Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,33,6}

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

Overview

Group
SmallGroup(1056,1015)
Rank
4
Schläfli Type
{2,33,6}
Vertices, edges, …
2, 44, 132, 8
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)( 7,43)( 8,45)( 9,44)(10,46)(11,39)(12,41)(13,40)(14,42)(15,35)(16,37)(17,36)(18,38)(19,31)(20,33)(21,32)(22,34)(23,27)(24,29)(25,28)(26,30);;
s2 := ( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,43)(12,44)(13,46)(14,45)(15,39)(16,40)(17,42)(18,41)(19,35)(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33)(29,30);;
s3 := ( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)(39,42)(43,46);;
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*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(46)!(1,2);
s1 := Sym(46)!( 4, 5)( 7,43)( 8,45)( 9,44)(10,46)(11,39)(12,41)(13,40)(14,42)(15,35)(16,37)(17,36)(18,38)(19,31)(20,33)(21,32)(22,34)(23,27)(24,29)(25,28)(26,30);
s2 := Sym(46)!( 3, 7)( 4, 8)( 5,10)( 6, 9)(11,43)(12,44)(13,46)(14,45)(15,39)(16,40)(17,42)(18,41)(19,35)(20,36)(21,38)(22,37)(23,31)(24,32)(25,34)(26,33)(29,30);
s3 := Sym(46)!( 3, 6)( 7,10)(11,14)(15,18)(19,22)(23,26)(27,30)(31,34)(35,38)(39,42)(43,46);
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*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;