Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,4,4}

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

Overview

Group
SmallGroup(192,955)
Rank
4
Schläfli Type
{3,4,4}
Vertices, edges, …
3, 12, 16, 8
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
4
Also known as
{{3,4}3,{4,4}4}. if this polytope has another name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-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*s2*s3*s2*s1*s0*s3> of order 2

4 facets

3 vertex figures

Representations

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

References

None.

to this polytope.