Good exercises, but a bit vague perhaps? One way of leading the students in a particular direction might be to ask for an investigation of semi-regular polyhedra, built with two types of polygons rather than just one. Then the duality concept is somewhat different, in that the dual of such an object is not necessarily semi-regular at all. What can go wrong? What about truncating regular polyhedra, and for that matter semi-regular ones? What if you cut off half-way down each edge, or some other fixed amount? I think that working with these cases where symmetry is not automatic and duality is more complicated might lead to a better appreciation of how strong the regularity condition is.

What kinds of constructions corresponding to duality might we expect to find in higher dimensions?