A physically based system of interacting polyhedral objects is used to model self-assembly and spontaneous organization of complex structures. The surfaces of the polyhedra in the simulation are covered with bonding sites in states akin to those of cellular automata. The bonding sites interact with sites on neighbouring polyhedra to apply forces of attraction and repulsion between bodies and to trigger transitions in their states. Using only these mechanisms, the elements exhibit chaining, membrane and cluster formation, and differentiation / segregation. Examples of each of these phenomena are given along with explanations as to how they are formed. Assembly without the guidance of an external agent or central control is in-frequently used in the construction of complex artificial structures, but is the norm for biological construction. This paper presents a model by which the construction of complex structures may be simulated using multiple reactive, artificial agents, acting independently under artificial physical and chemical laws.