Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,24}

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

Overview

Group
SmallGroup(1152,155485)
Rank
4
Schläfli Type
{2,3,24}
Vertices, edges, …
2, 12, 144, 96
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 := ( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)(22,37)(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)(33,49)(34,50);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)(45,49)(46,47);;
s3 := ( 3,17)( 4,18)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12)(19,49)(20,50)(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,39)(30,40)(31,37)(32,38)(33,35)(34,36);;
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)(22,37)(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)(33,49)(34,50);
s2 := Sym(50)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)(45,49)(46,47);
s3 := Sym(50)!( 3,17)( 4,18)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12)(19,49)(20,50)(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,39)(30,40)(31,37)(32,38)(33,35)(34,36);
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, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2 >;