Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,22,2}

Atlas Canonical Name {2,4,22,2}*704

Overview

Group
SmallGroup(704,1363)
Rank
5
Schläfli Type
{2,4,22,2}
Vertices, edges, …
2, 4, 44, 22, 2
Order of s0s1s2s3s4
44
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

11-fold

22-fold

Covers minimal covers in bold

2-fold

Representations

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