{"paper":{"title":"Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","cond-mat.stat-mech","math.MG"],"primary_cat":"cond-mat.soft","authors_text":"Aaron S. Keys, Amir Haji-Akbari, Michael Engel, Peter Palffy-Muhoray, Rolfe G. Petschek, Sharon C. Glotzer, Xiaoyu Zheng","submitted_at":"2010-12-23T03:32:58Z","abstract_excerpt":"All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of {\\phi} = {\\pi}/\\sqrt18 ~ 0.7405. For many shapes, simple lattice packings easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with {\\phi} = 0.7786, which was subsequently compressed numerically to {\\phi} = 0.7820. Here we show that tetrahedra pack much better than this, and in a completely unexpected way. Following a conceptually different appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5138","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"}