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  • © 1994

Polytopes

Abstract, Convex and Computational

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
  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. Modern Developments in Regular Polytopes

      • Peter McMullen
      Pages 97-124
  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. On Volumes of Non-Euclidean Polytopes

      • Ruth Kellerhals
      Pages 231-239
    4. Generalized Stress and Motions

      • Carl W. Lee
      Pages 249-271
    5. Polytopes and Brunn-Minkowski Theory

      • Rolf Schneider
      Pages 273-299
    6. A Survey of Eulerian Posets

      • Richard P. Stanley
      Pages 301-333
  4. Computational

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

      • Antoine Deza, Michel Deza
      Pages 359-372
    2. On the Complexity of Some Basic Problems in Computational Convexity

      • Peter Gritzmann, Victor Klee
      Pages 373-466
    3. The Diameter of Polytopes and Related Applications

      • Peter Kleinschmidt
      Pages 467-492
  5. Problems

    1. Front Matter

      Pages 493-493

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

Bibliographic Information

Buy it now

Buying options

eBook USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access