 Solution

The body-centered tetragonal lattice has points at $(0,0,0)$ and $(1/2,1/2,1/2)$ in the conventional cell. Add the two-atom motif to each. Reducing coordinates modulo integer translations givesThus the cell contains four atoms, not merely the two lattice points. In projection along $[001]$, label each projected point by its fractional height $z/c$; the four sites do not all lie in the same plane.

The plotted repeat is $a=0.5831\mathrm{nm}$ in both horizontal directions. Atoms on the outer drawing boundary are repeated images needed to show neighboring cells, rather than additional unshared atoms in the four-cell counting volume.