Bravais classes, Voronoï cells, Delone symbols

Michel, Louis



This text correspond to a set of lectures given at Third international school at Zajaceskowo (Poznan) Polane on Symmetry and structural Properties of condensed matter

Abstract : We give the most refined intrinsic classification of three dimensional Euclidean lattices by combining the 14 Bravais classes, the 5 combinatorial types of Voronoï cells and the 24 Delone symbols. After recalling the fondamental concepts of group actions, we define Bravais classes and Voronoï celles in arbitrary dimension. We are quite explicit for the application to two and three dimensions.




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MICHEL, “Bravais classes, Voronoï cells, Delone symbols,” Archives de l'IHES, consulté le 22 juin 2024,