Convex Polytopes

The appearance of Gruenbaums book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the books immense influence made them quickly obsolete. Some other chapters promise beautiful, unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way. --Gil Kalai, The Hebrew University of Jerusalem