  While the hexagonal lattice is ubiquitous in two dimensions, the body
centered cubic lattice and the face centered lattice are both commonly observed
in three dimensions. A geometric variational problem motivated by the diblock
copolymer theory consists of a short range interaction energy and a long range
interaction energy. In three dimensions, and when the long range interaction is
given by the nonlocal operator $(-\Delta)^{-3/2}$, it is proved that the body
centered cubic lattice is the preferred structure.
