Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,33}

Atlas Canonical Name {2,6,33}*1056

Overview

Group
SmallGroup(1056,1015)
Rank
4
Schläfli Type
{2,6,33}
Vertices, edges, …
2, 8, 132, 44
Order of s0s1s2s3
44
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

11-fold

12-fold

22-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45);;
s2 := ( 5, 6)( 7,43)( 8,44)( 9,46)(10,45)(11,39)(12,40)(13,42)(14,41)(15,35)(16,36)(17,38)(18,37)(19,31)(20,32)(21,34)(22,33)(23,27)(24,28)(25,30)(26,29);;
s3 := ( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,46)(12,44)(13,45)(14,43)(15,42)(16,40)(17,41)(18,39)(19,38)(20,36)(21,37)(22,35)(23,34)(24,32)(25,33)(26,31)(27,30);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(46)!(1,2);
s1 := Sym(46)!( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45);
s2 := Sym(46)!( 5, 6)( 7,43)( 8,44)( 9,46)(10,45)(11,39)(12,40)(13,42)(14,41)(15,35)(16,36)(17,38)(18,37)(19,31)(20,32)(21,34)(22,33)(23,27)(24,28)(25,30)(26,29);
s3 := Sym(46)!( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,46)(12,44)(13,45)(14,43)(15,42)(16,40)(17,41)(18,39)(19,38)(20,36)(21,37)(22,35)(23,34)(24,32)(25,33)(26,31)(27,30);
poly := sub<Sym(46)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;