Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,15,2}

Atlas Canonical Name {6,15,2}*480

Overview

Group
SmallGroup(480,1193)
Rank
4
Schläfli Type
{6,15,2}
Vertices, edges, …
8, 60, 20, 2
Order of s0s1s2s3
20
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

10-fold

12-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

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