Past exam of the chemistry A course of the University of Cambridge / 2023 / Paper 2 / A9 / a / iii / Solution

Using the printed $x,y$ axes, take a lower vertex of cell B as origin. One allowed pair of primitive lattice translation vectors isBoth vectors connect nearest lattice points, have length $\sqrt{2}a$, and are perpendicular. Their determinant has magnitude $2a^2$, consistent with a primitive area. Exchanging them or reversing their directions gives equivalent basis conventions; the corresponding reciprocal lattice vectors must then use the same convention.