{
  "abstract": "We prove that the regular truncated octahedron uniquely minimizes surface area among all parallelohedra of fixed volume. Equivalently, every three-dimensional parallelohedron $P$ satisfies \\[ \\frac{\\mathcal H^2(\\partial P)}{|P|^{2/3}} \\ge \\frac{3(1+2\\sqrt3)}{4^{2/3}}, \\] with equality if and only if $P$ is similar to the regular truncated octahedron. Among the non-truncated Fedorov types we prove a stronger sharp bound, attained uniquely by the regular rhombic dodecahedron.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02384",
  "author_total": 2,
  "authors": [
    {
      "name": "Annalisa Cesaroni"
    },
    {
      "name": "Matteo Novaga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6r7s82vf17pb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02384",
  "fulltext_url": null,
  "id": "6r7s82vf17pb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02384",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7207716827",
  "pdf_url": "https://arxiv.org/pdf/2609.02384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6r7s82vf17pb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.02384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The truncated octahedron minimizes surface area among parallelohedra of equal volume",
  "title_text": "The truncated octahedron minimizes surface area among parallelohedra of equal volume",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/6r7s82vf17pb4",
  "venue": "arXiv",
  "versions": []
}