Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,6,2}

Atlas Canonical Name {2,6,6,2}*288b

Overview

Group
SmallGroup(288,1040)
Rank
5
Schläfli Type
{2,6,6,2}
Vertices, edges, …
2, 6, 18, 6, 2
Order of s0s1s2s3s4
6
Order of s0s1s2s3s4s3s2s1
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

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);;
s2 := ( 3, 7)( 4,11)( 5,15)( 6,13)( 9,19)(10,17)(14,16)(18,20);;
s3 := ( 3, 9)( 4, 5)( 6,10)( 7,18)( 8,17)(11,14)(12,13)(15,20)(16,19);;
s4 := (21,22);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);
s2 := Sym(22)!( 3, 7)( 4,11)( 5,15)( 6,13)( 9,19)(10,17)(14,16)(18,20);
s3 := Sym(22)!( 3, 9)( 4, 5)( 6,10)( 7,18)( 8,17)(11,14)(12,13)(15,20)(16,19);
s4 := Sym(22)!(21,22);
poly := sub<Sym(22)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;