Overview
- Group
- SmallGroup(672,1254)
- Rank
- 3
- Schläfli Type
- {4,6}
- Vertices, edges, …
- 56, 168, 84
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-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*s2*s1)^4, s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*s1> of order 4
24 facets
14 vertex figures
- 14 of {6}*12
P/N, where N=<(s0*s2*s1)^4, (s0*s1*s2*s1)^2*s0*(s1*s2)^2> of order 4
22 facets
14 vertex figures
- 14 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 2)( 3, 6)( 4, 8)( 5, 7)( 9,10);; s1 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,10);; s2 := (1,2)(3,5)(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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(10)!( 1, 2)( 3, 6)( 4, 8)( 5, 7)( 9,10); s1 := Sym(10)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,10); s2 := Sym(10)!(1,2)(3,5)(6,7); poly := sub<Sym(10)|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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.