2023
DOI: 10.48550/arxiv.2302.11764
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Intersection Bodies of Polytopes: Translations and Convexity

Abstract: We continue the study of intersection bodies of polytopes, focusing on the behavior of IP under translations of P . We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of I(P + t) can be extended to polynomials in variables t ∈ R d within each region of the arrangement. Establishing the convexity space as the set of translations such that I(P + t) is convex, we fully characterize it for two-dimensional polytopes and partially characterize it for higher dimensions… Show more

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