The Solid State

If a triangular void pointing up in one close-packed layer is covered by a triangular void pointing down in the adjacent layer, then a void surrounded by six spheres results Such a void is called an octahedral void since the six spheres surrounding it lie at the corners of a regular octahedron.

                    octahedral void

 In a cubic unit cell,there are 8 vertex, 12 edges, 6 faces and one body centre.

In AgI, if there are nI^- ions, there will be nAg⁺ ions. As I^- ions form the lattice, number of tetrahedral voids = 2n.
As there are nAg⁺ ions to occupy these voids, therefore fraction of tetrahedral voids occupied by Ag+ ions = n/2n = ½ = 50%.

For every atom in a close packed structure, there are two tetrahedral voids.

Let the number of close packed spheres be N, then:
The number of octahedral voids generated = N
The number of tetrahedral voids generated = 2N