centrosymmetri

Centrosymmetry, or centrosymmetri, is a geometric property of objects that have a center of symmetry. A point C is the center if for every point P in the object, the point P’ located on the line through C such that C is the midpoint of PP’ also lies in the object. Equivalently, the object is invariant under a 180-degree rotation about C or under inversion through C.

A wide range of shapes exhibit centrosymmetry. Common examples include circles, ellipses, rectangles, squares, rhombi, and line segments (including their filled interiors). Shapes such as an equilateral triangle typically do not possess a center of symmetry, since a 180-degree rotation around a central point does not map the figure onto itself.

In crystallography and chemistry, centrosymmetry refers to the presence of an inversion center in the structure or molecule. Molecules with a center of inversion have no permanent dipole moment, and bulk centrosymmetric materials generally do not exhibit second-order nonlinear optical effects, such as second-harmonic generation, although higher-order effects may occur. In crystals, centrosymmetric space groups contain an inversion center, which influences vibrational and electronic selection rules.

Centrosymmetry is a form of point symmetry and is related to, yet distinct from, mirror (reflection) symmetry and other rotational symmetries. It provides a useful criterion in geometry, materials science, and spectroscopy for understanding how a shape or structure responds to transformations and how its physical properties manifest under inversion.