Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,24,4}

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

Overview

Group
SmallGroup(1920,240809)
Rank
4
Schläfli Type
{2,24,4}
Vertices, edges, …
2, 120, 240, 20
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, 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 := ( 3,49)( 4,34)( 5,33)( 6, 8)( 7,46)( 9,19)(10,28)(11,31)(12,21)(13,30)(14,36)(15,23)(16,32)(17,26)(18,48)(20,43)(22,39)(24,50)(25,44)(27,45)(29,35)(37,38)(40,41)(42,47);;
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, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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, 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)!( 3,49)( 4,34)( 5,33)( 6, 8)( 7,46)( 9,19)(10,28)(11,31)(12,21)(13,30)(14,36)(15,23)(16,32)(17,26)(18,48)(20,43)(22,39)(24,50)(25,44)(27,45)(29,35)(37,38)(40,41)(42,47);
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, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;