Homometrische kubische Punktkonfigurationen

Abstract

AbstractWith the aid of an extension of Buerger's concept of complementary point sets it is possible to derive point configurations which are homometric, i.e., have the same self-image and diffraction pattern, though they are neither congruent nor enantiomorphic. Homometric point configurations of the cubic space group types have been determined. The significance of the combination of congruent, enantiomorphic and homometric point configurations, as well as multiple lattices, for the construction of homometric structures is discussed. Combinations of certain point configurations yield homometric quadruplets.