Intermediate surface area measures and projection functions of convex bodies (Q1345871)

It is proved that a convex polytopye in \(\mathbb{R}^ d\), whose faces satisfy a certain assumption of general position, is uniquely determined, up to translation or reflection, by its \(i\)th projection function if \(i\in \{2,\dots d-2\}\). For this, convex bodies in \(\mathbb{R}^ d\) whose \(i\)th area measure, \(i\in \{2,\dots, d-2\}\) is dominated by the sum of the \(i\)th area measures of two polytopes are investigated first. Also corresponding results for most convex bodies in terms of Baire category are studied.