Number of particles in cubic unit cells

The number of particles that actually belong to a given unit cell depends on how each particle is shared with the neighbouring cells.

i. Primitive or simple cubic unit cell (sc) : A particle at a corner of a cube is shared among the 8 cubes that meet at that corner, so it contributes only $\tfrac{1}{8}$ of itself to any one cell. With particles at the 8 corners only, an sc cell contains $\tfrac{1}{8}\times 8 =$ 1 particle per unit cell.

ii. Body-centred cubic unit cell (bcc) : The 8 corner particles together contribute $\tfrac{1}{8}\times 8 = 1$ particle, and the particle at the body centre belongs to that cell alone, contributing a full 1. A bcc cell therefore contains a total of 2 particles per bcc unit cell. …