Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,3,4}

Atlas Canonical Name {6,3,4}*576

Overview

Group
SmallGroup(576,8653)
Rank
4
Schläfli Type
{6,3,4}
Vertices, edges, …
24, 36, 24, 4
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

12-fold

Covers minimal covers in bold

2-fold

3-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*s2*(s1*s0)^2*s2*s1*s0*s1> of order 2

4 facets

  • 4 of 2-fold non-regular quotient of {6,3}*144

12 vertex figures

P/N, where N=<(s0*s1)^2> of order 3

4 facets

  • 4 of 3-fold non-regular quotient of {6,3}*144

8 vertex figures

P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2> of order 4

4 facets

  • 4 of 4-fold non-regular quotient of {6,3}*144

6 vertex figures

Representations

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

References

None.

to this polytope.