Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,5,6}

Atlas Canonical Name {4,5,6}*1920a

Overview

Group
SmallGroup(1920,240996)
Rank
4
Schläfli Type
{4,5,6}
Vertices, edges, …
16, 80, 120, 12
Order of s0s1s2s3
4
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

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=<(s1*s0*s1*s2)^2> of order 2

12 facets

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

8 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 5,10)( 8, 9);;
s1 := ( 1, 2)( 3, 5)( 4, 6)( 7,10);;
s2 := ( 2, 3)( 5, 8)( 6, 7)( 9,10);;
s3 := (1,2)(4,6);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3, 
s1*s0*s2*s1*s3*s2*s0*s1*s0*s1*s2*s3*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(10)!( 5,10)( 8, 9);
s1 := Sym(10)!( 1, 2)( 3, 5)( 4, 6)( 7,10);
s2 := Sym(10)!( 2, 3)( 5, 8)( 6, 7)( 9,10);
s3 := Sym(10)!(1,2)(4,6);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s3, 
s1*s0*s2*s1*s3*s2*s0*s1*s0*s1*s2*s3*s1*s2*s1*s0 >;

References

None.

to this polytope.