This volume is a collection of ten papers, most of which formed contributions to the workshop Polytopes and optimization held in Oberwolfach in November 1997. It offers a wide panorama of relations of polytope theory to other fields. It starts with a remarkable paper on the combinatorics and geometry of 0/1-polytopes, written by Günter M. Ziegler, who says that it is meant as an introduction and invitation rather than an extensive survey. Different aspects of the complexity of higher-dimensional 0/1-polytopes are presented in an elegant way, accessible also to non-specialists.

The collection contains the following papers: E. Gawrilow and M. Joswig: POLYMAKE: a framework for analyzing convex polytopes; G. Kalai, P. Kleinschmidt and G. Meisinger: Flag numbers and FLAGTOOL; A. Höppner and G. M. Ziegler: A census of flag-vectors of 4-polytopes; O. Aichholzer: Extremal properties of 0/1-polytopes of dimension 5; B. Büeler, A. Enge and K. Fukuda: Exact volume computation for polytopes: a practical study; H. Achatz and P. Kleinschmidt: Reconstructing a simple polytope from its graph; M. Joswig: Reconstructing a non-simple polytope from its graph; D. Avis: A revised implementation of the reverse search vertex enumeration algorithm; S. G. Bartels: The complexity of Yamnitsky and Levin’s simplices method.

Reviewer:

pv