# Relating a compound's radii and unit cell dimensions

We're asked often to calculate the density of a crystal, and there is a known formula for that related to the unit cell volume. Now, for simple geometric structures such as the bcc structure (and since it is close packed), I know how to relate the different radii of the constituent compounds with the unit cell's (unique in this case) dimension (the length a), but how do I relate it for such other complex structures?

In general given a certain crystal geometry (cubic , tetragonal , orthorhombic), how does one relate the unit cell dimension with the radii of the constituent atoms?

The ratio of the radius of the cation to the radius of the anion is called radius ratio. The ratio of the radius of cation and the radius of anion i.e, radius ratio ($r_+/r_-$) plays an important role in determining the structures of ionic solids and coordination number of ions. The possible coordination numbers and structural arrangements of anions around cations for different $r_+/r_-$ values are given below: