Convex polytopes are uniquely determined by their flotation surfaces (except at density 1/2) and by their buoyancy surfaces.
Applications de G´ eom´ etrie et de M´ echanique ´ a la marine, aux ponts et chauss´ ees
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Uniqueness of Flotation and Buoyancy Surfaces for Convex Polytopes
Convex polytopes are uniquely determined by their flotation surfaces (except at density 1/2) and by their buoyancy surfaces.