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

We present a unified framework for the fine structure constant α from icosahedral geometry that explains both CODATA 2018 and CODATA 2022 values as complementary geometric perspectives. A base formula α⁻¹ = e⁵ − 6√3 − 1 + 1/66 captures the quintic structure to 50 ppm. Harmonic corrections in powers of 1/66 refine this to parts-per-trillion accuracy, with vertex-centred corrections matching CODATA 2018 (475 ppt) and face-centred corrections matching CODATA 2022 (5 ppt). The closure equation π/α = 3[12² − ½ + 3(V−1)α/2⁶] is shown to be the 11:5 weighted average of vertex and face values. Crucially, we identify the physical mechanism: the proton IS the vertex perspective (inside the hyperfactorial 108, with 12 divisor channels), while the electron IS the face perspective (outside 108, with 36 coprime channels). Atom recoil measurements probe α through the proton and see vertex α; electron g−2 measurements probe α through the electron and see face α. The ~93 ppb discrepancy between CODATA releases is not experimental error—it is the geometric difference between proton and electron perspectives on the same underlying structure.