Overview
- Group
- SmallGroup(10,1)
- Rank
- 2
- Schläfli Type
- {5}
- Vertices, edges, …
- 5, 5
- Order of s0s1
- 5
- Also known as
- pentagon, {5}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
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Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := (1,2)(3,4);; poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(5)!(2,3)(4,5); s1 := Sym(5)!(1,2)(3,4); poly := sub<Sym(5)|s0,s1>;
Finitely Presented Group Representation (Magma)
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.