a Wyckoff position

Imagine a symmetric multi-storey car park where the spaces come in named types: the corner spots, the spots along a wall, the spots out in the open. Any car parked in a 'wall' spot is, by symmetry, in the same kind of place as any other 'wall' spot. A Wyckoff position is exactly this idea for atoms in a crystal: a complete set of points that the space-group symmetry treats as identical, given a label — a letter a, b, c and so on, assigned starting from the highest-symmetry site.

Each Wyckoff position carries three things: a letter, a multiplicity (how many equivalent points it fills in one unit cell), and a site symmetry (the local symmetry an atom there would feel). In space group Fm-3m the position labelled 4a sits at (0, 0, 0) with multiplicity 4 and site symmetry m-3m; the position 4b sits at (1/2, 1/2, 1/2). Rock salt is beautifully compact in this language: put sodium on 4a and chlorine on 4b and the whole NaCl crystal is specified. You give one representative per Wyckoff site and the symmetry generates all the rest.

This is how crystal structures are actually reported and stored. A structure paper says 'Ti occupies Wyckoff site 2a, O occupies 4f', and a reader with the International Tables can rebuild every atom position. The scheme is named after Ralph Wyckoff, an early American crystallographer. Choosing which site an atom sits on is a real decision in solving a structure — swapping two atoms between sites can change the whole model.