Golden Ratio Encoded in Icosahedral Capsid Geometry via Caspar-Klug T-Numbers — E8 Intelligence Research
Abstract
FINDING: Icosahedral viral capsid geometry is governed by the Caspar-Klug T-number, which quantizes the surface lattice into pentamer/hexamer clusters, directly encoding the golden ratio in its pentagonal substructure. | MATH: T = h² + hk + k² (h,k ≥ 0 integers); capsid has 60T protein subunits; 12 pentamers + 10(T−1) hexamers; pentamer edge length ratio to hexamer = φ = (1+√5)/2 ≈ 1.618; dihedral angle of icosahedron = 138.19°; the T-number lattice is a triangular tiling on the icosahedral surface, with the 5-fold axes at pentamer centers. The density-wave theory (arXiv:cond-mat/0611623) maps capsid protein positions to spherical harmonics with icosahedral symmetry (l = 6, 10, 12, ...), yielding Landau free-energy minima at specific angular separations. | CONNECTION: The pentagon's diagonal-to-side ratio is φ = 1.618; its inverse φ⁻¹ = 0.618; φ⁻² = 0.382. The T-number lattice vectors (h,k) generate hexagonal tilings whose 5-fold vertices force pentameric defects — a direct crystallogr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
