GlidePlanes

Glide planes are symmetry elements in crystallography that combine reflection in a plane with a fractional translation parallel to that plane. After reflecting a point across the plane, the operation translates the result by a portion of a lattice vector lying in the plane. The translation is commonly a half-lattice vector, and the combined operation is distinct from a pure mirror reflection.

Common types of glide planes are described by letters that indicate the direction of the translational component:

- a-glide: translation by half along the a-axis within the plane of reflection

- b-glide: translation by half along the b-axis

- c-glide: translation by half along the c-axis

- n-glide: translation by half along two in-plane directions, typically represented as a diagonal component (for example, half along both a and b directions)

Glide planes are one of the key symmetry elements used to describe the complete symmetry of a crystal, and they are part of the 230 space groups that classify crystal structures. They often appear together with other elements such as mirror planes, twofold or higher rotational axes, and screw axes, shaping the overall arrangement of atoms in a lattice.

Consequences in crystallography include constraints on atomic positions and systematic absences in X-ray and neutron diffraction, which help determine the space group of a crystal. The presence of a glide plane can enforce relationships between equivalent positions and influence the interpretation of diffraction patterns.

In practice, glide planes are represented in crystallographic notation and discussed within the frameworks of Schoenflies and Hermann–Max conventions. They are essential for accurate structural determination in mineralogy, materials science, and solid-state chemistry.