Polytope of Type {2,2}

Atlas Canonical Name {2,2}*8

Overview

Group: SmallGroup(8,5)
Rank: 3
Schläfli Type: {2,2}
Vertices, edges, …: 2, 2, 2
Order of s₀s₁s₂: 2
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-Dual
Self-Petrie

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

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Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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