E8 Decomposition into 600-Cell Roots and A4 Flavor Symmetry Limits — E8 Intelligence Research

FINDING: E8 root system decomposes under A4×A4 into 120 roots, with the 120-vertex structure of the 600-cell (icosahedral hyper-shell) and golden-ratio-derived coordinates; A4 flavor symmetry in neutrino physics fails to produce viable dimension-5 mass operators. | MATH: E8 has 240 roots; under A4×A4 (each A4 has 20 roots, 5D hyper-tetrahedral), the decomposition yields 120+120 = 240. The 120 roots of one A4×A4 block correspond to the 120 vertices of the 600-cell (4D polytope), whose coordinates involve φ = (1+√5)/2 = 1.618 and 1/φ = 0.618. The 600-cell has 120 icosahedral cells; its vertex figure is an icosahedron. The golden ratio appears in the 600-cell's edge length ratio: edge = 1, circumradius = φ, inradius = φ²/2. The Coxeter-Dynkin diagram for E8 has the A4×A4 sub-diagram (two A4 chains) linked by a single edge, with the Coxeter number h=30, and the ratio of root lengths squared = 2 (simply-laced). | CONNECTION: The 600-cell's 120 vertices split into 24-cell (24 vertices) + 96 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com