Polytope of Type {5,5} with group SmallGroup(1320,134)

Overview

Group: SmallGroup(1320,134)
Rank: 3
Schläfli Type: {5,5}
Vertices, edges, …: 132, 330, 132
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

2-fold

{5,5}*660

Covers minimal covers in bold

None in this atlas.

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*(s2*s1*s0)^2)^2*s2> of order 3

44 facets

44 of {5}*10

44 vertex figures

44 of {5}*10

P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s1> of order 11

12 facets

12 of {5}*10

12 vertex figures

12 of {5}*10

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 5, 9)( 6, 7)( 8,11)(12,13);;
s1 := ( 3, 5)( 4, 6)( 7,11)( 9,10)(12,13);;
s2 := ( 1,10)( 5, 7)( 6, 9)( 8,11)(12,13);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(13)!( 2, 3)( 5, 9)( 6, 7)( 8,11)(12,13);
s1 := Sym(13)!( 3, 5)( 4, 6)( 7,11)( 9,10)(12,13);
s2 := Sym(13)!( 1,10)( 5, 7)( 6, 9)( 8,11)(12,13);
poly := sub<Sym(13)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s1 >;

References

None.

to this polytope.