Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,20}

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

Overview

Group
SmallGroup(1920,240988)
Rank
4
Schläfli Type
{2,6,20}
Vertices, edges, …
2, 24, 240, 80
Order of s0s1s2s3
20
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

16-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

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