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The crystallographic point groups of the four-dimensional Euclidean space {\bb E}4 are a convenient means of studying some crystallized solids of physical space, for instance the groups of magnetic structures and the groups of mono-incommensurate structures, as is demonstrated by a simple example. The concept of polar crystallographic point groups defined here in {\bb E}4, and also in {\bb E}n enables the list and the WPV notation {geometric symbol of Weigel, Phan & Veysseyre [Acta Cryst. (1987), A43, 294-304]} of these special structures to be stated in a more precise way. This paper is especially concerned with the mono-incommensurate structures while a discussion on magnetic structures will be published later.
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