Generating triply periodic surfaces from crystal structures: the tiling approach and its application to zeolites

Physical properties of objects depend on topological features of the corresponding triply periodic surfaces; thus topological exploration and classification of the surfaces has practical relevance. A general method is developed for generating triply periodic surfaces from triply periodic crystal structures. A triply periodic surface is derived from the natural tiling of a crystal network by an appropriate removal of some tile faces and subsequent smoothing of the resulting facet surface. The labyrinth nets of a generated triply periodic surface are built from the natural tiling, and in turn the topological parameters of the labyrinth nets are used to determine if the surface is isomorphic to a minimal surface. This method has been applied to all known 253 zeolite frameworks and 98 triply periodic surfaces were obtained, which belong to 55 topological types. Twelve surfaces were found to be isomorphic to already known triply periodic minimal surfaces (TPMSs), while four surfaces can be treated as isomorphic to new TPMSs. A procedure has also been developed for transferring the generated surfaces to a 3D-printer-readable format.