Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,6,8}

Atlas Canonical Name {5,2,6,8}*960

Overview

Group
SmallGroup(960,8239)
Rank
5
Schläfli Type
{5,2,6,8}
Vertices, edges, …
5, 5, 6, 24, 8
Order of s0s1s2s3s4
120
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

Covers minimal covers in bold

2-fold

Representations

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