- Schläfli Type
- {12,4}
- Vertices, edges, …
- 108, 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
12-fold
27-fold
54-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=<(s2*s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 2
18 facets
- 18 of {12}*24
60 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2> of order 2
18 facets
- 18 of {12}*24
54 vertex figures
- 54 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2> of order 3
12 facets
- 12 of {12}*24
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
9 facets
- 9 of {12}*24
30 vertex figures
P/N, where N=<(s0*s1*s2*s1)^3, (s0*s1)^2*(s2*s1*s0*s1)^2*s2> of order 4
9 facets
- 9 of {12}*24
27 vertex figures
- 27 of {4}*8
P/N, where N=<(s0*s1)^6, (s0*s2*s1)^2*s0*s1*(s2*s1*s0)^2*s2*s1*s2> of order 4
10 facets
27 vertex figures
- 27 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1*s2> of order 6
6 facets
- 6 of {12}*24
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 6
6 facets
- 6 of {12}*24
18 vertex figures
- 18 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 6
6 facets
- 6 of {12}*24
24 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 6
6 facets
- 6 of {12}*24
24 vertex figures
P/N, where N=<(s0*s2*s1)^4, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^2> of order 6
6 facets
- 6 of {12}*24
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^6> of order 6
8 facets
18 vertex figures
- 18 of {4}*8
P/N, where N=<(s0*s1)^6, s0*s1*s2*s1*s0*s1*(s2*s1*s0)^2*s1*s2> of order 6
8 facets
18 vertex figures
- 18 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106);; s1 := ( 1, 2)( 4, 19)( 5, 21)( 6, 20)( 7, 12)( 8, 11)( 9, 10)( 13, 27)( 14, 26)( 15, 25)( 16, 18)( 22, 23)( 28, 29)( 31, 46)( 32, 48)( 33, 47)( 34, 39)( 35, 38)( 36, 37)( 40, 54)( 41, 53)( 42, 52)( 43, 45)( 49, 50)( 55, 83)( 56, 82)( 57, 84)( 58,100)( 59,102)( 60,101)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67,108)( 68,107)( 69,106)( 70, 99)( 71, 98)( 72, 97)( 73, 85)( 74, 87)( 75, 86)( 76,104)( 77,103)( 78,105)( 79, 96)( 80, 95)( 81, 94);; s2 := ( 1, 62)( 2, 61)( 3, 63)( 4, 59)( 5, 58)( 6, 60)( 7, 56)( 8, 55)( 9, 57)( 10, 71)( 11, 70)( 12, 72)( 13, 68)( 14, 67)( 15, 69)( 16, 65)( 17, 64)( 18, 66)( 19, 80)( 20, 79)( 21, 81)( 22, 77)( 23, 76)( 24, 78)( 25, 74)( 26, 73)( 27, 75)( 28, 89)( 29, 88)( 30, 90)( 31, 86)( 32, 85)( 33, 87)( 34, 83)( 35, 82)( 36, 84)( 37, 98)( 38, 97)( 39, 99)( 40, 95)( 41, 94)( 42, 96)( 43, 92)( 44, 91)( 45, 93)( 46,107)( 47,106)( 48,108)( 49,104)( 50,103)( 51,105)( 52,101)( 53,100)( 54,102);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 2, 3)( 4, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106); s1 := Sym(108)!( 1, 2)( 4, 19)( 5, 21)( 6, 20)( 7, 12)( 8, 11)( 9, 10)( 13, 27)( 14, 26)( 15, 25)( 16, 18)( 22, 23)( 28, 29)( 31, 46)( 32, 48)( 33, 47)( 34, 39)( 35, 38)( 36, 37)( 40, 54)( 41, 53)( 42, 52)( 43, 45)( 49, 50)( 55, 83)( 56, 82)( 57, 84)( 58,100)( 59,102)( 60,101)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67,108)( 68,107)( 69,106)( 70, 99)( 71, 98)( 72, 97)( 73, 85)( 74, 87)( 75, 86)( 76,104)( 77,103)( 78,105)( 79, 96)( 80, 95)( 81, 94); s2 := Sym(108)!( 1, 62)( 2, 61)( 3, 63)( 4, 59)( 5, 58)( 6, 60)( 7, 56)( 8, 55)( 9, 57)( 10, 71)( 11, 70)( 12, 72)( 13, 68)( 14, 67)( 15, 69)( 16, 65)( 17, 64)( 18, 66)( 19, 80)( 20, 79)( 21, 81)( 22, 77)( 23, 76)( 24, 78)( 25, 74)( 26, 73)( 27, 75)( 28, 89)( 29, 88)( 30, 90)( 31, 86)( 32, 85)( 33, 87)( 34, 83)( 35, 82)( 36, 84)( 37, 98)( 38, 97)( 39, 99)( 40, 95)( 41, 94)( 42, 96)( 43, 92)( 44, 91)( 45, 93)( 46,107)( 47,106)( 48,108)( 49,104)( 50,103)( 51,105)( 52,101)( 53,100)( 54,102); 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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.