the coordination number
Stand a cation in a crystal and count how many anions are touching it: that count is the coordination number. It is the local crowd size around an ion, the answer to how many neighbours. Common values in ceramics are 4, 6, and 8: a silicon sits among four oxygens, a magnesium among six, a large zirconium among eight. The same idea works from the anion's side too (how many cations surround each oxygen), and the two viewpoints must stay consistent with the crystal's formula.
For a mostly ionic crystal, coordination number is decided by simple packing geometry: a bigger cation, relative to the anion, can gather more neighbours before they start bumping into one another. That relative size is the radius ratio, and it comes with critical thresholds: below about 0.225 you get three neighbours (triangle), 0.225 to 0.414 gives four (tetrahedron), 0.414 to 0.732 gives six (octahedron), and above 0.732 gives eight (cube). The neighbours arrange themselves into a coordination polyhedron, the little cage of anions around the cation, which is the true building block of the structure.
Coordination number is the hinge between bonding and structure. It sets Pauling's electrostatic bond strength (an ion's charge divided by its coordination number), which must balance around every anion; it distinguishes structures built from the same atoms (silica's SiO4 tetrahedra versus a high-pressure form where silicon takes six oxygens); and it changes under pressure, as squeezing a mineral often forces its cations into higher coordination deep in the Earth. Directional covalent bonds, by contrast, fix low coordination by angle rather than by size.
Silicon almost always takes coordination 4 (the SiO4 tetrahedron), but under the enormous pressure deep in the Earth's mantle it flips to coordination 6 in the mineral stishovite: same SiO2, different coordination, a much denser crystal.
Coordination number, not composition alone, tells structures apart.
Coordination number is a geometric count of nearest neighbours, not a chemical bond order. And the radius-ratio prediction is only a guide: it gets the coordination right for roughly two-thirds of simple compounds and fails where bonding is strongly covalent.