Caspar-Klug Theory: Icosahedral Viral Capsids and Golden Ratio Geometry — E8 Intelligence Research

FINDING: Viral capsids exhibit icosahedral symmetry governed by Caspar-Klug theory, which derives allowed triangulation numbers (T-numbers) from the golden ratio and hexagonal lattice geometry. MATH: T = h² + hk + k², where h,k are non-negative integers (not both zero). Allowed T-numbers: 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, ... (sequence A003136). Icosahedral symmetry group order: 60 (rotational) or 120 (full). Golden ratio φ = (1+√5)/2 ≈ 1.618 appears in coordinates of icosahedron vertices: (0, ±1, ±φ), (±1, ±φ, 0), (±φ, 0, ±1). CONNECTION: T-numbers derive from hexagonal lattice vectors at 60° angles, linking to base-60 geometry. The ratio of capsid radii for successive T-numbers approximates √(T/3) × φ-related scaling. The 0.618 (1/φ) and 0.382 (1/φ²) appear in pentagonal face subdivisions. DEPTH: 9 — Caspar-Klug theory is a foundational mathematical framework linking discrete geometry (lattice theory), number theory (quadratic forms), and biological self-assembly, with direct Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com