Overview
- Group
- SmallGroup(20,4)
- Rank
- 2
- Schläfli Type
- {10}
- Vertices, edges, …
- 10, 10
- Order of s0s1
- 10
- Also known as
- decagon, {10}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
5-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
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100-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);; s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);; 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(10)!( 3, 4)( 5, 6)( 7, 8)( 9,10); s1 := Sym(10)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10); poly := sub<Sym(10)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.