Topological Methods and Tools for the Analysis of Big Crystallographic Data

We briefly overview mathematical models, methods and computer tools for the topological description, analysis and classification of crystal structures. We present ToposPro, a program package for comprehensive geometrical and topological analysis of periodic architectures of any composition and complexity. ToposPro is designed for the automated analysis of big crystallographic data, which are either collected in the world-wide electronic databases or generated by theoretical methods. ToposPro was used to create a system of topological databases, which are available both in the local version and as a number of interactive web-services integrated into the TopCryst system. All described topological tools are considered as applied to solving typical tasks of crystal chemistry and materials science.