A general type of symmetry axes that involves a rotation followed by an inversion operation, with a repeating set of rotation/inversion operations until “closure” (returning to the starting position in the rotation/inversion or repetition process) is reached. The one-fold rotoinversion axis (͞1) is equivalent to a center of symmetry, and the two-fold rotoinversion axis (͞2) corresponds to a mirror plane; only the latter are used, respectively. In addition, the ͞3 implies that the object possesses a center of symmetry and a 3-fold axis and a ͞6 is equivalent to a 3-fold and a mirror plane perpendicular to it. Thus, only the ͞4 is a unique symmetry operation.
Cf., symmetry