Polytope of Type {5,5} with group SmallGroup(60,5) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(60,5)
Rank: 3
Schläfli Type: {5,5}
Vertices, edges, …: 6, 15, 6
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 3
Also known as: {5,5}₃. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

4-fold

6-fold

8-fold

10-fold

12-fold

14-fold

16-fold

18-fold

20-fold

22-fold

24-fold

26-fold

28-fold

30-fold

32-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,4)(3,5);;
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*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(5)!(2,3)(4,5);
s1 := Sym(5)!(1,2)(3,4);
s2 := Sym(5)!(2,4)(3,5);
poly := sub<Sym(5)|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*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References