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Convex polytopes --- Polytopes convexes

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"The appearance of Grünbaum's 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 book's 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) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London).

Convex polytopes --- Polytopes convexes --- Convex polytopes. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Convex geometry . --- Discrete geometry. --- Convex and Discrete Geometry. --- Discrete mathematics --- Combinatorial geometry

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Geometry --- Convex polytopes --- Polytopes convexes --- 514.17 --- Polytopes --- Convex sets. Geometric figure arrangements. Geometric inequalities --- Convex polytopes. --- 514.17 Convex sets. Geometric figure arrangements. Geometric inequalities --- Convex geometry --- Polyhedra --- Géométrie convexe --- Polyèdres --- Géométrie --- Géométrie convexe --- Polyèdres --- Géométrie

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One way to advance the science of computational geometry is to make a comprehensive study of fundamental operations that are used in many different algorithms. This monograph attempts such an investigation in the case of two basic predicates: the counterclockwise relation pqr, which states that the circle through points (p, q, r) is traversed counterclockwise when we encounter the points in cyclic order p, q, r, p,...; and the incircle relation pqrs, which states that s lies inside that circle if pqr is true, or outside that circle if pqr is false. The author, Donald Knuth, is one of the greatest computer scientists of our time. A few years ago, he and some of his students were looking at amap that pinpointed the locations of about 100 cities. They asked, "Which ofthese cities are neighbors of each other?" They knew intuitively that some pairs of cities were neighbors and some were not; they wanted to find a formal mathematical characterization that would match their intuition.This monograph is the result.

Algorithmes --- Algorithms --- Algoritmen --- Convex polytopes --- Convexe polytopen --- Matroiden --- Matroides --- Matroids --- Polytopes convexes --- Matroïdes --- 519.1 --- Combinatorial designs and configurations --- Polytopes --- Algorism --- Algebra --- Arithmetic --- Combinatorics. Graph theory --- Foundations --- Algorithms. --- Convex polytopes. --- Matroids. --- 519.1 Combinatorics. Graph theory --- Matroïdes --- Information theory. --- Computer science. --- Computer graphics. --- Computer software. --- Combinatorics. --- Theory of Computation. --- Computer Applications. --- Discrete Mathematics. --- Computer Graphics. --- Algorithm Analysis and Problem Complexity. --- Combinatorics --- Mathematical analysis --- Software, Computer --- Computer systems --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Digital techniques