Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,2,40}

Atlas Canonical Name {8,2,40}*1280

Overview

Group
SmallGroup(1280,161916)
Rank
4
Schläfli Type
{8,2,40}
Vertices, edges, …
8, 8, 40, 40
Order of s0s1s2s3
40
Order of s0s1s2s3s2s1
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

5-fold

8-fold

10-fold

16-fold

20-fold

32-fold

40-fold

80-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (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);;
s3 := ( 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]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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)!(2,3)(4,5)(6,7);
s1 := Sym(48)!(1,2)(3,4)(5,6)(7,8);
s2 := 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);
s3 := 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>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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 >;