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Note on projection bodies of zonotopes with n + 1 generators

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Abstract

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⌋.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Sekr. MA 4-1, Straße des 17 Juni 136, 10623, Berlin, Germany

    Martin Henk

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  1. Martin Henk
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Correspondence to Martin Henk.

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Conflict of Interest The author declares no conflict of interest.

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Dedicated to the memory of Professor Delin REN

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Henk, M. Note on projection bodies of zonotopes with n + 1 generators. Acta Math Sci 45, 96–103 (2025). https://doi.org/10.1007/s10473-025-0107-9

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  • DOI: https://doi.org/10.1007/s10473-025-0107-9

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MSC2020