Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,10}

Atlas Canonical Name {2,4,10}*160

Overview

Group
SmallGroup(160,217)
Rank
4
Schläfli Type
{2,4,10}
Vertices, edges, …
2, 4, 20, 10
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

10-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

Representations

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