Polytope of Type {6,20} with group SmallGroup(480,956)

Overview

Group: SmallGroup(480,956)
Rank: 3
Schläfli Type: {6,20}
Vertices, edges, …: 12, 120, 40
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,6,20} ·960

Quotients maximal quotients in bold

2-fold

{6,10}*240c

4-fold

8-fold

{3,5}*60

Covers minimal covers in bold

2-fold

3-fold

{6,60}*1440a

4-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (6,7)(8,9);;
s1 := (2,3)(5,6)(8,9);;
s2 := (1,2)(3,4)(6,8)(7,9);;
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(9)!(6,7)(8,9);
s1 := Sym(9)!(2,3)(5,6)(8,9);
s2 := Sym(9)!(1,2)(3,4)(6,8)(7,9);
poly := sub<Sym(9)|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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0 >;

References