Self-assembled equilibrium amphiphilic phases with one-, two-, and three-dimensional order are simulated by a Monte Carlo technique using a simple Flory lattice model to describe the configurations and interactions of idealized single-site "oil", and "water", molecules and multi-site amphiphilic molecules. Self-assembled patterns with at least one zero wavevector, namely lamellar or hexagonal, select orientations on the three-dimensional lattice so that the finite wavevectors of the pattern are roughly independent of lattice size. Patterns with three-dimensional order, including cubic and noncubic packings of spheres, and a tetragonal intermediate phase, also self-assemble when the lattices are of sizes nearly commensurate with the wavevectors of the bulk equilibrium patterns. The relative stability of sphere packings can be assessed by allowing patterns induced on small lattices to relax on large lattices that are periodic replications of the small ones; for a surfactant dissolved in "water" with a head group much larger than its tail group, the stability appears to increase in the following order : simple cubic, face-centered cubic, body-centered cubic, hexagonally close packed. The average conformational states of the surfactant chain and its head and tail units are computed for various ordered phases; these results indicate that crowding of surfactant head groups, which can be swollen by solvent, is a significant factor influencing phase behavior. In lamellar phases with holes in the layers that contain the surfactant tails, defects in the patterns form easily; these facilitate changes in layer spacings when the temperature is changed.