Biomedical subjects
Publications and source records attributed to Olaf Delgado-Friedrichs.
28 three-periodic nets with two kinds of vertex and one kind of edge are identified. Some of their crystallographic properties and their natural tilings are described. Restrictions on site symmetry and coordination number of such nets are discussed and examples of their occurrence in crystal structures are given.
Some properties of an exceptional simple tiling by fullerenes, first described by Deza & Shtogrin [Southeast Asian Math. Soc. Bull. (1999), 23, 1-11], are presented.
All isohedral simple tilings of 3D Euclidian space by tiles with </=16 faces have been determined. There are no such tilings by polyhedra with less than 14 faces. For simple polyhedra with 14, 15 and 16 faces, there are respectively 10, 65 and 434 that fill space and a total of 23, 136 and 710 distinct tilings. The tilings by 14-face polyhedra are described in detail as are binodal (vertex 2-transitive) isohedral simple tilings.
The structures of all 1127 three-periodic extended metal-organic frameworks (MOFs) reported in the Cambridge Structure Database have been analyzed, and their underlying topology has been determined. It is remarkable that among the almost infinite number of net topologies that are available for MOFs to adopt, only a handful of nets are actually observed. The discovery of this inversion between expected and observed nets led us to deduce a system of classification "taxonomy" for interpreting and rationalizing known MOF structures, as well as those that will be made in future. The origin of this inversion is attributed to the different modes with which MOF synthesis has been approached. Specifically, three levels of complexity are defined that embody rules "grammar" for the design of MOFs and other extended structures. This system accounts for the present proliferation of MOF structures of high symmetry nets, but more importantly, it provides the basis for designing a building block that "codes" for a specific structure and, indeed, only that structure.
The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. (1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube into smaller tiles without introducing new vertices. Duals of such tilings with one vertex in the primitive cell have nets that are one of the minimal nets. Minimal nets without collisions are uniform.
Exact methods are presented to determine whether two periodic nets are combinatorially isomorphic and to compute the full combinatorial symmetry group of a net. It is found that for a large class of nets, which includes all known zeolite nets and most other known crystal nets, this group can be realized as a crystallographic space group.