Delone lattice studies in C 3, the space of three complex variables

Abstract

The Delone (Selling) scalars, which are used in unit-cell reduction and in lattice-type determination, are studied in C 3, the space of three complex variables. The three complex coordinate planes are composed of the six Delone scalars. The transformations at boundaries of the Selling-reduced orthant are described as matrices of operators. A graphical representation as the projections onto the three coordinates is described. Note, in his later publications, Boris Delaunay used the Russian version of his surname, Delone.