Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section D / 43 / b / iii / 2

The eight body-centred cubic neighbour vectors are $(a/\sqrt{3})(\pm 1,\pm 1,\pm 1)$ with independent signs. Their diagonal sums are $8a^2/3$ and the sign-paired off-diagonal sums cancel. HenceThe conventional cubic cell edge is $2a/\sqrt{3}$ in this comparison; using that edge as the hopping distance would spoil the stipulated equal-distance comparison.