Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,6,6}

Atlas Canonical Name {3,2,6,6}*1296d

Overview

Group
SmallGroup(1296,3538)
Rank
5
Schläfli Type
{3,2,6,6}
Vertices, edges, …
3, 3, 18, 54, 18
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

3-fold

6-fold

9-fold

18-fold

27-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 7,10)( 8,11)( 9,12)(13,22)(14,23)(15,24)(16,28)(17,29)(18,30)(19,25)(20,26)(21,27);;
s3 := ( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(10,19)(11,21)(12,20)(22,25)(23,27)(24,26)(29,30);;
s4 := ( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(21,30);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(30)!(2,3);
s1 := Sym(30)!(1,2);
s2 := Sym(30)!( 7,10)( 8,11)( 9,12)(13,22)(14,23)(15,24)(16,28)(17,29)(18,30)(19,25)(20,26)(21,27);
s3 := Sym(30)!( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(10,19)(11,21)(12,20)(22,25)(23,27)(24,26)(29,30);
s4 := Sym(30)!( 4, 5)( 7, 8)(10,11)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(19,29)(20,28)(21,30);
poly := sub<Sym(30)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s4*s2*s3 >;