Polytope of Type {20,6} with group SmallGroup(960,10871)

Overview

Group: SmallGroup(960,10871)
Rank: 3
Schläfli Type: {20,6}
Vertices, edges, …: 80, 240, 24
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

{20,6,2} ·1920

Vertex figure of

{2,20,6} ·1920

Quotients maximal quotients in bold

2-fold

{10,6}*480b

4-fold

8-fold

{5,6}*120a

60-fold

{4,2}*16

120-fold

{2,2}*8

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

12 facets

12 of {20}*40

40 vertex figures

40 of {6}*12

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^3> of order 2

12 facets

12 of {20}*40

40 vertex figures

40 of {6}*12

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.