Draw the face-centered cubic structure

(a) Draw the face-centered cubic structure. Find the positions of the atoms, and
the positions of the octahedral and tetrahedral voids within the structure. How many
lattice sites, octahedral and tetrahedral voids are contained in a cell?

(b) Let a material have the fcc structure, and consist of spherical atoms that just
touch one another. What is the radius of the largest sphere that will fit inside an octahedral
void without distorting the structure? What is the radius of the largest sphere that
will fit in a tetrahedral void without distortion? [Hint: the geometry of the tetrahedral
void is much easier to treat if you first show that the center of the void lies at the center of
a cube that is 1/8 the size of the fcc unit cell.]