= Solution
<Bond-centred inversion in diamond cubic> gives one <inversion centre> at the midpoint of a nearest-neighbor bond:
$$
\boxed{\mathbf c=(\tfrac18,\tfrac18,\tfrac18).}
$$
Mark its projected point $(1/8,1/8)$ and label its height \b[$z/a=1/8$]. Inversion about this point sends $\mathbf r$ to $(1/4,1/4,1/4)-\mathbf r$. It exchanges the two identical FCC sublattices and therefore preserves the crystal. An individual atom at the chosen origin is not an <inversion centre>.
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