How many faces, edges and vertices does a cube have?
Explain how you know that the cube is a regular polyhedron.
What can you say about the symmetries of the cube? Describe all the planes of symmetry. Describe all the axes of rotational symmetry and give the order of rotational symmetry for each axis.
There is a very good interactive version of this activity at http://illuminations.nctm.org/activity.aspx?id=3544