Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,4,4}

Atlas Canonical Name {6,4,4}*384a

Overview

Group
SmallGroup(384,12882)
Rank
4
Schläfli Type
{6,4,4}
Vertices, edges, …
6, 24, 16, 8
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
2
Also known as
{{6,4|2},{4,4}4}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

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)^2> of order 2

4 facets

6 vertex figures

  • 6 of 2-fold non-regular quotient of {4,4}*64
P/N, where N=<(s1*s2)^2> of order 2

6 facets

6 vertex figures

  • 6 of 2-fold non-regular quotient of {4,4}*64

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24);;
s1 := ( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,20)( 8,19)( 9,21)(10,23)(11,22)(12,24);;
s2 := (19,22)(20,23)(21,24);;
s3 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(24)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24);
s1 := Sym(24)!( 1,14)( 2,13)( 3,15)( 4,17)( 5,16)( 6,18)( 7,20)( 8,19)( 9,21)(10,23)(11,22)(12,24);
s2 := Sym(24)!(19,22)(20,23)(21,24);
s3 := Sym(24)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24);
poly := sub<Sym(24)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.