A fundamental problem arising out of the study of symmetrical point groups can be formulated as follows: Let N points in threedimensional space be connected two and two in every possible way by straight lines: what relations must exist between the lengths of these lines if the points are equivalent members of a symmetrical point group ?

The methods of projection used in crystallography (e.g. the stereographic projection) at once show that the points may be considered to be the images of straight lines or planes. The problem formulated above has therefore a direct application to descriptive crystallography and can in this connexion be stated as follows:

A complex of N planes is determined by the points of intersection of the normals with the surface of a unit sphere, i.e. by their poles. What now must the angular relations between the planes be if all are equivalent, that is to say, belong to one and the same simple form ?