Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,4,6}

Atlas Canonical Name {3,4,6}*1152a

Overview

Group
SmallGroup(1152,157478)
Rank
4
Schläfli Type
{3,4,6}
Vertices, edges, …
12, 48, 96, 24
Order of s0s1s2s3
12
Order of s0s1s2s3s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Orientable

Quotients maximal quotients in bold

2-fold

32-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)
s0 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);;
s1 := ( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22);;
s2 := ( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);;
s3 := ( 1, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)(21,22)(23,24);;
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, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);
s1 := Sym(24)!( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22);
s2 := Sym(24)!( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);
s3 := Sym(24)!( 1, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)(21,22)(23,24);
poly := sub<Sym(24)|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, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s2*s1*s0*s2*s1*s2*s3*s1*s0 >; 

References

None.

to this polytope.