X.The geometry of discrete vector maps

Abstract

The geometry of finite and periodic point sets in S₁ and of their corresponding vector sets in S ₂is discussed. Methods are given for deriving from any S₂ set the complete class of S₁ sets corresponding. The application of these ideas to crystal analysis is indicated. It is shown that by means of this technique X-ray data may be used to discover crystal structures, not merely to test structures already devised.