{"paper":{"title":"Rotors in triangles and tethrahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Javier Bracho, Luis Montejano","submitted_at":"2016-10-19T21:39:56Z","abstract_excerpt":"A polytope $P$ is circumscribed about a convex body $\\Phi\\subset \\mathbb{R}^n$ if $\\Phi\\subset P$ and each facet of $P$ is contained in a support hyperplane of $\\Phi$. We say that a convex body $\\Phi\\subset \\mathbb{R}^n$ is a rotor of a polytope $P$ if for each rotation $\\rho$ of $\\mathbb{R}^n$ there exist a translation $\\tau$ so that $P$ is circumscribed about $\\tau\\rho\\Phi$.\n  In this paper we shall prove that if $P$ is a triangle, then there is a baricentric formula that describes the curvature of bd$\\Phi$ at the contact points, $\\{A_1, A_2,A_3\\}$. We prove also that if $\\Phi\\subset \\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06232","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"}