# Group theory: point group of a cube

#### Entropia

what is the point group of a cube?

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#### matt grime

Homework Helper
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.

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#### 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 $$O_{h} = S_{4} x C_{2}$$.