Home | People | Seminar | Conferences | Resources


Title: 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
  1. a classification of the cubical d-polytopes with at most 2d+1 vertices, by Blind & Blind,
  2. a construction of neighborly cubical polytopes, and their combinatorial description, and
  3. a counterexample to Kalai's ``cubical upper bound conjecture'', both joint with Michael Joswig.

Return to the seminar page.

Home | People | Seminar | Conferences | Resources

Please send comments about this page to Maurice Rojas at rojas@math.tamu.edu.
Last Modified on 29/Mar/00