The atomic packing fraction for the FCC crystal structure is 0.74. This is the densest arrangement of atoms achievable in three dimensions when all atoms have the same radius R. If atoms in the hard sphere model occupy 74% of the volume of the unit cell, then the other 26% is empty space.
Imagine that the empty spaces located at the center of each edge and at the body–centered position of the FCC unit cell are filled with smaller spheres of radius r such that r = 0.414R. The smaller atoms fit perfectly in between the atoms of radius R.
(a) By counting in the usual way, how many atoms of radius r are there per FCC unit cell? 

(b) What are the coordinates of these atoms of radius r? Do not double count atoms. Provide the same number of coordinates as the number of atoms of radius r per unit cell.
(c) What is the atomic packing fraction for this structure?