Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,6,6,2,4}*1152b

Overview

Group
SmallGroup(1152,153175)
Rank
6
Schläfli Type
{2,6,6,2,4}
Vertices, edges, …
2, 6, 18, 6, 4, 4
Order of s0s1s2s3s4s5
12
Order of s0s1s2s3s4s5s4s3s2s1
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

4-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);;
s2 := ( 3, 7)( 4,11)( 5,15)( 6,13)( 9,19)(10,17)(14,16)(18,20);;
s3 := ( 3, 9)( 4, 5)( 6,10)( 7,18)( 8,17)(11,14)(12,13)(15,20)(16,19);;
s4 := (22,23);;
s5 := (21,22)(23,24);;
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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 7, 8)(11,12)(13,14)(15,16)(17,18)(19,20);
s2 := Sym(24)!( 3, 7)( 4,11)( 5,15)( 6,13)( 9,19)(10,17)(14,16)(18,20);
s3 := Sym(24)!( 3, 9)( 4, 5)( 6,10)( 7,18)( 8,17)(11,14)(12,13)(15,20)(16,19);
s4 := Sym(24)!(22,23);
s5 := Sym(24)!(21,22)(23,24);
poly := sub<Sym(24)|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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;