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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),

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