  Although intersection homology lacks a ring structure, certain expressions
(called uniform) in the intersection homology of an irreducible projective
variety $X$ always give the same value, when computed via the decomposition
theorem on any resolution $X_r\to X$. This paper uses uniform (and non-uniform)
expressions to define what is believed to be the usual intersection homology
(and its local-global variant) of a convex polytope (or a projective toric
variety). Such expressions are generated by the facets, and so may lead to
necessary numerical conditions on the flag vector. Most of the concepts,
however, apply to more general algebraic varieties, and perhaps some other
situations also.
