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).
Aleksandrov's Uniqueness Theorem
See also
Brightness, Shephard's Problem, TomographyExplore with Wolfram|Alpha
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 Web Resource. https://mathworld.wolfram.com/AleksandrovsUniquenessTheorem.html