Classification of impossible objects.

A mathematical scheme is proposed for the classification of impossible objects. Impossible objects are usually defined from a psychological point of view as mental images of 'solid objects' which cannot exist in a real three-dimensional world. From the mathematical point of view, however, various kinds of impossibility can be observed in such objects, and they are classified according to the kinds of impossibility they possess. Since impossible objects are treated in a purely mathematical way, the results afford a powerful basis for the psychological study of human visual perception of impossible objects. Several psychological problems arising from the present results are also discussed.