# The study of symmetry

Swlabr
Science 27 Aug '08 19:36
1. 27 Aug '08 19:36
I know that in mathematics, Group Theory is the formal study of symmetry. However, having done quite a lot of group theory I am left with this question:

How?

I understand that the dihedral groups, and subgroups thereof, represent symmetries wonderfully. But, for instance, what would be represented by the Symmetric groups? would it be some n-dimensional object (where the symmetric group is S_n)?
2. flexmore
Quack Quack Quack !
28 Aug '08 02:211 edit
Originally posted by Swlabr
... would it be some n-dimensional object (where the symmetric group is S_n)?
You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

S3 is like a 2d triangle,
and
S4 is like a 3d cube.
3. flexmore
Quack Quack Quack !
28 Aug '08 04:48
You could be meaning: Sn is symmetric in the same way as a regular (n-1) simplex.
4. 28 Aug '08 13:39
Originally posted by flexmore
You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

S3 is like a 2d triangle,
and
S4 is like a 3d cube.
Numbers: a mathematicians greatest weakness.
5. 28 Aug '08 13:44
Originally posted by flexmore
You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

S3 is like a 2d triangle,
and
S4 is like a 3d cube.
Yes-that makes sense. Thanks for that.