  Sufficiently thin films of type-I superconductor in a perpendicular magnetic
field exhibit a triangular vortex lattice, while thick films develop an
intermediate state. To elucidate what happens between these two regimes,
precise numerical calculations have been made within Ginzburg-Landau theory at
$\kappa=0.5$ and 0.25 for a variety of vortex lattice structures with one flux
quantum per unit cell. The phase diagram in the space of mean induction and
film thickness includes a narrow wedge in which a square lattice is stable,
surrounded by the domain of stability of the triangular lattice at thinner
films/lower fields and, on the other side, rectangular lattices with
continuously varying aspect ratio. The vortex lattice has an anomalously small
shear modulus within and close to the square lattice phase.
