 Vertical mirrors of the diamond cubic structure

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.