The Icosahedral Origin of the Fine Structure Constant

We derive the fine structure constant from icosahedral geometry. The formula α⁻¹ = e⁵ − 6√3 − 1 + 1/66 − (2 − 1/(e²√3))/66³ − (e² − 3 − (e² − 1)/(66e))/66⁵ achieves 0.05σ agreement with CODATA 2018 — effectively exact — using only the mathematical constants e and 3. The modulus 66 = D! × (V−1), where D = 3 (dimensions) and V = 12 (icosahedron vertices), is the same wheel modulus that governs prime distribution. The power 5 arises because 5 faces meet at each icosahedron vertex — the same 5 whose square 25 = 5² terminates the fermion generations at three. This suggests a deep connection between number theory and fundamental physics through icosahedral geometry.