Neighbourly cubical polytopes
Abstract: A cubical polytope is a (convex) polytope all of whose faces are (combinatorial) cubes. This simple definition leads us to a fascinating class of polytopes, whose combinatorics and geometry offers many striking problems and observations. In particular, there is an obvious parallelism to the theory of simplicial polytopes --- which, however, isn't perfect...
In this lecture I plan to give a (biased) survey of some research on cubical polytopes. Among the results we'll get to are