What question did this study set out to answer?

This research aims to derive all Standard Model particle masses using the geometry of Platonic solids.

February 28, 2026Open Access

Geometry of Sound: Platonic Solids as the Origin of Particle Masses (v2.0)

Key Points

This research aims to derive all Standard Model particle masses using the geometry of Platonic solids.
Developed a zero-parameter model for particle masses using Platonic solids.
Calculated G-factors from geometric properties such as faces, vertices, and edges.
Introduced exact algebraic identities and relations for particle mass predictions.
Included a prediction for dark matter and muon g-2 anomaly.
Validated findings with several testable predictions.
Derived all 15 Standard Model particle masses with high accuracy.
Predicted a dark matter mass of 123 GeV and W boson mass of 80.376 GeV.
Report on the muon g-2 anomaly with a prediction of Δa_μ = 2.481×10⁻⁹.
Demonstrated 27+ exact algebraic identities.
Established new geometric origins for scale levels N = {8,9,10,11,14}.

Abstract

A zero-parameter model deriving all 15 Standard Model particle masses from the geometry of five Platonic solids. The mass formula mᵢ = mPlanck × αN × Gᵢ uses the fine structure constant expressed through π and φ, scale levels N as Platonic combinatorial numbers, and geometric G-factors from faces, vertices, edges, dihedral angles, and vertex defects. Version 2. 0 includes: - All 15 G-factors (13 exact, 2 within 0. 01%) - 27+ exact algebraic identities - Closed W, u, ν₂, ν₃ algebra with Pythagorean relation - Koide formula explained as FTet/ETet = 2/3 - Muon g-2 prediction: Δa_μ = 2. 481×10⁻⁹ (0. 37%) - Dark matter prediction: 123 GeV - Radiative corrections (all σ < 3) - W boson mass: 80. 376 GeV (PDG σ = 0) - 7 mixing angles (PMNS + CKM) - 5 cosmological parameters (Ωₜotal = 1 exact) - Gauge coupling mirror symmetry - NEW: 7 nested Merkabas in Flower of Life - NEW: Scale level identities (9×10=90=ΣE, 8×11=88 in α) - NEW: Geometric origin of N = 8, 9, 10, 11, 14 - 9 testable predictions Previous version: DOI 10. 5281/zenodo. 18764285

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Yuriy S. Vinogradov

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Geometry of Sound: Platonic Solids as the Origin of Particle Masses (v2.0)

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