{"paper":{"title":"Polytopes of Maximal Volume Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Artem Zvavitch, Matthew Alexander, Matthieu Fradelizi","submitted_at":"2017-08-26T01:33:56Z","abstract_excerpt":"For a convex body $K \\subset {\\mathbb R}^n$, let $K^z = \\{y\\in{\\mathbb R}^n : \\langle y-z, x-z\\rangle\\le 1, \\mbox{\\ for all\\ } x\\in K\\}$ be the polar body of $K$ with respect to the center of polarity $z \\in {\\mathbb R}^n$. The goal of this paper is to study the maximum of the volume product $\\mathcal{P}(K)=\\min_{z\\in {\\rm int}(K)}|K||K^z|$, among convex polytopes $K\\subset {\\mathbb R}^n$ with a number of vertices bounded by some fixed integer $m \\ge n+1$. In particular, we prove that the supremum is reached at a simplicial polytope with exactly $m$ vertices and we provide a new proof of a res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07914","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}