Standard atomic physics treats electrons as point particles orbiting a nucleus. This paper reframes the atom without particles — electrons are eigenmode occupancies of the Coulomb operator on the 600-cell, not localised objects. The periodic table emerges as different concentrations of light in different eigenmode configurations. The paper builds a complete 17-section treatment with 50 display equations, deriving atomic structure from the same spectral geometry that produces the fine structure constant and nuclear masses. The title's subtitle — 'The Elements Are Different Concentrations of Light' — is the central claim: matter is not made of particles. It is made of standing waves in a self-referential field.