Abstract Knowledge of the atomic structure is a basis to characterize and understand the properties of a material. However, automatic solution ( e.g ., by direct methods) of thousands of crystal structures, which span any type of materials, must not lead to the conclusion that unconventional methods for solving crystal structures belong now to the past. In fact, besides direct-methods-resistant structures, numberless “crystalline” materials exist whose crystal structure cannot be obtained by standard automatic methods because suitable diffraction intensities are not available: e.g ., poorly crystalline or microcrystalline materials and “non-classical crystals”, as modulated and composite crystals and quasi crystals (Yamamoto, 1996). The problem is particularly stringent in materials science, including minerals, where it is often mandatory to characterize a specific material and the by-pass of using derivatives or related materials might not be practicable. To be noted that the growing possibility of obtaining powder diffraction patterns of high quality is paralleled by a variety of efforts aiming at finding methods able to extract structural information from the unidimensional data of these patterns [ cf., e.g ., Artioli et al . (1997) and Ferraris & Pavese (1997)]. Modern structural classifications of a large number of inorganic structures [ e.g ., Liebau (1985) and Lima-de-Faria (1994)] reveal recurring features which can be exploited for modelling unknown structures. Theories involving these features, as in the case of polysomatic (Thompson, 1978; Veblen, 1991; Zvyagin, 1993, 1997) and homologous series (Makovicky, 1997) are of particular interest. The theory of polysomatism, which in its turn has been indicated as a basis of classification (Ferraris et al ., 1986),

Abstract The concept of polysomatism developed in the ’70s with the fundamental work by Thompson (1970, 1978) on biopyriboles. Since then, this concept proved to be of invaluable help in the description – sometimes in the prediction – of relevant crystal chemical features in several mineralogical families. In what follows we shall illustrate, as examples, two polysomatic families of silicate minerals, the former displaying in addition extensive polytypic features. These families are the polysomatic series existing between pyroxene and spinel, and the polysomatic series of lintisite. Our choice depends on two main reasons: the former is related to the didactics: the aim is to present polysomatic families having different characteristics. Therefore we shall first discuss the pyroxene–spinel family, in which there exist two building blocks only and the various polysomes arise from different ratio between them, and from different sequences; then we shall discuss the lintisite family, which are based on three distinct building blocks, which can link between each other in pairs or individually. the second – more practical – reason is related to the fact that the crystallographic team at the University of Pisa has been concerned with the polytypic and polysomatic features of both the pyroxene-spinel and the lintisite families since a long time. Finally, we shall briefly describe the relationship between shattuckite and planchéite, two copper silicates. These minerals can be considered as two members of a possible polysomatic family which should have striking resemblance with the famed family of biopyriboles.