Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,6,4,4}*768a

Overview

Group
SmallGroup(768,1036279)
Rank
5
Schläfli Type
{2,6,4,4}
Vertices, edges, …
2, 6, 24, 16, 8
Order of s0s1s2s3s4
12
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

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

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