We show that the structures and phases developed in a variety of polysomatic series, including the biopyroboles, are similar to those predicted by a simple spin model—the Axial Next-Nearest-Neighbour Ising (ANNNI) model in a magnetic field. We argue that the different polysomatic structures can be considered as thermodynamically stable phases, composed of ordered sequences of chemically distinct structural modules. We suggest that the key factors which determine the stability of polysomatic phases are (a) the chemical potential, which controls the proportion of the different structural modules, and (b) the competing interactions between first and second neighbour modules within the structures.