Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,3,4}

Atlas Canonical Name {4,3,4}*96

Overview

Group
SmallGroup(96,227)
Rank
4
Schläfli Type
{4,3,4}
Vertices, edges, …
4, 6, 6, 4
Order of s0s1s2s3
3
Order of s0s1s2s3s2s1
2
Also known as
{{4,3}3,{3,4}3}. if this polytope has another name.

Special Properties

  • Universal
  • Locally Projective
  • Non-Orientable
  • Flat
  • Self-Dual

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

14-fold

15-fold

17-fold

18-fold

19-fold

20-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 1, 2)( 3, 6)( 4, 5)( 7,14)( 8,15)( 9,10)(11,13)(12,16);;
s1 := ( 2, 4)( 3, 7)( 6,11)( 9,14)(10,13)(12,15);;
s2 := ( 3, 8)( 4, 5)( 6,15)( 9,16)(10,12)(11,13);;
s3 := ( 1, 8)( 2,15)( 3, 7)( 4,12)( 5,16)( 6,14)( 9,11)(10,13);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s0*s1*s2*s0*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(16)!( 1, 2)( 3, 6)( 4, 5)( 7,14)( 8,15)( 9,10)(11,13)(12,16);
s1 := Sym(16)!( 2, 4)( 3, 7)( 6,11)( 9,14)(10,13)(12,15);
s2 := Sym(16)!( 3, 8)( 4, 5)( 6,15)( 9,16)(10,12)(11,13);
s3 := Sym(16)!( 1, 8)( 2,15)( 3, 7)( 4,12)( 5,16)( 6,14)( 9,11)(10,13);
poly := sub<Sym(16)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s3*s2*s1*s3*s2*s1*s3*s2 >;

References

None.

to this polytope.