A MATHEMATICAL-ANALYSIS OF ROD PACKINGS

Crystal structures in which atoms, molecules, or coordination polyhedra are repeated along infinite nonintersecting lines can easily be explained in terms of rod packings. A mathematical analysis of rod packings that are constructed from braids of slanting rods around a central, vertical rod, possessing three- or fourfold symmetry, is presented. The radius relation between the two types of rods and the density of the rod packing is determined by the elevation angle of the slanting rods and by the symmetry of repetition of the braid. The derived rod packings can be transferred into lower symmetry cases by asymmetric modulation of the rod radii, and by tilting the vertical rods. More complex packings can be created by using the same method of construction, and as an example, the sixfold braid rod packing is given. (C) 1995 Academic Press, Inc.