  To speak about fundamental measure theory obliges to mention dimensional
crossover. This feature, inherent to the systems themselves, was incorporated
in the theory almost from the beginning. Although at first it was thought to be
a consistency check for the theory, it rapidly became its fundamental pillar,
thus becoming the only density functional theory which possesses such a
property. It is straightforward that dimensional crossover connects, for
instance, the parallel hard cube system (three-dimensional) with that of
squares (two-dimensional) and rods (one-dimensional). We show here that there
are many more connections which can be established in this way. Through them we
deduce from the functional for parallel hard (hyper)cubes in the simple
(hyper)cubic lattice the corresponding functionals for the nearest-neighbor
exclusion lattice gases in the square, triangular, simple cubic, face-centered
cubic, and body-centered cubic lattices. As an application, the bulk phase
diagram for all these systems is obtained.
