Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,84,2}

Atlas Canonical Name {2,84,2}*672

Overview

Group
SmallGroup(672,1235)
Rank
4
Schläfli Type
{2,84,2}
Vertices, edges, …
2, 84, 84, 2
Order of s0s1s2s3
84
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat
  • Self-Dual

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

2-fold

Representations

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