Resumen de On bodies in R5 with directly congruent projections or sections

M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin

• 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.