Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,4,22}

Atlas Canonical Name {5,2,4,22}*1760

Overview

Group
SmallGroup(1760,1190)
Rank
5
Schläfli Type
{5,2,4,22}
Vertices, edges, …
5, 5, 4, 44, 22
Order of s0s1s2s3s4
220
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)(36,47)(37,48)(38,49);;
s3 := ( 6,28)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,39)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40);;
s4 := ( 6, 7)( 8,16)( 9,15)(10,14)(11,13)(17,18)(19,27)(20,26)(21,25)(22,24)(28,29)(30,38)(31,37)(32,36)(33,35)(39,40)(41,49)(42,48)(43,47)(44,46);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(49)!(2,3)(4,5);
s1 := Sym(49)!(1,2)(3,4);
s2 := Sym(49)!(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)(36,47)(37,48)(38,49);
s3 := Sym(49)!( 6,28)( 7,38)( 8,37)( 9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,39)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40);
s4 := Sym(49)!( 6, 7)( 8,16)( 9,15)(10,14)(11,13)(17,18)(19,27)(20,26)(21,25)(22,24)(28,29)(30,38)(31,37)(32,36)(33,35)(39,40)(41,49)(42,48)(43,47)(44,46);
poly := sub<Sym(49)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;