Here is a link to the extremely useful and well written FAQ in polyhedral computation by Fukuda. Here is a PDF version.
See the sections on face-lattice, polarity aka. duality and Minkowski-Weyl. The number of facets of a d-dimensional, n-vertex polytope grows linearly with n. However, its slope is so high that it grows intractable within no time (fascinating!).
Note: See the sub-sections where many problems, simple and hard, are discussed.
11/25: Probably the polylib-page on Polyhedra , with material taken from Schrijver's book is useful for definitions.