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On the metrical properties of lattices. (English) Zbl 1239.11074
Summary: It is shown that the Delaunay reduction procedure is a suitable tool for the simple derivation of the conventional unit cell for any crystal lattice. In cases with orthorhombic and monoclinic symmetry additional standardization conventions must be applied. Triclinic lattices need special treatment. All lattices with symmetry higher than monoclinic were embedded into the monoclinic case. The relations are described in terms of the standardized conventional parameters. The comparison between the Niggli and the Delaunay classification shows rather low correlation.

MSC:
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
20H15 Other geometric groups, including crystallographic groups
82D25 Statistical mechanics of crystals
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