the ionic radius
If ions really are little marbles, each should have a definite size, a radius. The ionic radius is that assigned size: roughly, half the distance between two touching ions of opposite charge, split between them. We can measure the total distance between neighbouring ions very precisely by X-ray diffraction (in NaCl the Na-to-Cl centre distance is about 0.28 nm); the harder job is deciding how much of that gap belongs to the cation and how much to the anion, and tabulated ionic radii (most famously Shannon's) are careful, self-consistent answers to that split.
A single element does not have one radius; it depends on two things. Charge: strip more electrons off and the ion shrinks (Fe2+ is bigger than Fe3+), while adding electrons swells it, so anions are large and cations small. Coordination: an ion squeezed among more neighbours is pushed out to a slightly larger effective radius, so Al3+ measures about 0.039 nm with four oxygen neighbours but about 0.054 nm with six. This is why any good radius table lists a value for each coordination number, not one number per element.
Ionic radii are the raw material for predicting structure. Their ratio (cation over anion) forecasts coordination number, and hence which crystal structure forms; their sum predicts bond lengths and, through the lattice-energy formulas, melting points and stiffness. Get the radii right and a surprising amount of ceramic behaviour falls out of pure geometry, but remember they are model quantities chosen to be consistent, not hard edges you could photograph.
Oxygen's O2- radius is about 0.140 nm (six-coordinated). Against it, Mg2+ (0.072 nm) gives a ratio of 0.51 and takes six oxygen neighbours, while the far smaller Si4+ (0.026 nm) gives 0.19 and takes only four: the same anion, two different cations, two different structures.
Charge and coordination, not the element alone, fix an ion's radius.
There is no single true ionic radius: the cation/anion split of a measured bond length is a convention. Shannon and Pauling radii differ by up to about 0.02 nm, so always take a cation and anion radius from the same table before comparing them.