Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5}

Atlas Canonical Name {2,5}*20

Overview

Group
SmallGroup(20,4)
Rank
3
Schläfli Type
{2,5}
Vertices, edges, …
2, 5, 5
Order of s0s1s2
10
Order of s0s1s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

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Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(7)!(1,2);
s1 := Sym(7)!(4,5)(6,7);
s2 := Sym(7)!(3,4)(5,6);
poly := sub<Sym(7)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;