Polytopes, graphs, and complexes

Abstract

During the last few years the theory of convex polytopes has been developing at an ever accelerating pace. As a consequence, many parts of the book "Convex Polytopes" ([CP] =Grnbaum [1967a]), which was essentially completed early in 1966, are by now completely out of date. The same fate befell the surveys by Klee [1966] and Grnbaum [l967b]; even the more recent survey by The new achievements are scattered in the literature, and many of them are still in the preprint stage. Hence it seemed worthwhile to prepare an up-to-date summary of the new results, organized in a form that makes it readable without previous specialized knowledge of the theory of polytopes.