= Solution
For conventional cubic cell side $a$, the <face-centered cubic lattice> has corner and face-centre sites, giving four lattice points per cell; the <body-centered cubic lattice> has corners and a body centre, giving two. Their <primitive unit cells> each contain one lattice point. With reciprocal vectors written $\mathbf G=(2\pi/a)(h,k,l)$, <face-centered cubic lattice> allows $h,k,l$ all even or all odd, while <body-centred cubic> allows $h+k+l$ even. Hence
$$
\boxed{\text{fcc}\longleftrightarrow\text{bcc in reciprocal space},\qquad a^*=4\pi/a}.
$$
Here $a^*$ is the side of the <reciprocal lattice>'s conventional cubic cell. The parity conditions describe the reciprocal point sets; reciprocal space contains <wavevectors>, not a second arrangement of physical atoms.
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