{"paper":{"title":"On reduced polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexandr Polyanskii","submitted_at":"2016-05-22T13:46:18Z","abstract_excerpt":"A convex body $R$ in $\\mathbb R^d$ is called reduced if the minimal width $\\Delta(R')$ of each convex body $R'\\subset R$ different from $R$ is strictly smaller than the minimal width $\\Delta(R)$ of $R$. In this article we construct a reduced polytope in $\\mathbb R^3$, i.e. we answer the following question posed by Lassak: do there exist reduced polytopes in $\\mathbb R^d$, $d\\geqslant3$? Also, we prove some properties of reduced polytopes in $\\mathbb R^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06791","kind":"arxiv","version":2},"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"}