Caspar-Klug Theory: Icosahedral Symmetry and T-Number Geometry in Viral Capsids — E8 Intelligence Research

FINDING: Icosahedral symmetry dominates viral capsid architecture, with structural proteins arranged in pentameric and hexameric clusters (T-number theory). | MATH: Caspar-Klug theory: T = h² + hk + k², where (h,k) are integers (e.g., T=1,3,4,7,9,12,13,16...). Icosahedral rotation group order = 60. Pentamers (5-fold) + hexamers (6-fold) = 12 pentamers + 10(T-1) hexamers. Key ratio: 12/60 = 0.2 (1/5). | CONNECTION: T-numbers correspond to discrete lattice points on a hexagonal net, linking to 0.618 (golden ratio) via pentagon geometry: diagonal/side = φ = (1+√5)/2 ≈ 1.618. Icosahedron vertices define 3 orthogonal golden rectangles (ratio 1:φ). | DEPTH: 8 — Caspar-Klug theory is a foundational geometric classification, directly linking viral evolution to crystallographic constraints and Fibonacci-like packing. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com