Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,20}

Atlas Canonical Name {2,8,20}*640a

Overview

Group
SmallGroup(640,12556)
Rank
4
Schläfli Type
{2,8,20}
Vertices, edges, …
2, 8, 80, 20
Order of s0s1s2s3
40
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 := (1,2);;
s1 := (13,18)(14,19)(15,20)(16,21)(17,22)(33,38)(34,39)(35,40)(36,41)(37,42)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82);;
s2 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,63)(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,78)(34,82)(35,81)(36,80)(37,79)(38,73)(39,77)(40,76)(41,75)(42,74);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,64)(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)(54,73)(55,77)(56,76)(57,75)(58,79)(59,78)(60,82)(61,81)(62,80);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(82)!(1,2);
s1 := Sym(82)!(13,18)(14,19)(15,20)(16,21)(17,22)(33,38)(34,39)(35,40)(36,41)(37,42)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82);
s2 := Sym(82)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,63)(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,78)(34,82)(35,81)(36,80)(37,79)(38,73)(39,77)(40,76)(41,75)(42,74);
s3 := Sym(82)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,64)(44,63)(45,67)(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)(54,73)(55,77)(56,76)(57,75)(58,79)(59,78)(60,82)(61,81)(62,80);
poly := sub<Sym(82)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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 >;