The combinatorics of cation-deficient close-packed structures

Pólya's enumeration theorem is used to derive an algorithm for counting all hexagonal close-packed structures with a unit cell of given size, having composition MX₂, where X is an hcp anion, M is an octahedrally coordinated cation, and no face sharing is permitted between octahedra. Generalizations of this algorithm to enumerate ordered derivatives of these structures, hcp structures with tetrahedral instead of octahedral cations, and similar structures having different stacking sequences among the close-packed layers are sketched.