Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,3,3,4}

Atlas Canonical Name {3,3,3,4}*1920

Overview

Group
SmallGroup(1920,240996)
Rank
5
Schläfli Type
{3,3,3,4}
Vertices, edges, …
5, 20, 40, 40, 16
Order of s0s1s2s3s4
5
Order of s0s1s2s3s4s3s2s1
4
Also known as
hemi-5-cross-polytope, {3,3,3,4}5. if this polytope has another name.

Special Properties

  • Projective
  • Locally Spherical
  • 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=<s2*(s3*s2*s4)^2*s3*s4> of order 2

8 facets

5 vertex figures

P/N, where N=<s2*(s3*s2*s4)^2*s3*s4, s1*s2*s3*s2*s4*s3*s2*s1*s4*s3*s4> of order 4

4 facets

5 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 5, 8)( 9,10);;
s1 := ( 3, 5)( 7,10);;
s2 := (2,3)(6,7);;
s3 := (1,2)(4,6);;
s4 := ( 2, 6)( 3, 7)( 5,10)( 8, 9);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s0*s3*s1*s2*s1*s0*s4*s3*s2*s4*s3*s4*s1*s2*s3*s4*s0*s1*s2*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(10)!( 5, 8)( 9,10);
s1 := Sym(10)!( 3, 5)( 7,10);
s2 := Sym(10)!(2,3)(6,7);
s3 := Sym(10)!(1,2)(4,6);
s4 := Sym(10)!( 2, 6)( 3, 7)( 5,10)( 8, 9);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s0*s1*s2*s0*s3*s1*s2*s1*s0*s4*s3*s2*s4*s3*s4*s1*s2*s3*s4*s0*s1*s2*s3*s4 >;

References

None.

to this polytope.