Part of the Atlas of Small Regular Polytopes

Polytope of Type {}

Atlas Canonical Name {}*2

Overview

Group
SmallGroup(2,1)
Rank
1
Schläfli Type
{}
Vertices, edges, …
2
Also known as
line segment, 1-simplex. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
poly := Group([s0]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0");;
s0 := F.1;;  
rels := [ s0*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(2)!(1,2);
poly := sub<Sym(2)|s0>;
Finitely Presented Group Representation (Magma) 
poly<s0> := Group< s0 | s0*s0 >;

References

None.

to this polytope.