CRYSTALLOGRAPHY, GEOMETRY AND PHYSICS IN HIGHER DIMENSIONS .15. REDUCIBLE CRYSTAL FAMILIES OF 6-DIMENSIONAL SPACE

This paper and the following one of the series deal with the counting and the construction of the crystal families of Euclidean space E(6); this paper deals with the geometrically Z-reducible (gZ-red.) crystal families and paper XVI deals with the geometrically Z-irreducible (gZ- irr.) crystal familes. The method explained in previous papers for the construction of crystal families of Euclidean space E(5) has been ado pted; for the reader's convenience, the main lines of this method are recalled. The method depends on two basic elements, namely, all the sp littings of space E(6) into two-by-two orthogonal subspaces and the li st of the gZ-irr. crystal families of one- to five-dimensional spaces. Besides the counting of the crystal families, this new geometrical me thod gives the names of these families and both the symbols and orders of their holohedries. The name of the crystal family directly introdu ces its 'conventional' -cell geometrical description and the various p arameters (lengths and angles) defining the cell.