  We consider a system of $N$ hard spheres sitting on the nodes of either the
$\mathrm{FCC}$ or $\mathrm{HCP}$ lattice and interacting via a sticky-disk
potential. As $N$ tends to infinity (continuum limit), assuming the interaction
energy does not exceed that of the ground-state by more than $N^{2/3}$ (surface
scaling), we obtain the variational coarse grained model by
$\Gamma$-convergence. More precisely, we prove that the continuum limit
energies are of perimeter type and we compute explicitly their Wulff shapes.
Our analysis shows that crystallization on $\mathrm{FCC}$ is preferred to that
on $\mathrm{HCP}$ for $N$ large enough. The method is based on integral
representation and concentration-compactness results that we prove for general
periodic lattices in any dimension.
