the glide plane

Look at a line of footprints left in wet sand: left foot, step forward, right foot (a mirror image of the left), step forward, and on it goes. Neither a pure mirror nor a pure step alone reproduces the trail — you need BOTH, a reflection followed by a slide. A glide plane is that move made into a crystal symmetry: reflect the pattern across a plane, then translate it by half a lattice step in a direction lying IN the plane. Like the screw axis, it is a symmetry that only a translation-repeating crystal can possess; a lone molecule cannot have one.

Glide planes come in named flavours according to which way, and how far, they slide. Axial glides slide by half a cell edge: an a-glide by a/2, a b-glide by b/2, a c-glide by c/2. A diagonal n-glide slides by half a face-diagonal, for example (a+b)/2. The diamond d-glide slides by a quarter of a diagonal, (a+b)/4, and gives diamond its name. Worked example: a c-glide whose mirror is perpendicular to b carries a point (x, y, z) to (x, -y, z+1/2) — flip y, then slide half a cell along c. Do it twice and you get (x, y, z+1), a plain translation by one c, confirming it is a genuine symmetry of the lattice.

Glide planes are the workhorses of low-symmetry crystals. The very common mineral space group Pnma is built almost entirely from an n-glide, a mirror m, and an a-glide. Because the operation hides a fractional translation, it too leaves systematic absences: a c-glide perpendicular to b removes every h0l reflection with l odd. Reading those absences backwards is how a crystallographer spots a glide plane from a diffraction pattern alone.