We discuss some properties of spherical projections, and consider the related question regarding their congruency for two convex bodies. In particular, let P and Q be two convex polytopes both contained in the interior of an Euclidean ball rBd. We prove that P=Q provided that their spherical projections from any point on the sphere rSd−1 are congruent. We also prove an analogous result for a pair of Euclidean balls.