Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,3,3}

Atlas Canonical Name {4,3,3}*192

Overview

Group
SmallGroup(192,955)
Rank
4
Schläfli Type
{4,3,3}
Vertices, edges, …
8, 16, 12, 4
Order of s0s1s2s3
4
Order of s0s1s2s3s2s1
4
Also known as
hemi-4-cube, {4,3,3}4. if this polytope has another name.

Special Properties

  • Projective
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

Covers minimal covers in bold

2-fold

4-fold

6-fold

10-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

4 facets

  • 4 of 2-fold non-regular quotient of {4,3}*48

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 3, 4)( 7, 8)(11,12);;
s1 := ( 5,11)( 6,12)( 7, 9)( 8,10);;
s2 := (1,5)(2,6)(3,7)(4,8);;
s3 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
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, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s2*s3*s2*s0*s1*s0*s1*s2*s3*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(12)!( 3, 4)( 7, 8)(11,12);
s1 := Sym(12)!( 5,11)( 6,12)( 7, 9)( 8,10);
s2 := Sym(12)!(1,5)(2,6)(3,7)(4,8);
s3 := Sym(12)!( 5, 9)( 6,10)( 7,11)( 8,12);
poly := sub<Sym(12)|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, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s2*s3*s2*s0*s1*s0*s1*s2*s3*s1 >;

References

None.

to this polytope.