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On pyramids and reducedness

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Abstract

A convex body K in ℝd is said to be reduced if the minimum width of each convex body properly contained in K is strictly smaller than the minimum width of K. We study the question of Lassak on the existence of reduced polytopes of dimension larger than two. We show that a pyramid of dimension larger than two with equal numbers of facets and vertices is not reduced. This generalizes the main result from [8].

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Authors and Affiliations

  1. Faculty of Mathematics, University of Magdeburg, D-39106, Magdeburg, Germany

    Gennadiy Averkov

  2. Faculty of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany

    Horst Martini

Authors
  1. Gennadiy Averkov
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  2. Horst Martini
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Correspondence to Gennadiy Averkov.

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Averkov, G., Martini, H. On pyramids and reducedness. Period Math Hung 57, 117–120 (2008). https://doi.org/10.1007/s10998-008-8117-x

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  • DOI: https://doi.org/10.1007/s10998-008-8117-x

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