{"ID":2896147,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.07779","arxiv_id":"2507.07779","title":"Approximation Depth of Convex Polytopes","abstract":"We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approximate a target polytope by polytopes of a given depth. Our main results imply that simplices can only be ``trivially approximated''. On the way, we obtain a characterization of simplices as the only ``outer additive'' convex bodies.","short_abstract":"We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approximate a target polytope by polytopes of a given depth. Our main results imply that simplices can only be ``trivially approximated''. On the wa...","url_abs":"https://arxiv.org/abs/2507.07779","url_pdf":"https://arxiv.org/pdf/2507.07779v1","authors":"[\"Egor Bakaev\",\"Florestan Brunck\",\"Amir Yehudayoff\"]","published":"2025-07-10T13:58:55Z","proceeding":"math.MG","tasks":"[\"math.MG\",\"cs.CG\",\"cs.LG\",\"math.CO\"]","methods":"[]","has_code":false}