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Approximation of convex bodies by polytopes with uniformly bounded valences

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Abstract

Given any convex bodyK in Euclideann-spaceR n and any number ɛ>0, does there always exist a polytopeP(K, ɛ)⊂R n such that the number of vertices of a facet ofP and the number of facets meeting in a common vertex are bounded by a constant depending on the dimensiond only and such that the Hausdorff-distance ϱ (K, P) ofK andP is less than ɛ? This question of Ewald posed at the Durham symposium in 1975 is answered in the affirmative.

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References

  1. Bokowski, J.: Konvexe Körper approximierende Polytopklassen. Elem. Math.32, 88–90 (1977).

    MATH  MathSciNet  Google Scholar 

  2. Bokowski, J., Schulz, Chr.: Dichte Klassen konvexer Polytope. Math. Z.160, 173–182 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  3. Bokowski, J., Mani, P.: Zur Approximation konvexer Körper imE n. Annals of Discrete Math.20, 319–320 (1984).

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  4. Grünbaum, B.: Convex Polytopes. London: Interscience Publ. 1967.

    MATH  Google Scholar 

  5. Larman, D., Rogers, C. A.: Durham Symposium on the relations between infinite- and finite-dimensional convexity. Bull. London Math. Soc.8, 1–33 (1976).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-6100, Darmstadt, Germany

    Jürgen Bokowski

  2. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3000, Bern, Switzerland

    Peter Mani-Levitska

Authors
  1. Jürgen Bokowski
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  2. Peter Mani-Levitska
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Bokowski, J., Mani-Levitska, P. Approximation of convex bodies by polytopes with uniformly bounded valences. Monatshefte für Mathematik 104, 261–264 (1987). https://doi.org/10.1007/BF01294649

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  • DOI: https://doi.org/10.1007/BF01294649

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