The E₈ root system decomposes into two 600-cells sharing a common D₄ substructure. Each nucleon species fills one 600-cell. The D₄ bridge is the strong proton–neutron coupling. All seven observed magic numbers drop out; the eighth is predicted at 184.
E₈ contains 240 root vectors. They decompose as two copies of the 600-cell (120 vertices each) sharing a common D₄ substructure of 24 roots. This paper identifies that decomposition with the atom: all Z protons share one copy, all N neutrons the other, lying in orthogonal four-dimensional subspaces of ℝ⁸. The D₄ bridge is the strong coupling between them. The electron is a standing wave at the Galois boundary of ℚ(√5) inside each cell.