Impossible object
Two famous undecidable figures, the Penrose triangle and devil's pitchfork
The theme of impossible objects embraces the gamut of representations of mathematical constructs, fictional ideas, representational drawings, etc, which clearly and unambiguously purport to describe, define or otherwise represent artifacts which are contrary to the known physical natural laws. Drawings of objects that cannot exist are called "undecidable figures". A good example of a world defined by impossible objects is that of the well-known graphical artist M. C. Escher, whose (for example) symmetrical staircases lead inexorably and beautifully into infinity.
See also: Optical illusion, paradox
In the Star Trek: The Next Generation 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.
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