Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,24}

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

Overview

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