In three dimensions, every figure that possesses a mirror plane of symmetry S, an inversion center of symmetry S, or a higher improper rotation (rotoreflection) S axis 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.
Achiral figures can have a center axis.