Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,6}

Atlas Canonical Name {2,20,6}*1920d

Overview

Group
SmallGroup(1920,240977)
Rank
4
Schläfli Type
{2,20,6}
Vertices, edges, …
2, 80, 240, 24
Order of s0s1s2s3
8
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

8-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

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