Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,44,2}

Atlas Canonical Name {6,44,2}*1056b

Overview

Group
SmallGroup(1056,1015)
Rank
4
Schläfli Type
{6,44,2}
Vertices, edges, …
6, 132, 44, 2
Order of s0s1s2s3
66
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

11-fold

22-fold

Covers minimal covers in bold

None in this atlas.

Representations

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