BFIP: an online tool to calculate the best fitted idealized polyhedron

Distortion of polyhedra is frequently used in the structure–property analysis of inorganic materials. The commonly used Baur distortion index (BDI) loses efficacy in dealing with equi-length polyhedra. This work provides an online calculator to characterize the polyhedral distortion on the basis of the best fitted idealized polyhedron (BFIP) method. This method can determine any subtle change between distorted and corresponding idealized polyhedra. It works by fitting an idealized oriented polyhedron of user-selected type to a collection of center and vertex coordinates on an orthonormal basis. The input only needs the coordinates of the center and ligand atoms. It can be accessed at http://bfip.crystalstructure.cn. The function is demonstrated using a distorted MgO₆ octahedron. Examples of the application and comparison with the BDI are given, including a tetrahedron, octahedron, eight-vertex triangular dodecahedron/cube and cuboctahedron.