A parsimonious structural model of the four forms of suicide -- egoism, altruism, anomie, and fatalism -- defined in Durkheim's Suicide is developed. The model explicitly defines the structural position of each form of suicide by focusing on duality of social structure, while retaining an analytic distinction between social integration and normative regulation. A payoff from this approach is that fatalism and anomie are interpreted in the same framework as altruism and egoism. The result is a consistent account of the four forms of suicide that is faithful to Durkheim's intentions to account for the aggregate suicide rate without recourse to the motivations of actors.