Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,2,4,20}

Atlas Canonical Name {2,2,2,4,20}*1280

Overview

Group
SmallGroup(1280,1076200)
Rank
6
Schläfli Type
{2,2,2,4,20}
Vertices, edges, …
2, 2, 2, 4, 40, 20
Order of s0s1s2s3s4s5
20
Order of s0s1s2s3s4s5s4s3s2s1
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

20-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,72)(28,73)(29,74)(30,75)(31,76)(32,67)(33,68)(34,69)(35,70)(36,71)(37,82)(38,83)(39,84)(40,85)(41,86)(42,77)(43,78)(44,79)(45,80)(46,81);;
s4 := ( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)(16,33)(17,37)(18,41)(19,40)(20,39)(21,38)(22,42)(23,46)(24,45)(25,44)(26,43)(47,67)(48,71)(49,70)(50,69)(51,68)(52,72)(53,76)(54,75)(55,74)(56,73)(57,77)(58,81)(59,80)(60,79)(61,78)(62,82)(63,86)(64,85)(65,84)(66,83);;
s5 := ( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,38)(28,37)(29,41)(30,40)(31,39)(32,43)(33,42)(34,46)(35,45)(36,44)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(62,63)(64,66)(67,78)(68,77)(69,81)(70,80)(71,79)(72,83)(73,82)(74,86)(75,85)(76,84);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(86)!(1,2);
s1 := Sym(86)!(3,4);
s2 := Sym(86)!(5,6);
s3 := Sym(86)!( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,72)(28,73)(29,74)(30,75)(31,76)(32,67)(33,68)(34,69)(35,70)(36,71)(37,82)(38,83)(39,84)(40,85)(41,86)(42,77)(43,78)(44,79)(45,80)(46,81);
s4 := Sym(86)!( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)(16,33)(17,37)(18,41)(19,40)(20,39)(21,38)(22,42)(23,46)(24,45)(25,44)(26,43)(47,67)(48,71)(49,70)(50,69)(51,68)(52,72)(53,76)(54,75)(55,74)(56,73)(57,77)(58,81)(59,80)(60,79)(61,78)(62,82)(63,86)(64,85)(65,84)(66,83);
s5 := Sym(86)!( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,38)(28,37)(29,41)(30,40)(31,39)(32,43)(33,42)(34,46)(35,45)(36,44)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(62,63)(64,66)(67,78)(68,77)(69,81)(70,80)(71,79)(72,83)(73,82)(74,86)(75,85)(76,84);
poly := sub<Sym(86)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;