Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,24,3}

Atlas Canonical Name {2,24,3}*1152

Overview

Group
SmallGroup(1152,155485)
Rank
4
Schläfli Type
{2,24,3}
Vertices, edges, …
2, 96, 144, 12
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

4-fold

12-fold

16-fold

24-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Representations

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