The Fine Structure Constant from First Principles: Feynman's Answer from Icosahedral Geometry

Feynman asked whether the fine structure constant α is "related to pi or perhaps to the base of natural logarithms." We answer: it is e, combined with √3 from Eisenstein geometry, encoded in the icosahedron. The formula α⁻¹ = e⁵ − 6√3 − 1 + 1/(66 + e/93) predicts 137.035999046, which is 0.89σ from CODATA 2018 (137.035999084 ± 0.000000021) — within experimental uncertainty. Every term derives directly from icosahedral geometry (V=12 vertices, D=3 dimensions): e⁵ from exponential closure, 6√3 = D!×√D from Eisenstein structure, 66 = (V−1)×D! and 93 = 66 + D³. No fitting, no free parameters — pure geometric necessity. The same scaffold yields the Euler-Mascheroni constant γ to 66 digits, confirming that physics is built from number theory.