Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,2,42}

Atlas Canonical Name {8,2,42}*1344

Overview

Group
SmallGroup(1344,11133)
Rank
4
Schläfli Type
{8,2,42}
Vertices, edges, …
8, 8, 42, 42
Order of s0s1s2s3
168
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

3-fold

4-fold

6-fold

7-fold

8-fold

12-fold

14-fold

21-fold

24-fold

28-fold

42-fold

56-fold

84-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 := (11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,42)(43,46)(44,45)(47,50)(48,49);;
s3 := ( 9,25)(10,19)(11,17)(12,27)(13,15)(14,37)(16,21)(18,31)(20,29)(22,39)(23,26)(24,47)(28,33)(30,43)(32,41)(34,49)(35,38)(36,48)(40,45)(42,44)(46,50);;
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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(50)!(2,3)(4,5)(6,7);
s1 := Sym(50)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(50)!(11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,42)(43,46)(44,45)(47,50)(48,49);
s3 := Sym(50)!( 9,25)(10,19)(11,17)(12,27)(13,15)(14,37)(16,21)(18,31)(20,29)(22,39)(23,26)(24,47)(28,33)(30,43)(32,41)(34,49)(35,38)(36,48)(40,45)(42,44)(46,50);
poly := sub<Sym(50)|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*s2*s3*s2*s3 >;