{
  "abstract": "FINDING: The rhombic dodecahedron is the Voronoi cell of the FCC lattice, whose geometry encodes tetrahedral coordination (arccos(1/√3)) and face-diagonal ratios tied to √2 and √3, with dual relationship to the cuboctahedron. | MATH: FCC Voronoi cell = rhombic dodecahedron (12 rhombic faces, 24 edges, 14 vertices). Face diagonal ratio: short/long = 1/√2 ≈ 0.7071. Tetrahedral angle between face normals: arccos(1/√3) ≈ 54.7356°. Dihedral angle of rhombic dodecahedron: arccos(−1/3) ≈ 109.471° (tetrahedral angle complement). Packing fraction FCC = π/(3√2) ≈ 0.7405. Reciprocal lattice of FCC = BCC (cube Voronoi). Rhombus acute angle = arccos(1/3) ≈ 70.528°, obtuse = 109.471°. | CONNECTION: The rhombic dodecahedron's face diagonal ratio 1/√2 = 0.7071 is NOT a golden ratio, but its dihedral angle 109.471° = 180° − 70.528°; note 70.528° = 2 × 35.264° (half of tetrahedral angle). The ratio √2 appears in FCC stacking (ABCABC), and √3 in face diagonal of cube. No direct φ (1.618) or 0.618/0.786/2\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1hta6p9ra2y88.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431086",
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  "id": "1hta6p9ra2y88",
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  "landing_url": "https://zenodo.org/records/23431086",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1hta6p9ra2y88.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:05Z",
      "native_id": "23431086",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431086"
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  "subjects": [],
  "title": "FCC Voronoi Geometry: Rhombic Dodecahedron, Tetrahedral Angles, and Dual Cuboctahedron — E8 Intelligence Research",
  "title_text": "FCC Voronoi Geometry: Rhombic Dodecahedron, Tetrahedral Angles, and Dual Cuboctahedron — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:05Z",
  "url": "https://research.draconitic.com/paper/1hta6p9ra2y88",
  "venue": "Zenodo",
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}