This is a Space Plane model built by Aurora Plastics in the 1960s. The model is plastic and has the emblem of the former Pan American Airways on it. No such Space Plane was ever built in real life, however.
G. Harry Stine, one of the American pioneers in the field of flying rocket and missile models, donated this model, in 1973.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.