Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,6,2,4,9}*1728

Overview

Group
SmallGroup(1728,46115)
Rank
6
Schläfli Type
{2,6,2,4,9}
Vertices, edges, …
2, 6, 6, 4, 18, 9
Order of s0s1s2s3s4s5
18
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

2-fold

3-fold

6-fold

9-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := (10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)(33,41)(35,42)(37,43);;
s4 := ( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);;
s5 := ( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)(23,24)(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43);;
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, s2*s3*s2*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, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(44)!(1,2);
s1 := Sym(44)!(5,6)(7,8);
s2 := Sym(44)!(3,7)(4,5)(6,8);
s3 := Sym(44)!(10,15)(11,17)(12,19)(13,21)(16,26)(18,28)(22,32)(29,38)(31,40)(33,41)(35,42)(37,43);
s4 := Sym(44)!( 9,10)(11,14)(12,13)(15,23)(16,22)(17,24)(18,20)(19,21)(25,31)(26,32)(27,29)(28,30)(33,39)(34,40)(35,37)(36,38)(41,44)(42,43);
s5 := Sym(44)!( 9,14)(10,12)(11,22)(13,18)(15,19)(16,31)(17,32)(20,27)(21,28)(23,24)(25,39)(26,40)(29,35)(30,36)(33,37)(34,44)(38,42)(41,43);
poly := sub<Sym(44)|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, s2*s3*s2*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, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;