From the wiki “Sphere” entry: “The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area.”
Does this statement, particularly the latter part, imply that of all possible configurations of the same volume V, the sphere also maximizes the minimum-distance from any point inside the sphere to the sphere’s surface? (If so, I’m assuming this would only apply to genus-0 objects.)