Crystallographers, chemists and physicists understand crystal structures primarily as geometrical arrangements of atoms in space. Each group of atoms represents an inherent closed unit, not only of molecules, but also of crystal structures. Quantum chemical approaches like LCAO can only therefore be an approximation to the truth. Andersson and Jacob have developed a relatively simple and easily understood method for the formulation of analytical mathematical expressions representing the complete arrangement of crystal structures. This book represents a new collection of topological structure relationships, which reveal an unexpected and aesthetic insight into the forms of topologies and their interdependence. The reader will discover numerous possibilities for further progress and creation, also for his own purposes, e.g. for topological transformations of phase transitions, reactions and interfaces. These transformations offer a wide range of possible investigations with this new approach.

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