Intersection Bodies of Polytopes
Algebraic Geometry
2025-06-02 v2 Combinatorics
Metric Geometry
Abstract
We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytope is always a semialgebraic set and provide an algorithm for its computation. Moreover, we compute the irreducible components of the algebraic boundary and provide an upper bound for the degree of these components.
Cite
@article{arxiv.2110.05996,
title = {Intersection Bodies of Polytopes},
author = {Katalin Berlow and Marie-Charlotte Brandenburg and Chiara Meroni and Isabelle Shankar},
journal= {arXiv preprint arXiv:2110.05996},
year = {2025}
}
Comments
As published in Beitr\"age zur Algebra und Geometrie. Correction of a scaling factor from previous version