# Group theory: point group of a cube

1. Feb 29, 2004

### Entropia

what is the point group of a cube?

2. Mar 1, 2004

### matt grime

it is the same as the ordinary symmetry group. (rotations and reflections). if the question was what's this group, then it is a group of order 48, you can get a presentation of it by labelling the vertices. It is abstractly isomorphic to S_4 x C_2, symmetric group on 4 letters direct product cyclic group of order 2.

To see the iso with S_4xC_2 imagine drawing in the diagonals of the box, there are 4 of them. the symmetries permute these 4 objects, the C_2 part is because there are reflections too.

Last edited: Mar 1, 2004
3. Mar 1, 2004

### Dr Transport

If I remember my solid state course correctly, the group for a cube is $$O_{h}$$. This takes into account the inversion symmetry. I believe it is written as $$O_{h} = S_{4} x C_{2}$$.

dt