Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,2,5,3}

Atlas Canonical Name {5,2,2,5,3}*1200

Overview

Group
SmallGroup(1200,944)
Rank
6
Schläfli Type
{5,2,2,5,3}
Vertices, edges, …
5, 5, 2, 10, 15, 6
Order of s0s1s2s3s4s5
10
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10)(11,12);;
s4 := ( 8, 9)(10,11);;
s5 := ( 9,12)(10,11);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(12)!(2,3)(4,5);
s1 := Sym(12)!(1,2)(3,4);
s2 := Sym(12)!(6,7);
s3 := Sym(12)!( 9,10)(11,12);
s4 := Sym(12)!( 8, 9)(10,11);
s5 := Sym(12)!( 9,12)(10,11);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4 >;