{"paper":{"title":"Multiples of lattice polytopes without interior lattice points","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Benjamin Nill, Victor Batyrev","submitted_at":"2006-02-15T17:57:58Z","abstract_excerpt":"Let $\\Delta$ be an $n$-dimensional lattice polytope. The smallest non-negative integer $i$ such that $k \\Delta$ contains no interior lattice points for $1 \\leq k \\leq n - i$ we call the degree of $\\Delta$. We consider lattice polytopes of fixed degree $d$ and arbitrary dimension $n$. Our main result is a complete classification of $n$-dimensional lattice polytopes of degree $d=1$. This is a generalization of the classification of lattice polygons $(n=2)$ without interior lattice points due to Arkinstall, Khovanskii, Koelman and Schicho. Our classification shows that the secondary polytope of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602336","kind":"arxiv","version":3},"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"}