Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,5,2}

Atlas Canonical Name {5,5,2}*320

Overview

Group
SmallGroup(320,1636)
Rank
4
Schläfli Type
{5,5,2}
Vertices, edges, …
16, 40, 16, 2
Order of s0s1s2s3
4
Order of s0s1s2s3s2s1
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

4-fold

6-fold

Representations

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