Part of the Atlas of Small Regular Polytopes

Polytope of Type {33,4,2,2}

Atlas Canonical Name {33,4,2,2}*1056

Overview

Group
SmallGroup(1056,1017)
Rank
5
Schläfli Type
{33,4,2,2}
Vertices, edges, …
33, 66, 4, 2, 2
Order of s0s1s2s3s4
66
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

11-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 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);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,41)(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(26,27);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44);;
s3 := (45,46);;
s4 := (47,48);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 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);
s1 := Sym(48)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,41)(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(17,33)(18,35)(19,34)(20,36)(21,29)(22,31)(23,30)(24,32)(26,27);
s2 := Sym(48)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44);
s3 := Sym(48)!(45,46);
s4 := Sym(48)!(47,48);
poly := sub<Sym(48)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;