Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,6,2}

Atlas Canonical Name {6,6,2}*432c

Overview

Group
SmallGroup(432,545)
Rank
4
Schläfli Type
{6,6,2}
Vertices, edges, …
18, 54, 18, 2
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

18-fold

27-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

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