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Constructing a polytope to approximate a convex body

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Abstract

We develop an algorithm to construct a convex polytopeP withn vertices, contained in an arbitrary convex bodyK inR d, so that the ratio of the volumes |K/P|/|K| is dominated byc ·. d/n 2/(d−1).

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Authors and Affiliations

  1. Department of Mathematics, Technion I.I.T., 32000, Haifa, Israel

    Yehoram Gordon

  2. Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, 2, rue de la Butte Verte, 93166, Noisy-le-Grand Cedex, France

    Mathieu Meyer

  3. Department of Mathematics and School of Education — Oranim, University of Haifa, 31905, Haifa, Israel

    Shlomo Reisner

Authors
  1. Yehoram Gordon
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  2. Mathieu Meyer
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  3. Shlomo Reisner
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Supported in part by the fund for the promotion of research in the Technion

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Gordon, Y., Meyer, M. & Reisner, S. Constructing a polytope to approximate a convex body. Geom Dedicata 57, 217–222 (1995). https://doi.org/10.1007/BF01264939

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  • DOI: https://doi.org/10.1007/BF01264939

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