Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(576,8660)
Rank
6
Schläfli Type
{3,2,4,3,4}
Vertices, edges, …
3, 3, 4, 6, 6, 4
Order of s0s1s2s3s4s5
3
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

2-fold

3-fold

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 5)( 6, 9)( 7, 8)(10,17)(11,18)(12,13)(14,16)(15,19);;
s3 := ( 5, 7)( 6,10)( 9,14)(12,17)(13,16)(15,18);;
s4 := ( 6,11)( 7, 8)( 9,18)(12,19)(13,15)(14,16);;
s5 := ( 4,11)( 5,18)( 6,10)( 7,15)( 8,19)( 9,17)(12,14)(13,16);;
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*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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s5*s4*s3*s5*s4*s3*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(19)!(2,3);
s1 := Sym(19)!(1,2);
s2 := Sym(19)!( 4, 5)( 6, 9)( 7, 8)(10,17)(11,18)(12,13)(14,16)(15,19);
s3 := Sym(19)!( 5, 7)( 6,10)( 9,14)(12,17)(13,16)(15,18);
s4 := Sym(19)!( 6,11)( 7, 8)( 9,18)(12,19)(13,15)(14,16);
s5 := Sym(19)!( 4,11)( 5,18)( 6,10)( 7,15)( 8,19)( 9,17)(12,14)(13,16);
poly := sub<Sym(19)|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, 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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5, 
s4*s2*s3*s4*s2*s3*s4*s2*s3, s3*s5*s4*s3*s5*s4*s3*s5*s4 >;