A three-dimensional puzzle of a familiar object, the puzzle including a support structure having the shape of the familiar object and a plurality of rigid, non-planar interlocking pieces that engage an outer surface of the support structure to form a representation of the familiar object. The familiar object may be a beverage container such as a soda can, a bottle or a coffee mug, or it may be an apple, a baseball, a model car, or a model of a familiar landmark. The puzzle may include a release mechanism for separating the puzzle pieces from the support structure.