Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,42,2,5}

Atlas Canonical Name {2,42,2,5}*1680

Overview

Group
SmallGroup(1680,990)
Rank
5
Schläfli Type
{2,42,2,5}
Vertices, edges, …
2, 42, 42, 5, 5
Order of s0s1s2s3s4
210
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

3-fold

6-fold

7-fold

14-fold

21-fold

Covers minimal covers in bold

None in this atlas.

Representations

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