These are ight flying rocket model launching lugs manufactured by Model Rocket Industries. Made of pasteboard, they are attached to the body of a model. The vertical rod extending from the launch platform goes through the lug, and this insures that the model's liftoff will be in a vertical direction. These launching lugs were donated by G. Harry Stine, one of the American pioneers in the field of flying rocket models.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.