The structure of a simple salt can often be determined using the radius ratio rule. To use this rule, one calculates the ratio of the radius of the smaller of the two ions to that of the larger of the two ions. If the ratio is $-0\mathrm{.}225$ to $0\mathrm{.}414,$ then the smaller ion occupies tetrahedral holes in the structure formed by the packing of the larger ion. If the ratio is $0\mathrm{.}414$ to $-0\mathrm{.}732,$ then the smaller ion occuples octahedral holes. Given the diameter of shooter marbles $(-16mm),$ jumbo marbles $(-35mm),$ and play balls $(60mm),$ determine which holes in a lattice of play balls each marble should occupy. Show all work.

Why in the zinc blende structure do the zinc cations occupy only half of the tetrahedral holes?