Overview
- Group
- SmallGroup(960,10882)
- Rank
- 3
- Schläfli Type
- {10,4}
- Vertices, edges, …
- 120, 240, 48
- 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
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*s0)^2*s2*(s1*s0)^2*s1*s2> of order 2
24 facets
- 24 of {10}*20
60 vertex figures
- 60 of {4}*8
P/N, where N=<(s1*s0)^2*s1*s2*(s1*s0)^3*s2*s1*s0*s2*s1*s2> of order 2
24 facets
- 24 of {10}*20
60 vertex figures
- 60 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
12 facets
- 12 of {10}*20
30 vertex figures
- 30 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1, s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*s2*s1*s2> of order 4
12 facets
- 12 of {10}*20
34 vertex figures
P/N, where N=<(s0*s1)^5, (s1*s2*s1*s0)^2*(s1*s2)^2> of order 4
18 facets
32 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s2*s1)^4> of order 6
8 facets
- 8 of {10}*20
20 vertex figures
- 20 of {4}*8
P/N, where N=<(s0*s2*s1)^4, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1> of order 6
8 facets
- 8 of {10}*20
24 vertex figures
P/N, where N=<(s0*s1)^2, s1*s2*(s1*s0)^3*s2*s1*s0*s2*s1*s2> of order 10
8 facets
12 vertex figures
- 12 of {4}*8
P/N, where N=<(s1*s2)^2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s0> of order 10
8 facets
16 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 6, 7)( 8, 9)(10,11);; s1 := (1,3)(2,4)(5,6)(7,8);; s2 := (3,4)(6,7);; 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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(11)!( 6, 7)( 8, 9)(10,11); s1 := Sym(11)!(1,3)(2,4)(5,6)(7,8); s2 := Sym(11)!(3,4)(6,7); poly := sub<Sym(11)|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*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.