Which polyhedron is closest and how distorted is it?

What is it about?

Crystal structures, i.e. three-dimensional repetitive arrangements of atoms and molecules, are regularly described in terms of polyhedra, often surrounding certain atoms. These polyhedral can be of high symmetry, however, are frequently distorted to a certain extend. Identification of such polyhedra to the closest matching ideal polyhedron and quantification of distortion with respect to different model polyhedra is a persistent difficult problem, particularly for computer programs. The computer program Polynator overcomes most of the inherent problems by fitting the vertices of a model to a selected set of atoms. In contrast to earlier programs, models can be deformable, which allows them to represent a point group or a range of shapes such as the set of all trigonal prisms, rather than a specific, rigid shape such as the equilateral trigonal prism. The program is freely avaliable at https://www.iac.uni-stuttgart.de/en/research/akniewa/downloads/

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Why is it important?

The quantification of distortion of polyhedra enables and simplyfies the analysis of structure distortions of similar compounds and crystal structures, analysis of structural transformations and similar. It can add to a deeper understanding of such processes.