Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,4,42}

Atlas Canonical Name {2,2,4,42}*1344a

Overview

Group
SmallGroup(1344,11661)
Rank
5
Schläfli Type
{2,2,4,42}
Vertices, edges, …
2, 2, 4, 84, 42
Order of s0s1s2s3s4
84
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

6-fold

7-fold

12-fold

14-fold

21-fold

28-fold

42-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)(67,88);;
s3 := ( 5,47)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,61)(13,67)(14,66)(15,65)(16,64)(17,63)(18,62)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,68)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,82)(34,88)(35,87)(36,86)(37,85)(38,84)(39,83)(40,75)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76);;
s4 := ( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)(22,24)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)(47,55)(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66)(68,76)(69,75)(70,81)(71,80)(72,79)(73,78)(74,77)(82,83)(84,88)(85,87);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(88)!(1,2);
s1 := Sym(88)!(3,4);
s2 := Sym(88)!(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)(67,88);
s3 := Sym(88)!( 5,47)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,61)(13,67)(14,66)(15,65)(16,64)(17,63)(18,62)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)(26,68)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,82)(34,88)(35,87)(36,86)(37,85)(38,84)(39,83)(40,75)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76);
s4 := Sym(88)!( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)(22,24)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)(47,55)(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66)(68,76)(69,75)(70,81)(71,80)(72,79)(73,78)(74,77)(82,83)(84,88)(85,87);
poly := sub<Sym(88)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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*s3*s4*s3*s4 >;