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Polytopes

Abstract, Convex and Computational

  • Book
  • © 1994

Overview

Editors:
  1. T. Bisztriczky

    1. Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

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  2. P. McMullen

    1. Department of Mathematics, University College, London, UK

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  3. R. Schneider

    1. Mathematisches Institut, Universität Freiburg, Freiburg, Germany

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  4. A. Ivić Weiss

    1. Department of Mathematics and Statistics, York University, North York, Canada

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Part of the book series: Nato Science Series C: (ASIC, volume 440)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xix
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  2. Abstract

    1. Recent Results on Coxeter Groups

      • Arjeh Marcel Cohen
      Pages 1-19

    2. The Evolution of Coxeter-Dynkin Diagrams

      • H. S. M. Coxeter
      Pages 21-42

    3. Polyhedra with Hollow Faces

      • Branko Grünbaum
      Pages 43-70

    4. A Hierarchical Classification of Euclidean Polytopes with Regularity Properties

      • Horst Martini
      Pages 71-96

    5. Modern Developments in Regular Polytopes

      • Peter McMullen
      Pages 97-124

    6. Classification of Locally Toroidal Regular Polytopes

      • Egon Schulte
      Pages 125-154

  3. Convex

    1. Face Numbers and Subdivisions of Convex Polytopes

      • Margaret M. Bayer
      Pages 155-171

    2. Approximation by Convex Polytopes

      • P. M. Gruber
      Pages 173-203

    3. Some Aspects of the Combinatorial Theory of Convex Polytopes

      • Gil Kalai
      Pages 205-229

    4. On Volumes of Non-Euclidean Polytopes

      • Ruth Kellerhals
      Pages 231-239

    5. Manifolds in the Skeletons of Convex Polytopes, Tightness, and Generalized Heawood Inequalities

      • Wolfgang Kühnel
      Pages 241-247

    6. Generalized Stress and Motions

      • Carl W. Lee
      Pages 249-271

    7. Polytopes and Brunn-Minkowski Theory

      • Rolf Schneider
      Pages 273-299

    8. A Survey of Eulerian Posets

      • Richard P. Stanley
      Pages 301-333

  4. Computational

    1. On Recent Progress in Computational Synthetic Geometry

      • Jürgen Bokowski
      Pages 335-358

    2. The Ridge Graph of the Metric Polytope and Some Relatives

      • Antoine Deza, Michel Deza
      Pages 359-372

    3. On the Complexity of Some Basic Problems in Computational Convexity

      • Peter Gritzmann, Victor Klee
      Pages 373-466

    4. The Diameter of Polytopes and Related Applications

      • Peter Kleinschmidt
      Pages 467-492

  5. Problems

    1. Front Matter

      Pages 493-493
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Keywords

About this book

The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject.
The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex.
With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes.
For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Editors and Affiliations

  • Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

    T. Bisztriczky

  • Department of Mathematics, University College, London, UK

    P. McMullen

  • Mathematisches Institut, Universität Freiburg, Freiburg, Germany

    R. Schneider

  • Department of Mathematics and Statistics, York University, North York, Canada

    A. Ivić Weiss

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