Golden Ratio and Coxeter Group H₃ in Icosahedral Quasicrystal Diffraction — E8 Intelligence Research

FINDING: Quasicrystal diffraction patterns exhibit icosahedral point group symmetry and irrational, aperiodic order, linked to Coxeter group H₃ and golden ratio eigenvalues. | MATH: Icosahedral point group symmetry (H₃ Coxeter group); golden ratio φ = (1+√5)/2 ≈ 1.618; its reciprocal φ⁻¹ ≈ 0.618; eigenvalues of H₃ Coxeter element involve φ and its algebraic conjugates. | CONNECTION: Golden ratio φ and its reciprocal 0.618 are central to H₃ root system and quasicrystal diffraction indices; the irrationality of φ enforces aperiodic order; the diffraction series follows hierarchical scaling by φ. | DEPTH: 8 — Directly ties number theory (golden ratio, irrationality) to crystallographic symmetry (H₃ Coxeter group) and physical quasicrystal diffraction, revealing a deep geometric-harmonic structure in matter. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com