{
  "abstract": "FINDING: The Voronoi/Delone cells of the A_n root lattice project to rhombus and equilateral triangle prototiles, unifying hexagonal tiling geometry with higher-dimensional lattice structure. | MATH: A_n root lattice: {x ∈ ℤ^(n+1) : Σx_i = 0}; Voronoi cell facets are rhombuses (angles 60°/120°); Delone cell facets are equilateral triangles; orthogonal projection yields 2D tilings with rhombus:triangle area ratio = √3 : 1 (or 1 : √3); hexagonal tiling emerges as A_2 Voronoi cell (regular hexagon, side s, area = (3√3/2)s²). | CONNECTION: Direct crystallographic link — A_2 is the hexagonal lattice; its Voronoi cell is the regular hexagon (angles 120°, dihedral symmetry D_6). The rhombus prototile has diagonals in ratio √3:1, related to 1.732, not directly to 0.618/1.618, but the hexagonal packing density π/(3√3) ≈ 0.6046 (not golden). However, the A_n family connects to E_8 (via A_8 ⊂ E_8) and to the Leech lattice via A_24 — deep lattice hierarchy. | DEPTH: 8 — This is a rigorous geometri\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/466nk2x3jq19c.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23410003",
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  "id": "466nk2x3jq19c",
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  "landing_url": "https://zenodo.org/records/23410003",
  "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/466nk2x3jq19c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:23Z",
      "native_id": "23410003",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23410003"
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  "subjects": [],
  "title": "A_n Lattice Projections Unify Rhombus and Triangle Tilings via Voronoi-Delone Cells — E8 Intelligence Research",
  "title_text": "A_n Lattice Projections Unify Rhombus and Triangle Tilings via Voronoi-Delone Cells — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:20Z",
  "url": "https://research.draconitic.com/paper/466nk2x3jq19c",
  "venue": "Zenodo",
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}