Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {5,2,2,2}*80

Overview

Group
SmallGroup(80,51)
Rank
5
Schläfli Type
{5,2,2,2}
Vertices, edges, …
5, 5, 2, 2, 2
Order of s0s1s2s3s4
10
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

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8-fold

9-fold

10-fold

11-fold

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20-fold

21-fold

22-fold

23-fold

24-fold

25-fold

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := (8,9);;
s4 := (10,11);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(11)!(2,3)(4,5);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!(6,7);
s3 := Sym(11)!(8,9);
s4 := Sym(11)!(10,11);
poly := sub<Sym(11)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;