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We define an extension of the toric (middle perversity intersection homology)$g$-vector of a convex polytope $X$. The extended $g(X)$ encodes the whole ofthe flag vector $f(X)$ of $X$, and so is called complete. We find that for manyexamples that $g_k(X)\geq 0$ for most $k$ (independent of $X$).

A complete $g$-vector for convex polytopes