Empirical modeling study demonstrates derivation of 12 fundamental particle masses from nested Platonic solids, highlighting a potential geometric framework for Standard Model parameters.
Geometry of Sound (GoS) v19 is an empirical geometric model of fundamental particle masses based on five nested Platonic solids. Mass formula: m = m_P * alpha^N * G * R The model reproduces 12 particle masses (6 quarks, 3 charged leptons, W, Z, Higgs) within 1 sigma of PDG 2024. A Monte Carlo test with 50,000,000 random universes gives p < 2e-8 (significance > 20 sigma). This version includes:- New: full 3D visualization of the geometric cascade (Plotly interactive scene)- lepton hierarchy through the golden ratio- equilibrium sphere uniting cube, octahedron, icosahedron, dodecahedron- exact algebraic identities for G-factors- proton and neutron masses- nuclear magic numbers- dark matter invisibility mechanism- color structure of dodecahedron (8 gluon-like fields)- Cabibbo angle formula- cosmological parameters via golden ratio Note on alpha: mass calculations use the rounded value alpha = 1/137.036004. Using the exact CODATA value 1/137.035999084 yields chi2 = 5.32 (difference is negligible, see scripts). The model is empirical and intended as a geometric basis for further theoretical development.
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Yuriy S. Vinogradov (2026) studied this question.
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