Can One Flat Net of Squares Fold into Two or More Different Cuboids?

A net of squares (or polyomino) is a flat figure composed of squares of equal size and coincident sides. A cuboid is a box with three pairs of rectangular faces joined at right angles.

Any cuboid with integral edge lengths may be disassembled and flattened into a polyomino which, when folded up correctly (with no gaps or overlapping faces), forms the original cuboid. But is there a polyomino which can be folded into two or more different cuboids?

Nobody knew the answer to this question before 1999.