Abstract
Main aspects of a new division of crystallography based on the concept of polytopes (four-dimensional polyhedrons) are considered. The possibilities of this concept for describing composite crystal structures of intermetallic compounds and the atomic mechanism of polymorphic transformations are discussed. In all the cases studied icosahedral polyhedrons containing fifth-order symmetry axes play a special role. In its turn, this is a manifestation of the role of golden section in the structure of condensed phases.
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