Polytope of Type {4,4} with group SmallGroup(72,40) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(72,40)
Rank: 3
Schläfli Type: {4,4}
Vertices, edges, …: 9, 18, 9
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 3
Also known as: {4,4}_(3,0), {4,4|3}. if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
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

{4,4}*144

3-fold

4-fold

{4,4}*288

6-fold

8-fold

9-fold

10-fold

12-fold

14-fold

16-fold

18-fold

20-fold

22-fold

24-fold

25-fold

{4,4}*1800

26-fold

27-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (5,6);;
s1 := (1,2)(3,5)(4,6);;
s2 := (2,3);;
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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(6)!(5,6);
s1 := Sym(6)!(1,2)(3,5)(4,6);
s2 := Sym(6)!(2,3);
poly := sub<Sym(6)|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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References