Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. I. Crystal families in five-dimensional space with two-, three-, four- and sixfold symmetries

The Weigel-Phan-Veysseyre symbols are explained and their properties are described. These symbols are then assigned to the point groups of several families of space E⁵.

Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. II. Cubic families in five- and n-dimensional spaces

The definition, properties and symbols of the iso cubic groups are given. The mono cubic crystal families of space Eⁿ are defined and listed for n = 3 to n = 7. As an application, four crystal families of space E⁵ are studied in detail.