Polytope of Type {4,6} with group SmallGroup(240,189)

Overview

Group: SmallGroup(240,189)
Rank: 3
Schläfli Type: {4,6}
Vertices, edges, …: 20, 60, 30
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 3
Also known as: {4,6|3}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

{2,4,6} ·480

Quotients maximal quotients in bold

2-fold

{4,6}*120

Covers minimal covers in bold

2-fold

3-fold

{12,6}*720b

4-fold

6-fold

8-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s0*s2)^4*s1*s2> of order 2

15 facets

15 of {4}*8

11 vertex figures

9 of {6}*12
2 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.