The spectrum of hadron masses is a mystery that the prevalent theory is unable to elucidate: there are no mass rules. In fact the hadron mass system is linear, with an increment of about 70 MeV/c^2. This rule was anticipated in 1952 already, re-discovered independently by several authors but never made it to the accepted body of knowledge. In 2003 this rule has been reassessed by this author for all the mesons listed by the RPP of the PDG, with evaluation of the statistical significance by Monte Carlo. This analysis confirms the rule with greater precision, and shows that the slightly different values of the mass unit u for the various meson groups defined by quark composition and J^PC are quantized on a u-grid of 12 equal intervals, and their location on the grid is correlated with the quantum numbers. A conjecture about shell-structured hadrons, combined with the meson mass rules, suggests that mesons are geometrically similar to nuclei, while their mass patterns imply solid-phase aggregates on an FCC lattice. The equivalent baryon analysis shows that the baryon masses are quantized with the same basic mass unit and on the same u-grid as the mesons. Baryonic shells grow with a lower increment compared to the mesons, and start only at shell 3 with the nucleon, suggesting that mesons and baryons differ for the lattice arrangement. These mass rules were obtained with a largely automatic analysis of the full hadron spectrum, and are statistically significant beyond doubt. Combined with the shells, they may offer an alternative, simpler interpretation of the structure of hadrons, their constituents, and the nature of the strong interaction.