Point reflection

A point reflection, also called a point inversion or central inversion, is a geometric transformation that reflects every point in a space through one fixed center point, so that the center becomes the midpoint between each original point and its image; for a point a reflected through a center p, the image is 2p minus a. In a Euclidean space a point reflection preserves distance and so is an isometry. In two dimensions it is equivalent to a rotation by 180 degrees, while in three dimensions it combines a 180 degree rotation with a reflection across a plane perpendicular to the rotation axis. Applying a point reflection twice returns every point to its original position, and in even-dimensional spaces the transformation preserves orientation while in odd-dimensional spaces it reverses it. Objects with point symmetry, called centrosymmetric objects, look identical after the transformation, a property with real significance in crystallography and molecular chemistry, where it affects properties such as a molecule's dipole moment and how it interacts with light.