  We determine crystal-like materials that can be fabricated by using a
standing acoustic wave to arrange small particles in a non-viscous liquid
resin, which is cured afterwards to keep the particles in the desired
locations. For identical spherical particles with the same physical properties
and small compared to the wavelength, the locations where the particles are
trapped correspond to the minima of an acoustic radiation potential which
describes the net forces that a particle is subject to. We show that the global
minima of spatially periodic acoustic radiation potentials can be predicted by
the eigenspace of a small real symmetric matrix corresponding to its smallest
eigenvalue. We relate symmetries of this eigenspace to particle arrangements
composed of points, lines or planes. Since waves are used to generate the
particle arrangements, the arrangement's periodicity is limited to certain
Bravais lattice classes that we enumerate in two and three dimensions.
