Chirality (mathematics) - Chirality in Three Dimensions

Chirality in Three Dimensions

In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral. (A plane of symmetry of a figure is a plane, such that is invariant under the mapping, when is chosen to be the --plane of the coordinate system. A center of symmetry of a figure is a point, such that is invariant under the mapping, when is chosen to be the origin of the coordinate system.) Note, however, that there are achiral figures lacking both plane and center of symmetry. An example is the figure

which is invariant under the orientation reversing isometry and thus achiral, but it has neither plane nor center of symmetry. The figure

also is achiral as the origin is a center of symmetry, but it lacks a plane of symmetry.

Note also that achiral figures can have a center axis.