  The band structure of a Bose-Einstein condensate is studied for lattice traps
of sinusoidal, Jacobi elliptic, and Kronig-Penney form. It is demonstrated that
the physical properties of the system are independent of the choice of lattice.
The Kronig-Penney potential, which admits a full exact solution in closed
analytical form, is then used to understand in a novel way the swallowtails, or
loops, that form in the band structure. Their appearance can be explained by
adiabatically tuning a second lattice with half the period. Such a two-color
lattice, which can be easily realized in experiments, has intriguing new
physical properties. For instance, swallowtails appear even for weak
nonlinearity, which is the experimental regime. We determine the stability
properties of this system and relate them to current experiments.
