{"paper":{"title":"Most Reinhardt polygons are sporadic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.MG","authors_text":"Kevin G. Hare, Michael J. Mossinghoff","submitted_at":"2014-05-20T20:25:44Z","abstract_excerpt":"A \\textit{Reinhardt polygon} is a convex $n$-gon that, for $n$ not a power of $2$, is optimal in three different geometric optimization problems, for example, it has maximal perimeter relative to its diameter. Some such polygons exhibit a particular periodic structure; others are termed \\textit{sporadic}. Prior work has described the periodic case completely, and has shown that sporadic Reinhardt polygons occur for all $n$ of the form $n=pqr$ with $p$ and $q$ distinct odd primes and $r\\geq2$. We show that (dihedral equivalence classes of) sporadic Reinhardt polygons outnumber the periodic ones"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5233","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"}