Overview
- Group
- SmallGroup(480,1186)
- Rank
- 3
- Schläfli Type
- {6,4}
- Vertices, edges, …
- 60, 120, 40
- Order of s0s1s2
- 10
- 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
4-fold
60-fold
Covers minimal covers in bold
2-fold
3-fold
4-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)^3*s2*s1*s2> of order 2
20 facets
- 20 of {6}*12
30 vertex figures
- 30 of {4}*8
P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1> of order 2
20 facets
- 20 of {6}*12
30 vertex figures
- 30 of {4}*8
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 4
10 facets
- 10 of {6}*12
18 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0> of order 4
12 facets
16 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^2*(s1*s2)^2> of order 4
10 facets
- 10 of {6}*12
16 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*s1*s0*s1*s2*s1> of order 4
10 facets
- 10 of {6}*12
16 vertex figures
P/N, where N=<(s0*s1)^2, s1*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 6
10 facets
10 vertex figures
- 10 of {4}*8
P/N, where N=<(s0*s1)^2, s0*s1*(s2*s1*s0)^3*s2*s1*s2> of order 6
8 facets
10 vertex figures
- 10 of {4}*8
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2*s0*s1*s2> of order 6
8 facets
10 vertex figures
- 10 of {4}*8
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 6
8 facets
12 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*(s1*s0)^2*s2*s1*s0*s1, s0*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0> of order 8
6 facets
9 vertex figures
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2> of order 12
6 facets
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := (3,5);; s1 := (1,2)(4,5)(6,7)(8,9);; s2 := (2,4)(6,8)(7,9);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(9)!(3,5); s1 := Sym(9)!(1,2)(4,5)(6,7)(8,9); s2 := Sym(9)!(2,4)(6,8)(7,9); poly := sub<Sym(9)|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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.