Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,6}

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

Overview

Group
SmallGroup(432,759)
Rank
4
Schläfli Type
{2,6,6}
Vertices, edges, …
2, 18, 54, 18
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

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 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26);;
s2 := ( 3,15)( 4,17)( 5,16)( 6,12)( 7,14)( 8,13)( 9,18)(10,20)(11,19)(21,24)(22,26)(23,25)(28,29);;
s3 := ( 3, 4)( 6, 7)( 9,10)(12,22)(13,21)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(29)!(1,2);
s1 := Sym(29)!( 6, 9)( 7,10)( 8,11)(12,21)(13,22)(14,23)(15,27)(16,28)(17,29)(18,24)(19,25)(20,26);
s2 := Sym(29)!( 3,15)( 4,17)( 5,16)( 6,12)( 7,14)( 8,13)( 9,18)(10,20)(11,19)(21,24)(22,26)(23,25)(28,29);
s3 := Sym(29)!( 3, 4)( 6, 7)( 9,10)(12,22)(13,21)(14,23)(15,25)(16,24)(17,26)(18,28)(19,27)(20,29);
poly := sub<Sym(29)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 >;