On bodies in R⁵ with directly congruent projections or sections

Original · EN

Let K and L be two convex bodies in R⁵ with countably many diameters, such that their projections onto all 4 dimensional subspaces containing one fixed diameter are directly congruent. We show that if these projections have no rotational symmetries, and the projections of K,L on certain 3 dimensional subspaces have no symmetries, then K=± L up to a translation. We also prove the corresponding result for sections of star bodies.