The structure classification of crystal point symmetries

The current classification of crystal point symmetries, which dates back to the 1935 edition of the International Tables, is readily updated on the basis of the lattice. The seven lattice point symmetries define the 'crystal systems'. First, for each lattice symmetry, the shape of the conventional cell and the resulting co- ordinate axes are chosen and labelled on metrical considerations. The possible oriented crystal symmetries are then all the subgroups of the lattice symmetry, down to its lowest merohedry, such as the ogdohedry 311 (subgroup of index 8) of the hexagonal lattice (6/m 2/m 2/m) or the tetartohedry 31 of the rhombohedral lattice (2/m). The resulting 44 symmetry symbols are encountered in crystallographic practice. As to the celebrated 32 'crystal classes', which hark back to 1830, they are the only possibilities for wooden crystal models, which obey the Law of Rationality but ignore the orientation of the underlying crystal lattice. Combination of the 44 oriented crystal symmetries with the lattice-centering modes yields 96 oriented representations for the 73 symmorphic space groups.