Bottom-up assembly of DNA nanostructures have been proposed for a variety of biotech uses ranging from targeted drug delivery to scaffolding of new materials. Rationally-designed 3D DNA motif units, often based on the tensegrity triangle, provide a wide range of DNA crystallographic assemblies. The sequence design possibilities of these building blocks, together with nucleotide stacking, give ever-increasing geometric complexities to form vast arrays of three-dimensional structures. We show an experimentally verified mathematical model that explains occurrences of diverse chiral topologies within the crystals. We introduce several measures to describe chirality of DNA strands at building block levels and at structural levels in 3D. We also present methods based on periodic graphs and topological graph theory that enable design and analysis of various crystallographic constructs.