Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,6,2}

Atlas Canonical Name {24,6,2}*1152a

Overview

Group
SmallGroup(1152,155485)
Rank
4
Schläfli Type
{24,6,2}
Vertices, edges, …
48, 144, 12, 2
Order of s0s1s2s3
6
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

3-fold

4-fold

12-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

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