Crystallography, geometry and physics in higher dimensions. III. Geometrical symbols for the 227 crystallographic point groups in four-dimensional space

A geometrical 'WPV' notation for crystallographic point symmetry groups (PSG) in four-dimensional space is proposed. This simple notation generalizes the Hermann-Mauguin notation and makes it possible to retrieve the PSG elements easily. Tables classifying all elements of each PSG for systems 1 to 28 are presented. For higher systems, from 29 up to 33 inclusive, the results of the work are not reported owing to the space required, but they are at the disposal of the reader upon request.