Icosian Units as Quaternionic Generators of the 600-Cell and H₄ Root System — E8 Intelligence Research

FINDING: The 600-cell (hexacosichoron) and its quaternionic construction are directly generated by the 120 icosian units, which encode the H₄ root system scaled by the golden ratio, linking 4D regular polytopes to E₈ and quaternion rotation groups. | MATH: The 600-cell has 120 vertices; these are precisely the unit quaternions of the icosian group (binary icosahedral group, order 120). The H₄ root system has 120 roots, expressible as quaternions: {±1, ±i, ±j, ±k, (±1±i±j±k)/2, and golden-ratio-scaled permutations involving (0, ±1, ±φ) and (±1/2, ±φ/2, ±φ⁻¹/2) with φ = (1+√5)/2 ≈ 1.618}. The snub 24-cell, derived from E₈ via quaternionic projection, has symmetry group W(D₄):C₃ of order 576, and its vertices are unit quaternions from the icosian representation of E₈. Key constants: φ = 1.618, φ⁻¹ = 0.618, φ² = 2.618. | CONNECTION: Direct geometric harmony — the golden ratio φ appears explicitly in the coordinates of the 600-cell vertices. The 600-cell's symmetry group H₄ has order 14400 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com