Let and be two convex bodies in 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 on certain 3 dimensional subspaces have no symmetries, then up to a translation. We also prove the corresponding result for sections of star bodies.
Cite this article
M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin, On bodies in with directly congruent projections or sections. Rev. Mat. Iberoam. 35 (2019), no. 6, pp. 1745–1762DOI 10.4171/RMI/1100