Icosahedral Symmetry Unites Quasicrystals and Viral Capsids via A₅ Group — E8 Intelligence Research

FINDING: Icosahedral symmetry bridges Platonic solids, quasicrystals, and viral capsid self-assembly through shared rotational group structure (A₅ ≅ I), with quasicrystals exhibiting forbidden 5-fold order and capsids exploiting icosahedral geometry for minimal-energy enclosure. MATH: - Icosahedral rotational symmetry group: I ≅ A₅, order 60, with conjugacy classes: identity (1), 12×C₅ (72° rotations), 12×C₅² (144°), 20×C₃ (120°), 15×C₂ (180°). - Quasicrystal diffraction: non-crystallographic 5-fold axes (θ = 72°) violate Bravais lattice constraints; Penrose tiling inflation factor τ = (1+√5)/2 ≈ 1.618, with area ratios τ² = 2.618 and τ⁻¹ = 0.618. - Viral capsid: Caspar–Klug theory — T-number = h² + hk + k² (h,k integers), yielding icosahedral triangulation numbers T = 1, 3, 4, 7, 9, 13, …; capsid radius scales as √T. - Electrostatic core model (arXiv:0808.2204): capsid assembly free energy ΔG = ΔG₀ + (Z²e²)/(8πε₀εr) · (1/R_core − 1/R_capsid), where Z is core charge — equilibr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com