Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,20}

Atlas Canonical Name {4,2,20}*320

Overview

Group
SmallGroup(320,1221)
Rank
4
Schläfli Type
{4,2,20}
Vertices, edges, …
4, 4, 20, 20
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

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

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