Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,8,2}

Atlas Canonical Name {6,8,2}*192

Overview

Group
SmallGroup(192,1313)
Rank
4
Schläfli Type
{6,8,2}
Vertices, edges, …
6, 24, 8, 2
Order of s0s1s2s3
24
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

4-fold

6-fold

8-fold

12-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Representations

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