On the determination of convex bodies by projection and girth functions

It is known that (in the sense of Baire category) most n-dimensional convex bodies are uniquely determined, up to translation or reflection, by the i-dimensional volumes of the orthogonal projections on i-planes, provided that i ∈ {2,…, n ? 2}. This result is strengthened by showing that small sets of projections are sufficient for such determinations. The proof yields an extension of the result, where volumes are generalized to intrinsic volumes.