Abstract
In a recent paper [Weigel, Phan & Veysseyre (1987). Acta Cryst. A43, 294-304] the 'WPV' notation was proposed for the crystallographic point symmetry groups (PSGs) in four-dimensional space \bb E4. The geometry of crystal families, systems and cells of \bb E4 is illustrated with a few geometrical examples of crystallographic point symmetry operations (PSOs). The cells of the 33 crystal systems in \bb E4 are described and various polytopes are analysed. Some examples of geometry in higher dimensions are explained.
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