Convex Polytopes

Graduate Texts in Mathematics

Branko Grünbaum

466 pages, parution le 16/06/2003 (2^eme édition)

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Résumé

The appearance of Gruenbaum'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 Gruenbaum 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

The combinatorial study of convex polytopes is today an extremely active and healthy area of mathematical research, and the number and depth of its relationships to other parts of mathematics have grown astonishingly since Convex Polytopes was first published in 1966. The new edition contains the full text of the original and the addition of notes at the end of each chapter. The notes are intended to bridge the thirty five years of intensive research on polytopes that were to a large extent initiated, guided, motivated and fuelled by the first edition of Convex Polytopes. The new material provides a direct guide to more than 400 papers and books that have appeared since 1967. Branko Grünbaum is Professor of Mathematics at the University of Washington.

Preface
Notation and prerequisites
Convex sets
Polytopes
Examples
Fundamental properties and constructions
Polytopes with few vertices
Neighborly polytopes
Euler's relation
Analogues of Euler's relation
Extremal problems concerning numbers of faces
Properties of boundary complexes
k-Equivalence of polytopes
3-Polytopes
Angle-sums relations; the Steiner point
Addition and decomposition of polytopes (by G.C. Shephard)
Diameters of Polytopes (by Victor Klee)
Long paths and cicuits on polytopes (by Victor Klee)
Arrangements of hyperplanes
Concluding remarks

Tables
Addendum
Errata
Bibliography
Index of terms
Index of symbols

L'auteur - Branko Grünbaum

University of Washington, Seattle, WA, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Branko Grünbaum
Parution	16/06/2003
Édition	2^eme édition
Nb. de pages	466
Format	16 x 24
Couverture	Relié
Poids	925g
Intérieur	Noir et Blanc
EAN13	9780387004242
ISBN13	978-0-387-00424-2