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<p>We show that the volume of the projection body Π(<i>Z</i>) of an <i>n</i>-dimensional zonotope <i>Z</i> with <i>n</i> + 1 generators and of volume 1 is always exactly 2<sup><i>n</i></sup>. Moroever, we point out that an upper bound on the volume of Π(<i>K</i>) of a centrally symmetric <i>n</i>-dimensional convex body of volume 1 is at least 2<sup><i>n</i></sup> (9/8)<sup>⌊<i>n</i>/3⌋</sup>.</p>

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Note on projection bodies of zonotopes with n + 1 generators

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Martin Henk

摘要

We show that the volume of the projection body Π(Z) of an n-dimensional zonotope Z with n + 1 generators and of volume 1 is always exactly 2n. Moroever, we point out that an upper bound on the volume of Π(K) of a centrally symmetric n-dimensional convex body of volume 1 is at least 2n (9/8)⌊n/3⌋.