Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,6,9}

Atlas Canonical Name {4,2,6,9}*864

Overview

Group
SmallGroup(864,2462)
Rank
5
Schläfli Type
{4,2,6,9}
Vertices, edges, …
4, 4, 6, 27, 9
Order of s0s1s2s3s4
36
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

9-fold

18-fold

Covers minimal covers in bold

2-fold

Representations

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