{
  "abstract": "FINDING: The icosahedron's dihedral angle is arccot(1/φ²) — derivable from its golden-ratio-based vertex coordinates and face normals. | MATH: For a regular icosahedron with edge length 2 and vertices (±1, ±φ, 0), (0, ±1, ±φ), (±φ, 0, ±1) where φ = (1+√5)/2 ≈ 1.618. Dihedral angle δ satisfies cos(δ) = −(1/φ²) / √(1 + 1/φ⁴) — equivalently δ = arccos(−1/√5) ≈ 138.19°. The tangent of the supplementary angle (π − δ) = 1/φ² ≈ 0.382. | CONNECTION: Direct golden ratio link: 1/φ² = 2 − φ = (3−√5)/2 ≈ 0.382 (the \"small\" golden section). The icosahedral group (order 120) is isomorphic to A₅ × C₂, and its root system H₃ contains 15 pairs of opposite vertices — all coordinates are φ‑linear combinations of the standard basis. The dihedral angle's complement (41.81°) relates to the central angle of the pentagon (72°) via 72° − 30.19° — but the cleanest link is δ/2 ≈ 69.095°, whose cosine = 1/√(2φ+3) — a crystallographic‑forbidden angle (no 5‑fold symmetry in periodic lattices, but allowed in quasicr\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
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  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/dqepqcbgd946n.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587214",
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  "id": "dqepqcbgd946n",
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  "published": "2026-10-23",
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  "ris": "https://research.draconitic.com/paper/dqepqcbgd946n.ris",
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      "first_seen": "2026-11-06T12:21:50Z",
      "native_id": "23587214",
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  "title": "Golden Ratio Encodes the Icosahedron's Dihedral Angle — E8 Intelligence Research",
  "title_text": "Golden Ratio Encodes the Icosahedron's Dihedral Angle — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:50Z",
  "url": "https://research.draconitic.com/paper/dqepqcbgd946n",
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