Convex Polytopes: Prepared by Volker Kaibel, Victor Klee, and Gnter Ziegler

Paperback | November 3, 2003

byBranko GrünbaumEditorGünter M. Ziegler

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"The original edition [...] 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

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From the Publisher

"The original edition [...] 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 ...

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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 appe...

Format:PaperbackDimensions:487 pages, 9.21 × 6.14 × 0.04 inPublished:November 3, 2003Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387404090

ISBN - 13:9780387404097

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Table of Contents

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.

Editorial Reviews

"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)From the reviews of the second edition:"Branko Grünbaum's book is a classical monograph on convex polytopes . . As was noted by many researchers, for many years the book provided a central reference for work in the field and inspired a whole generation of specialists in polytope theory. . Every chapter of the book is supplied with a section entitled 'Additional notes and comments' . these notes summarize the most important developments with respect to the topics treated by Grünbaum. . The new edition . is an excellent gift for all geometry lovers." (Alexander Zvonkin, Mathematical Reviews, 2004b)