An impossible object is a kind of optical illusion. Impossible objects are also known as undecidable figures. In this kind of illusion, a person looks at a two-dimensional picture. The vision center of the brain does much of its work subconsciously  and automatically. It interprets the figure as a three-dimensional object.

The viewer usually knows such an object is impossible soon after looking at the figure. However, the impression of a 3D figure may still remain even when the viewer knows it is impossible in reality.

Some of these figures are more subtle. In these cases it is not obvious that they are impossible right away. The viewer carefully needs to look at the geometry of the object to find out that it is indeed impossible.

Impossible objects are of interest to psychologists, mathematicians and artists.

History 
Swedish artist Oscar Reutersvärd was the first person to draw many impossible objects. He has been called "the father of impossible figures". In 1934, he drew the Penrose triangle, some years before the Penroses. The way Reutersvärd drew it, the sides of the triangle are broken up into cubes.

In 1956, British psychiatrist Lionel Penrose and his son, mathematician Roger Penrose, submitted a short article to the British Journal of Psychology titled Impossible objects: a special type of visual illusion. This was illustrated with the Penrose Triangle and Penrose stairs. The article referenced Escher, whose work had sparked their interest in the subject, but not Reutersvärd, whom they were unaware of. The article was only published in 1958.

From the 1930s onwards Dutch artist M.C. Escher produced many drawings with paradoxes of perspective. In 1957 he produced his first drawing containing a true impossible object: Cube with Magic Ribbons. He produced many other drawings of impossible objects, sometimes with the entire drawing being an undecidable figure. His work did much to draw the attention of the public to impossible objects. Some artists of the time are also experimenting with impossible figures, for example, Jos de Mey, Shigeo Fukuda, Sandro del Prete, István Orosz (Utisz), Guido Moretti, Tamás F. Farkas and Mathieu Hamaekers.

In fiction 
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.
In the computer game Diablo II, the "Arcane Sanctuary" region was based on impossible drawings.
Alan Moore's miniseries 1963 features a character called the Hypernaut that lives in a space station shaped like an impossible object.
In the video game Eternal Darkness: Sanity's Requiem the Essence of Xel'lotath, the Sigil of Xel'lotath, is an impossible artifact resembling a warped angel.
In The Simpsons episode "Treehouse of Horror VIII", a blivet (or devil's tuning fork) can be seen on Professor Frink's yard sale. In The Simpsons Movie, Homer falls down miles of the impossible infinite House of Stairs while having an epiphany.
The video game Echochrome for the PSP and PS3 features a mannequin who must traverse a series of impossible objects.
The set of the climactic scene in the Goblin King's castle in the 1986 fantasy film, Labyrinth, directed by Jim Henson, is based on M. C. Escher's "Relativity", and features impossible staircases and perspectives.
In Pokemon Platinum there is an area full of impossibilities such as these.

Related pages 
Optical illusion
Necker cube
Paradox
Surrealism
Puzzle

References 
Mathematical Circus, Martin Gardner 1979  (Chapter 1 — Optical Illusions)
Optical Illusions, Bruno Ernst 2006

Other websites 
Art of Reutersvard 
Real Escher Objects 
Impossible World, a repository of impossible object images

Illusions
Art