Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,3,4,2}

Atlas Canonical Name {2,6,3,4,2}*576

Overview

Group
SmallGroup(576,8659)
Rank
6
Schläfli Type
{2,6,3,4,2}
Vertices, edges, …
2, 6, 9, 6, 4, 2
Order of s0s1s2s3s4s5
6
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

3-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14);;
s3 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14);;
s4 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s5 := (15,16);;
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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, 
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(16)!(1,2);
s1 := Sym(16)!( 7,11)( 8,12)( 9,13)(10,14);
s2 := Sym(16)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(13,14);
s3 := Sym(16)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14);
s4 := Sym(16)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s5 := Sym(16)!(15,16);
poly := sub<Sym(16)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*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, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;