On recognizing shapes of polytopes from their shadows

Abstract

Let $P$ and $Q$ be two convex polytopes both contained in the interior of an Euclidean ball $r{\text{B}}^d$. We prove that $P=Q$ provided that their sight cones from any point on the sphere $r{S}^{d-1}$ are congruent. We also prove an analogous result for spherical projections.