Neighbour shells of a body-centred cubic lattice ($r_1=\sqrt{3}a/2,r_2=a$)

In a body-centred cubic lattice of conventional edge $a$, a lattice site has eight nearest neighbours along body half-diagonals at distance $\sqrt{3}a/2$, then six next-nearest neighbours along the coordinate axes at distance $a$. There are two sites per conventional cell, so identical atoms of mass $m$ and mass density $\rho$ obey $\rho a^3=2m$. Specifying a neighbour shell matters: the nearest and next-nearest distances differ.