Polytope of Type {4,5,3} with group SmallGroup(960,11358)

Overview

Group: SmallGroup(960,11358)
Rank: 4
Schläfli Type: {4,5,3}
Vertices, edges, …: 16, 80, 60, 6
Order of s₀s₁s₂s₃: 5
Order of s₀s₁s₂s₃s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Non-Orientable
Flat

Quotients maximal quotients in bold

No regular quotients.

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> of order 2

6 facets

6 of 2-fold non-regular quotient of {4,5}*160

8 vertex figures

8 of {5,3}*60

Representations

Permutation Representation (GAP)

s0 := (4,8)(5,7);;
s1 := (2,4)(3,5)(6,7)(8,9);;
s2 := ( 1, 2)( 4, 5)( 7, 8)( 9,10);;
s3 := (2,3)(4,5)(6,9)(7,8);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
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*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(10)!(4,8)(5,7);
s1 := Sym(10)!(2,4)(3,5)(6,7)(8,9);
s2 := Sym(10)!( 1, 2)( 4, 5)( 7, 8)( 9,10);
s3 := Sym(10)!(2,3)(4,5)(6,9)(7,8);
poly := sub<Sym(10)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, 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*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;

References

None.

to this polytope.