InhaltsangabePreface. Abstract. Recent results on Coxeter groups; A.M. Cohen. The evolution of Coxeter--Dynkin diagrams; H.S.M. Coxeter. Polyhedra with hollow faces; B. Grünbaum. A hierarchical classification of Euclidean polytopes with regularity properties; H. Martini. Modern developments in regular polytopes; P. McMullen. Classification of locally toroidal regular polytopes; E. Schulte. Convex. Face numbers and subdivisions of convex polytopes; M.M. Bayer. Approximation by convex polytopes; P.M. Gruber. Some aspects of the combinatorial theory of convex polytopes; G. Kalai. On volumes of non--Euclidean polytopes; R. Kellerhals. Manifolds in the skeletons of convex polytopes, tightness, and generalized Heawood inequalities; W. Kühnel. Generalized stress and motions; C.W. Lee. Polytopes and Brunn--Minkowski theory; R. Schneider. A survey of Eulerian posets; R.P. Stanley. Computational. On recent progress in computational synthetic geometry; J. Bokowski. The ridge graph of the metric polytope and some relatives; A. Deza, M. Deza. On the complexity of some basic problems in computational convexity: II. volume and mixed volumes; P. Gritzmann, V. Klee. The diameter of polytopes and related applications; P. Kleinschmidt. Problems. Contributed problems; J. Schaer (editor). Three problems about 4-polytopes; G.M. Zielger. Index.