2 problems

Let $b$ be a prescribed brightness, and consider convex bodies of revolution in three-dimensional space with constant brightness $b$. Campi–Colesanti–Gronchi conjecture. The body c…

Let $d$ be a prescribed thickness, and consider convex bodies in three-dimensional space with thickness $d$. The Heil body is the convex hull of six circular arcs of radius $d$, ce…