Aleksandrov's Uniqueness Theorem
A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each projection).
See also
Brightness, Shephard's Problem, TomographyExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Gardner, R. J. "Geometric Tomography." Not. Amer. Math. Soc. 42, 422-429, 1995.Referenced on Wolfram|Alpha
Aleksandrov's Uniqueness TheoremCite this as:
Weisstein, Eric W. "Aleksandrov's Uniqueness Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AleksandrovsUniquenessTheorem.html