  This paper defines, for each convex polytope $\Delta$, a family $H_w\Delta$
of vector spaces. The definition uses a combination of linear algebra and
combinatorics. When what is called exact calculation holds, the dimension
$h_w\Delta$ of $H_w\Delta$ is a linear function of the flag vector $f\Delta$.
It is expected that the $H_w\Delta$ are examples, for toric varieties, of the
new topological invariants introduced by the author in "Local-global
intersection homolog" (preprint alg-geom/9709011).
