Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,3,2,4,6}

Atlas Canonical Name {6,3,2,4,6}*1728a

Overview

Group
SmallGroup(1728,47341)
Rank
6
Schläfli Type
{6,3,2,4,6}
Vertices, edges, …
6, 9, 3, 4, 12, 6
Order of s0s1s2s3s4s5
12
Order of s0s1s2s3s4s5s4s3s2s1
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

4-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (4,5)(6,7)(8,9);;
s1 := (1,4)(2,8)(3,6)(7,9);;
s2 := (1,2)(4,7)(5,6)(8,9);;
s3 := (11,14)(15,18)(16,19);;
s4 := (10,11)(12,16)(13,15)(14,17)(18,21)(19,20);;
s5 := (10,12)(11,15)(14,18)(17,20);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(21)!(4,5)(6,7)(8,9);
s1 := Sym(21)!(1,4)(2,8)(3,6)(7,9);
s2 := Sym(21)!(1,2)(4,7)(5,6)(8,9);
s3 := Sym(21)!(11,14)(15,18)(16,19);
s4 := Sym(21)!(10,11)(12,16)(13,15)(14,17)(18,21)(19,20);
s5 := Sym(21)!(10,12)(11,15)(14,18)(17,20);
poly := sub<Sym(21)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;