What is Centrosymmetry?

The formalization of centrosymmetry emerged alongside the development of transformation geometry. It became a cornerstone of crystallography in the 19th and 20th centuries as scientists mapped the internal structures of minerals.

The inversion center is found in all parallelograms, including squares and rhombi. In chemistry, many molecules possess an inversion center, which dictates their spectroscopic properties.

A figure is centrosymmetric if it possesses a center of inversion. Formally, for every point P in the figure, there exists a point P' such that the center of symmetry is the midpoint of the line segment PP'.

In physics, centrosymmetry determines whether a material can exhibit certain properties, such as the piezoelectric effect or second-harmonic generation. If a crystal is centrosymmetric, these effects are typically forbidden.

The operation is defined by the mapping r → -r. If the set of points defining the object remains invariant under this inversion, the object is centrosymmetric. This is distinct from reflectional symmetry across a plane.