dimensional units

How many vertices in 0 dimensions? How many vertices and edges in 1 dimension? How many vertices, edges and faces in 2 dimensions? How many vertices, edges, faces and cubes in 3 dimensions? How many vertices, edges, faces, and cubes in 4 dimensions? What questions could / would you ask your students based on this applet?
adapted from an applet by Juan Carlos Ponce Campuzano