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arXiv · 2302.11764

Intersection Bodies of Polytopes: Translations and Convexity

Marie-Charlotte Brandenburg·Chiara Meroni
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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 $t\in \mathbb{R}^d$ within each region of the arrangement. In dimension $2$, we give a full characterization of those polygons such that their intersection body is convex. We give a partial characterization for general dimensions.

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Marie-Charlotte Brandenburg, Chiara Meroni. 2023-02-23. Intersection Bodies of Polytopes: Translations and Convexity. https://doi.org/10.1007/s10801-024-01328-9

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