Diamond cubic structure

An FCC Bravais lattice with a two-atom basis at fractional positions $(0,0,0)$ and $(1/4,1/4,1/4)$. Its conventional cubic cell contains eight atoms. Equal scattering amplitudes at the two basis sites produce additional systematic absences beyond the FCC parity selection rule.

Nearest neighbors are separated by $a\sqrt{3}/4$, so touching spheres have radius $a\sqrt{3}/8$. Eight atoms in a conventional cell occupy fraction $\pi \sqrt{3}/16\simeq 0.3401$. The underlying FCC Bravais lattice does not make this two-atom network close packed.

The point $(1/8,1/8,1/8)$ is an inversion centre when an atom is at the origin. Inversion sends $\mathbf{r}$ to $(1/4,1/4,1/4)-\mathbf{r}$ and exchanges the identical FCC sublattices. The individual atomic sites are not inversion centres.

With one atom at the origin and the second FCC sublattice displaced by $(1/4,1/4,1/4)$, the vertical mirrors normal to directions perpendicular to $[001]$ have traces $x-y=n/2$ or $x+y=n/2$ in fractional coordinates. Checking the atomic heights distinguishes a genuine mirror from a misleading planar projection.