Wyckoff positions used for the classification of Bravais classes of modulated crystals

Wyckoff positions of centrosymmetric symmorphic space groups, if properly interpreted, can be used to derive the Bravais classes of modulated crystals. This program is worked out here for the incommensurate case and assuming that the modulation wave vectors are symmetry related, i.e. are (integral combinations of) vectors of one star. The corresponding classes are called elementary Bravais classes (EBC's). It is shown that for three-dimensional crystals the maximal internal dimension for these EBC's is nine. It is explained in what sense this approach leads to a complete list.