Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,24}

Atlas Canonical Name {2,4,24}*1920a

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{2,4,24}
Vertices, edges, …
2, 20, 240, 120
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

Covers minimal covers in bold

None in this atlas.

Representations

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