Graphic representation and nomenclature of the four-dimensional crystal classes. I. Classes with symmetry operations of order not greater than two

Hyperstereographic projections have been prepared (in the form of stereo-pairs) of the sixteen four-dimensional (geometric) crystal classes that contain only symmetry operations of order not greater than 2. These provide an initial demonstration of the usefulness of the hyperstereographic projection in visualizing the nature of four-dimensional symmetry elements and symmetry groups. The clarification thus introduced into the subject has suggested a rationalized system of symbolic nomenclature following the general principles of the Hermann-Mauguin notation.