  We consider the physical implementation of a 2D optical lattice with schemes
involving 3 and 4 light fields. We illustrate the wide range of geometries
available to the 3 beam lattice, and compare the general potential properties
of the two lattice schemes. Numerically calculating the band structure we
obtain the Wannier states and evaluate the parameters of the Bose-Hubbard
models relevant to these lattices. Using these results we demonstrate lattices
that realize Bose-Hubbard models with 2, 4, or 6 nearest neighbors, and
quantify the extent that these different lattices effect the superfluid to
Mott-insulator transition.
