Part of the Atlas of Small Regular Polytopes

Polytope of Type {80,2,2}

Atlas Canonical Name {80,2,2}*640

Overview

Group
SmallGroup(640,15814)
Rank
4
Schläfli Type
{80,2,2}
Vertices, edges, …
80, 80, 2, 2
Order of s0s1s2s3
80
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

4-fold

5-fold

8-fold

10-fold

16-fold

20-fold

40-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

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