Convex polytopes and linear algebra

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