The Quintic Resolution of α: Deriving the Fine Structure Constant from Icosahedral Geometry

We derive the fine structure constant α from icosahedral geometry and Klein's resolution of the quintic equation. The formula α⁻¹ = e⁵ − 2(3√3 − 5) − 11 + 1/66 + (harmonics) emerges from four geometric necessities: (1) e⁵ = e^(E/D!) where E = 30 edges and D! = 6, giving the icosahedral growth exponent, (2) the kissing sphere gap 3√3 − 5 = (three-phase RMS) − (vertex degree), the difference between continuous Eisenstein closure and discrete icosahedral structure, (3) Klein's coefficient 11 = V − 1 from the icosahedral vertex invariant, and (4) the prime wheel modulus 66 = D! × (V − 1) from dimensional and vertex structure. Harmonic corrections built entirely from icosahedral invariants (V = 12, E = 30, F = 20)…