The Size of the Universe from Icosahedral Geometry: N = e^(6π³) × (6/41) = 10^79.96 Baryons
Abstract
We derive the baryon count of the observable universe from icosahedral geometry alone. The lattice capacity e^(6π³) = 10^80.80, multiplied by the crystallization efficiency 6/41 (where 6 = D! and 41 = (V−1) + E from Klein's icosahedral modes), gives N = 10^79.96. This matches the observed 10^79.95 baryons to within 2% — with zero free parameters. The crystallization efficiency 6/41 is derived entirely from icosahedral geometry: • 6 = D! = 3! (dimensional factorial) • 41 = (V−1) + E = 11 + 30 (Klein's locally accessible modes) • This same factor appears in glass physics as the structural arrest threshold The Schwarzschild radius for the derived mass approximately equals the observable radius, implying gravitational self-closure. The central prediction is falsifiable: the observable universe IS the total universe — there is nothing beyond the cosmic horizon except topological images of the same structures. Key result: N = e^(6π³) × (6/41) = 10^79.96 matches observation to 2%.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Cosmology and Gravitation Theories
Relativity and Gravitational Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 29 January 2026
- Document type
- Preprint