Point configuration

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The concept of point configuration is closely related to that of crystallographic orbit, but differs from it by the fact that point configurations are detached from their generating space groups. The concept of point configuration is the basis for the definition of lattice complexes.

Two crystallographic orbits are said configuration-equivalent if and only if their sets of points are identical. A point configuration is the set of all points that is common to a class of configuration-equivalent crystallographic orbits.

This definition uniquely assigns crystallographic orbits to point configurations but not vice versa.

The inherent symmetry of a point configuration is the most comprehensive space group that maps the point configuration onto itself. One crystallographic orbit out of each class of configuration-equivalent ones stands out because its generating space group coincides with the inherent symmetry of its point configuration.