Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,20,3}

Atlas Canonical Name {2,2,20,3}*1920

Overview

Group
SmallGroup(1920,240988)
Rank
5
Schläfli Type
{2,2,20,3}
Vertices, edges, …
2, 2, 80, 120, 12
Order of s0s1s2s3s4
20
Order of s0s1s2s3s4s3s2s1
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

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,14)( 7,16)( 8,21)( 9,23)(11,42)(15,32)(17,48)(18,47)(19,38)(24,27)(25,40)(26,41)(28,30)(33,37)(34,35)(36,39)(43,51)(44,50)(45,49)(46,52);;
s3 := ( 5, 8)( 6,17)( 7,12)( 9,20)(10,21)(11,47)(13,34)(14,39)(15,31)(16,26)(18,28)(19,29)(22,23)(24,50)(25,32)(27,37)(30,33)(35,44)(36,43)(38,46)(40,42)(41,51)(45,48)(49,52);;
s4 := ( 5,13)( 6,23)( 7,17)( 8,28)( 9,14)(10,31)(11,41)(12,22)(15,33)(16,48)(18,34)(19,39)(20,29)(21,30)(24,46)(25,49)(26,42)(27,52)(32,37)(35,47)(36,38)(40,45)(43,50)(44,51);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 6,14)( 7,16)( 8,21)( 9,23)(11,42)(15,32)(17,48)(18,47)(19,38)(24,27)(25,40)(26,41)(28,30)(33,37)(34,35)(36,39)(43,51)(44,50)(45,49)(46,52);
s3 := Sym(52)!( 5, 8)( 6,17)( 7,12)( 9,20)(10,21)(11,47)(13,34)(14,39)(15,31)(16,26)(18,28)(19,29)(22,23)(24,50)(25,32)(27,37)(30,33)(35,44)(36,43)(38,46)(40,42)(41,51)(45,48)(49,52);
s4 := Sym(52)!( 5,13)( 6,23)( 7,17)( 8,28)( 9,14)(10,31)(11,41)(12,22)(15,33)(16,48)(18,34)(19,39)(20,29)(21,30)(24,46)(25,49)(26,42)(27,52)(32,37)(35,47)(36,38)(40,45)(43,50)(44,51);
poly := sub<Sym(52)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3 >;