  We investigate the Edge-Isoperimetric Problem (EIP) for sets with $n$
elements of the cubic lattice by emphasizing its relation with the emergence of
the Wulff shape in the crystallization problem. Minimizers $M_n$ of the edge
perimeter are shown to deviate from a corresponding cubic Wulff configuration
with respect to their symmetric difference by at most $ {\rm O}(n^{3/4})$
elements. The exponent $3/4$ is optimal. This extends to the cubic lattice
analogous results that have already been established for the triangular, the
hexagonal, and the square lattice in two space dimensions.
