{
  "abstract": "FINDING: Penrose tilings arise as 2D projections of the 5D hypercubic lattice, with vertex configurations encoded by the A4 root system; the search results confirm the tiling's aperiodic fivefold symmetry but the lattice-projection link is implicit in the references, not explicitly derived in the snippets. MATH: Penrose tiling uses two rhombi (angles 36°/144° and 72°/108°), with edge lengths in ratio 1:1 (both rhombi share equal edge length). The inflation factor is the golden ratio φ = (1+√5)/2 ≈ 1.618, and the area ratio of thick to thin rhombus is φ. The vertex configurations in the 2D projection correspond to the 5D hypercubic lattice Z⁵ projected onto a 2D plane perpendicular to the (1,1,1,1,1) direction; the relevant root system is A4 (rank 4, 20 roots, Weyl group order 120). The projection yields a set of 5 basis vectors in 2D at angles 0°, 72°, 144°, 216°, 288° — the pentagonal star. The golden ratio appears as φ = 2cos(36°) = (1+√5)/2, and its inverse φ⁻¹ = φ−1 ≈ 0.618. The\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/ec4h2tfabm00j.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23430986",
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  "id": "ec4h2tfabm00j",
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  "landing_url": "https://zenodo.org/records/23430986",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ec4h2tfabm00j.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:08Z",
      "native_id": "23430986",
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      "url": "https://zenodo.org/records/23430986"
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  "subjects": [],
  "title": "Penrose Tilings as Projections of 5D Lattice via A4 Root System — E8 Intelligence Research",
  "title_text": "Penrose Tilings as Projections of 5D Lattice via A4 Root System — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:08Z",
  "url": "https://research.draconitic.com/paper/ec4h2tfabm00j",
  "venue": "Zenodo",
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