{"paper":{"title":"The seven dimensional perfect Delaunay polytopes and Delaunay simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mathieu Dutour Sikiric","submitted_at":"2015-05-14T11:22:49Z","abstract_excerpt":"For a lattice $L$ of $R^n$, a sphere $S(c,r)$ of center $c$ and radius $r$ is called {\\em empty} if for any $v\\in L$ we have $\\Vert v - c\\Vert \\geq r$. Then the set $S(c,r)\\cap L$ is the vertex set of a {\\em Delaunay polytope} $P=conv(S(c,r)\\cap L)$. A Delaunay polytope is called {\\em perfect} if any affine transformation $\\phi$ such that $\\phi(P)$ is a Delaunay polytope is necessarily an isometry of the space composed with an homothety.\n  Perfect Delaunay polytopes are remarkable structure that exist only if $n=1$ or $n\\geq 6$ and they have shown up recently in covering maxima studies. Here w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03687","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"}