Gaps in Direct Sources on H3 Golden Ratio Root Coordinates — E8 Intelligence Research

FINDING: The search results are primarily pedagogical videos and one abstract on involution products in Coxeter groups — none directly address the H3 golden ratio root system coordinates, though the topic is implicitly central to the geometry of icosahedral symmetry. MATH: - Coxeter group H3 (icosahedral symmetry) has order 120, generated by reflections with relations: \( s_1^2 = s_2^2 = s_3^2 = (s_1 s_2)^5 = (s_2 s_3)^3 = (s_1 s_3)^2 = 1 \) - H3 root system coordinates (in \(R^3\)) involve the golden ratio \(φ = (1+√5)/2 ≈ 1.618\) and its inverse \(φ⁻¹ = φ - 1 ≈ 0.618\). Example roots (normalized): \((0, ± 1, ± φ)\), \((± 1, ± φ, 0)\), \((± φ, 0, ± 1)\) — 30 roots total. - The abstract (arXiv:1405.3051) proves for finite Coxeter groups \(W = W\) (all elements are products of two involutions) and defines a minimal length invariant \((x)+(y)-(w)\) — but gives no speci Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com