Polytope of Type {6,2} with group SmallGroup(24,14) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(24,14)
Rank: 3
Schläfli Type: {6,2}
Vertices, edges, …: 6, 6, 2
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Related Polytopes

Constructions

Vertex figure of

Quotients maximal quotients in bold

Covers minimal covers in bold

Representations

Permutation Representation (GAP)

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
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, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(8)!(3,4)(5,6);
s1 := Sym(8)!(1,5)(2,3)(4,6);
s2 := Sym(8)!(7,8);
poly := sub<Sym(8)|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, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;