  The simplest way to generate a lattice of convex sets is to consider an
initial set of points and draw segments, triangles, and any convex hull from
it, then intersect them to obtain new points, and so forth. The result is an
infinite lattice for most sets, while only a few initial sets of points perform
a finite lattice. By giving an adequate notion of the configuration of points,
we identify which sets in the plane define a finite convex hull lattice: four
regular families and one sporadic configuration. We explore configurations in
the space and higher dimensions.
