Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,4}

Atlas Canonical Name {2,20,4}*1920d

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{2,20,4}
Vertices, edges, …
2, 120, 240, 24
Order of s0s1s2s3
24
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

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