  We establish a correspondence between simplicial fans, not necessarily
rational, and certain foliated compact complex manifolds called LVMB-manifolds.
In the rational case, Meersseman and Verjovsky have shown that the leaf space
is the usual toric variety. We compute the basic Betti numbers of the foliation
for shellable fans. When the fan is in particular polytopal, we prove that the
basic cohomology of the foliation is generated in degree two. We give evidence
that the rich interplay between convex and algebraic geometries embodied by
toric varieties carries over to our nonrational construction. In fact, our
approach unifies rational and nonrational cases.
