The Fine Structure Constant from Icosahedral Geometry: Vertex, Face, and Holographic Perspectives

The fine structure constant α admits a basic geometric derivation from icosahedral structure: α⁻¹ = e⁵ − 6√3 − 1 + 1/66 = 137.036006, matching CODATA at ~50 ppb relative (≈ 0.05 ppm) with zero free parameters, all integers and operations forced by S³/2I geometry. This basic derivation is the load-bearing structural result of the paper and is offered at STATUS: DERIVED. Harmonic corrections in the icosahedral 1/66 basis can be constructed that match CODATA 2018 (vertex perspective, 2 terms at orders 66³ and 66⁴) and CODATA 2022 (face perspective, 3 terms at orders 66³, 66⁴, 66⁵) to parts-per-trillion precision. The structural basis (powers of 1/66 = 1/(D!×(V−1)) where D = 3, V = 12) is icosahedrally forced. The…