If a face-centered cubic crystal structure has all of its octahedral sites filled with atoms that fit perfectly into each octahedral site, what is the atomic packing factor?

APF = (number of atoms per unit cell x atomic volume) / unit cell volume

There are four atoms per unit cell in the FCC structure with a radius R. These are four octahedral sites in the FCC structure with radius r. The unit cell has a volume (a is the lattice parameter or axial length of the unit cell). For the FCC structure,

a3 a=24R