{
  "abstract": "FINDING: The rhombic dodecahedron appears as the Voronoi cell of the face-centered cubic (FCC) lattice, and its golden-ratio variant arises from icosidodecahedral radial expansion, linking it to icosahedral symmetry breaking. | MATH: Rhombic dodecahedron = Voronoi cell of FCC lattice (coordination number 12, packing density π/(3√2) ≈ 0.7405). Its 12 rhombic faces have diagonals in ratio √2:1 (not golden). However, the *golden rhombus* (diagonals in ratio φ:1, φ = (1+√5)/2 ≈ 1.618) forms the rhombic triacontahedron, not the dodecahedron. The icosidodecahedron has 30 vertices, 20 triangles, 12 pentagons; its radial expansion to a rhombic dodecahedron of icosidodecahedra implies a lattice with icosahedral point group (I_h, order 120) — a *quasicrystalline* precursor. The golden ratio appears in the icosidodecahedron's edge-to-circumradius ratio: edge = 2R sin(π/5) = R·√(2−2/φ) ≈ 0.618R·√2? Actually: edge = 2R sin(36°) = R·√(2−φ) ≈ 0.618R? No — sin(36°) = √(10−2√5)/4 ≈ 0.5878, so edge ≈ 1.\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"
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  "bibtex": "https://research.draconitic.com/paper/as7brr4hnvx54.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23409581",
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  "id": "as7brr4hnvx54",
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  "landing_url": "https://zenodo.org/records/23409581",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/as7brr4hnvx54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:28Z",
      "native_id": "23409581",
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      "url": "https://zenodo.org/records/23409581"
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  "subjects": [],
  "title": "Golden Rhombus and Rhombic Dodecahedron: FCC Voronoi Cells and Icosahedral Symmetry Breaking — E8 Intelligence Research",
  "title_text": "Golden Rhombus and Rhombic Dodecahedron: FCC Voronoi Cells and Icosahedral Symmetry Breaking — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:28Z",
  "url": "https://research.draconitic.com/paper/as7brr4hnvx54",
  "venue": "Zenodo",
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