Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes

Susanna Dann, Orli Herscovici, Sergii Myroshnychenko

We prove that a convex polytope $P\subset {\mathbb{R}}^d$, $d\ge 2$, of uniform density $\delta \in (0,1)$ floating in a liquid of density $1$, is uniquely determined by its surface of f…