H4 Coxeter Group Generates 600-Cell and 120-Cell via Golden Ratio Quaternions — E8 Intelligence Research

FINDING: Coxeter group H4 generates the 600-cell and 120-cell via quaternion multiplication, encoding golden ratio symmetries in 4D. | MATH: H4 Coxeter group order = 14400; root system contains 120 quaternions; golden ratio φ = (1+√5)/2 ≈ 1.618; φ² = φ+1 ≈ 2.618; 1/φ = φ-1 ≈ 0.618; 1/φ² = 2-φ ≈ 0.382; quaternion norm condition: |q|² = 1 for unit quaternions forming the 600-cell vertices. | CONNECTION: H4 root system vertices are precisely the 120 unit quaternions of the 600-cell, with edge lengths involving φ; the 120-cell (dual) has 600 vertices; both exhibit icosahedral symmetry (H3) as subgroups; ratios 0.618, 1.618, 2.618 appear in edge lengths and dihedral angles; base-60 not explicit but quaternion multiplication is cyclic of order 120 (related to 60° rotations). | DEPTH: 9 — H4 is the largest exceptional finite Coxeter group, directly linking golden ratio to 4D polytopes and quaternion algebra, a foundation for E8 and possible physics models (e.g., 4D spacetime symmetries). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com