Overview
- Group
- SmallGroup(672,1254)
- Rank
- 3
- Schläfli Type
- {4,8}
- Vertices, edges, …
- 42, 168, 84
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-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.
Representations
Permutation Representation (GAP)
s0 := ( 1, 2)( 3, 6)( 4, 8)( 5, 7)( 9,10);; s1 := (1,4)(2,3)(5,8)(6,7);; s2 := (3,7)(4,8)(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*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2 ];;
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); s2 := Sym(10)!(3,7)(4,8)(5,6); 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*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2 >;
References
None.
to this polytope.