1. Geometric elements

Each symmetry operation of a point group or space group belongs to one of the eight categories in Table 1, column 1. In order to describe these operations, a geometric element (Table 1, column 2) may be assigned to each but the first two. The geometric element is defined as a geometric item that allows the reduced symmetry operation in space to be located and oriented. It does not contain numerical parameters such as a rotation angle or the components of the glide vector of glide reflections (last column). It may, however, be defined much less ambiguously so as to yield almost exactly the entries in the second column, cf. Appendix.

**Table 1:** *Geometric elements of symmetry operations in point groups and space groups*
Symmetry operation	Geometric element	Additional parameters
Identity	Not required	None
Translation	Not required	Vector t
Reflection in plane A	Plane A	None
Glide reflection = reflection in plane A and translation v parallel to A	Plane A	Glide vector v
Rotation about line b	Line b	Angle and sense of rotation
Screw rotation = rotation about line b and translation u parallel to b	Line b	Angle and sense of rotation, screw vector u
Rotoinversion = rotation about line b and inversion through point P on b	Line b and point P on b	Angle (not equal to $\pi$ ) and sense of rotation
Inversion through point P	Point P	None