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An impossible object is an object that cannot exist according to the known laws of nature, but has a description or representation suggesting, at first sight, that it can.
Drawings of objects that cannot exist are called "undecidable figures". The undecidability of these figures invariably rests on them being interpreted as two-dimensional projections of what would be an impossible higher-dimensional object. Artist M. C. Escher is notable for many drawings that feature undecidable figures, sometimes with the entire drawing being an undecidable figure.
Notable undecidable figures include:
In the episode " I, Borg", a plan was made to destroy the entire race of Borg – malevolent cybernetic aliens whose minds were interconnected – by showing one of the borg a picture of a highly-complex impossible object. This image would be transmitted back to the Borg hive, overloading its consciousness in larger and larger attempts to understand the image. This plan was dismissed as being genocide, so its potential results were never seen.