= Solution
With the convention $\mathbf a_i\cdot\mathbf b_j=2\pi\delta_{ij}$, the <reciprocal lattice> of a <face-centered cubic lattice> is a <body-centered cubic lattice>. The reciprocal conventional cube is parallel to the direct conventional cube and has side $4\pi/a$. In direct-cubic coordinates its points are
$$
\boxed{\mathbf G=\frac{2\pi}{a}(h,k,l),\qquad h,k,l\text{ all even or all odd}.}
$$
The even triples supply the corners of that reciprocal cube and the odd triples its body centres. The <atomic basis> can change <diffraction intensities> through its <structure factor>; it does not change the <reciprocal lattice> determined by the translation lattice.
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