Overview
- Group
- SmallGroup(960,10871)
- Rank
- 3
- Schläfli Type
- {4,6}
- Vertices, edges, …
- 80, 240, 120
- Order of s0s1s2
- 20
- 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
8-fold
60-fold
120-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)^2*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 2
60 facets
- 60 of {4}*8
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1*s0*s1*s2*s1> of order 2
60 facets
- 60 of {4}*8
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s2> of order 2
64 facets
40 vertex figures
- 40 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 2
60 facets
- 60 of {4}*8
40 vertex figures
- 40 of {6}*12
P/N, where N=<s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 3
40 facets
- 40 of {4}*8
32 vertex figures
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, (s0*s2*s1)^2*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 4
30 facets
- 30 of {4}*8
20 vertex figures
- 20 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1*s0*s1*s2*s1> of order 4
30 facets
- 30 of {4}*8
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
30 facets
- 30 of {4}*8
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^2, (s1*s2)^2*s1*s0*s2*s1*s0*(s2*s1)^2*s2> of order 4
34 facets
20 vertex figures
- 20 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1*s0*s1*s2*s1> of order 4
30 facets
- 30 of {4}*8
21 vertex figures
P/N, where N=<(s1*s2)^3, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1*s0*s1*s2> of order 4
32 facets
22 vertex figures
P/N, where N=<(s1*s2)^3, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 4
30 facets
- 30 of {4}*8
22 vertex figures
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2> of order 5
24 facets
- 24 of {4}*8
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2*s2, s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 6
20 facets
- 20 of {4}*8
16 vertex figures
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 6
20 facets
- 20 of {4}*8
16 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0*s1)^2, s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 6
24 facets
16 vertex figures
P/N, where N=<(s1*s2)^3, s1*s0*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 6
20 facets
- 20 of {4}*8
18 vertex figures
P/N, where N=<(s0*s1)^2, (s1*s2)^2*s1*s0*s2*s1*s0*(s2*s1)^2*s2, (s0*s2*s1)^2*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
17 facets
10 vertex figures
- 10 of {6}*12
P/N, where N=<(s0*s1)^2, (s1*s2)^3> of order 8
17 facets
11 vertex figures
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1*s0*s1)^2> of order 10
16 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<(s0*(s2*s1)^2)^2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 10
12 facets
- 12 of {4}*8
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*(s1*s0*s2)^3*s1*s2, (s0*s1*s2*s1)^3> of order 10
12 facets
- 12 of {4}*8
8 vertex figures
- 8 of {6}*12
P/N, where N=<s0*(s2*s1)^2*s0*(s1*s2)^2, s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 12
10 facets
- 10 of {4}*8
12 vertex figures
P/N, where N=<s0*(s1*s2)^2*s1*s0*s2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 12
10 facets
- 10 of {4}*8
9 vertex figures
Representations
Permutation Representation (GAP)
s0 := (2,3)(7,9);; s1 := (1,2)(3,4)(6,7)(8,9);; s2 := (5,6);; 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*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(9)!(2,3)(7,9); s1 := Sym(9)!(1,2)(3,4)(6,7)(8,9); s2 := Sym(9)!(5,6); 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, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.