Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,6,9}

Atlas Canonical Name {5,2,6,9}*1080

Overview

Group
SmallGroup(1080,286)
Rank
5
Schläfli Type
{5,2,6,9}
Vertices, edges, …
5, 5, 6, 27, 9
Order of s0s1s2s3s4
90
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

9-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(29,30)(31,32);;
s3 := ( 6, 9)( 7,15)( 8,12)(11,21)(13,16)(14,18)(17,27)(19,22)(20,24)(23,31)(25,28)(26,29)(30,32);;
s4 := ( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(20,23)(21,25)(22,24)(27,30)(28,29)(31,32);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(32)!(2,3)(4,5);
s1 := Sym(32)!(1,2)(3,4);
s2 := Sym(32)!( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(29,30)(31,32);
s3 := Sym(32)!( 6, 9)( 7,15)( 8,12)(11,21)(13,16)(14,18)(17,27)(19,22)(20,24)(23,31)(25,28)(26,29)(30,32);
s4 := Sym(32)!( 6, 7)( 8,11)( 9,13)(10,12)(14,17)(15,19)(16,18)(20,23)(21,25)(22,24)(27,30)(28,29)(31,32);
poly := sub<Sym(32)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;