Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,2,40}

Atlas Canonical Name {2,6,2,40}*1920

Overview

Group
SmallGroup(1920,235349)
Rank
5
Schläfli Type
{2,6,2,40}
Vertices, edges, …
2, 6, 6, 40, 40
Order of s0s1s2s3s4
120
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

4-fold

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

16-fold

20-fold

24-fold

30-fold

40-fold

60-fold

Covers minimal covers in bold

None in this atlas.

Representations

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