Part of the Atlas of Small Regular Polytopes

Polytope of Type {9,2,42}

Atlas Canonical Name {9,2,42}*1512

Overview

Group
SmallGroup(1512,560)
Rank
4
Schläfli Type
{9,2,42}
Vertices, edges, …
9, 9, 42, 42
Order of s0s1s2s3
126
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

6-fold

7-fold

9-fold

14-fold

18-fold

21-fold

42-fold

63-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,43)(44,47)(45,46)(48,51)(49,50);;
s3 := (10,26)(11,20)(12,18)(13,28)(14,16)(15,38)(17,22)(19,32)(21,30)(23,40)(24,27)(25,48)(29,34)(31,44)(33,42)(35,50)(36,39)(37,49)(41,46)(43,45)(47,51);;
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*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(51)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(51)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(51)!(12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,43)(44,47)(45,46)(48,51)(49,50);
s3 := Sym(51)!(10,26)(11,20)(12,18)(13,28)(14,16)(15,38)(17,22)(19,32)(21,30)(23,40)(24,27)(25,48)(29,34)(31,44)(33,42)(35,50)(36,39)(37,49)(41,46)(43,45)(47,51);
poly := sub<Sym(51)|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*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 >;