Related to the questions <a href="https://mathoverflow.net/questions/137850/A-question-about-a-question-about-3-dimensional-convex-bodies">mathoverflow.net question No. 137850</a> and <a href="https://mathoverflow.net/questions/39127/is-the-sphere-the-only-surface-all-of-whose-projections-are-circles-or-can-we">mathoverflow.net question No. 39127</a>, is there a 3-dimensional convex body other than a ball whose perpendicular projections in all directions are of the same area?