Part of the Atlas of Small Regular Polytopes

Polytope of Type {5}

Atlas Canonical Name {5}*10

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

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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.