{
  "abstract": "FINDING: Penrose tiling is the 2D cut-and-project shadow of a higher-dimensional lattice; its 3D analogue is the icosahedral quasicrystal, both generated by the same projection formalism. | MATH: Kite/dart inflation ratio φ = (1+√5)/2 = 1.6180339...; vertex configurations from de Bruijn pentagrid (5 families of parallel lines, indices k ∈ ℤ, sum of grid coordinates = 0 or 1); cut-and-project: E₈ (or ℤ⁵ ⊂ ℝ⁵) → ℝ² via irrational 2-plane with slope φ; acceptance window = projection of unit hypercube. | CONNECTION: φ = 1.618, φ² = 2.618, 1/φ = 0.618, 1/φ² = 0.382 — all present as tile edge ratios and inflation eigenvalues. Icosahedral symmetry = H₃/H₄ Coxeter group; H₄ is the symmetry of the 600-cell whose vertices are the 120 icosians (unit quaternions), the binary icosahedral group 2I ⊂ unit quaternions. | DEPTH: 9\n\nFINDING: The icosian ring (Hurwitz quaternions) provides the exact algebraic coordinates for the 3D icosahedral quasicrystal — the same structure that underlies E₈ via the i\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/0m3w24qeabf3t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658835",
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  "id": "0m3w24qeabf3t",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0m3w24qeabf3t.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:31Z",
      "native_id": "23658835",
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      "url": "https://zenodo.org/records/23658835"
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  ],
  "subjects": [],
  "title": "Penrose Tiling and Icosahedral Quasicrystal as Cut-and-Project Shadows — E8 Intelligence Research",
  "title_text": "Penrose Tiling and Icosahedral Quasicrystal as Cut-and-Project Shadows — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:31Z",
  "url": "https://research.draconitic.com/paper/0m3w24qeabf3t",
  "venue": "Zenodo",
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}