Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,42,2}

Atlas Canonical Name {3,2,42,2}*1008

Overview

Group
SmallGroup(1008,942)
Rank
5
Schläfli Type
{3,2,42,2}
Vertices, edges, …
3, 3, 42, 42, 2
Order of s0s1s2s3s4
42
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 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,45)(43,44);;
s3 := ( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,32)(11,16)(13,26)(15,24)(17,34)(18,21)(19,42)(23,28)(25,38)(27,36)(29,44)(30,33)(31,43)(35,40)(37,39)(41,45);;
s4 := (46,47);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(47)!(2,3);
s1 := Sym(47)!(1,2);
s2 := Sym(47)!( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,37)(38,41)(39,40)(42,45)(43,44);
s3 := Sym(47)!( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,32)(11,16)(13,26)(15,24)(17,34)(18,21)(19,42)(23,28)(25,38)(27,36)(29,44)(30,33)(31,43)(35,40)(37,39)(41,45);
s4 := Sym(47)!(46,47);
poly := sub<Sym(47)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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 >;