Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6,4}

Atlas Canonical Name {4,6,4}*1152b

Overview

Group
SmallGroup(1152,157849)
Rank
4
Schläfli Type
{4,6,4}
Vertices, edges, …
6, 72, 72, 16
Order of s0s1s2s3
8
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s2*s3*s2*s1*(s2*s3)^2> of order 2

8 facets

6 vertex figures

P/N, where N=<s1*s2*s3*s2*s1*(s2*s3)^2, s2*s1*s2*s3*s2*s1*s3*s2*s3> of order 4

4 facets

6 vertex figures

Representations

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

References

None.

to this polytope.