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An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion consisting of a two-dimensional figure which is instantly and subconsciously interpreted by the visual system as representing a projection of a three-dimensional object although it is not geometrically possible for such an object to exist (at least not in the form interpreted by the visual system).
In most cases the impossibility becomes apparent after viewing the figure for a few seconds. However, the initial impression of a 3D object remains even after it has been contradicted. There are also more subtle examples of impossible objects where the impossibility does not become apparent spontaneously and it is necessary to consciously examine the geometry of the implied object to determine that it is impossible.
Notable examples 
Notable undecidable figures include:
Swedish artist Oscar Reutersvärd was the first to deliberately design many impossible objects. He has been called "the father of impossible figures". In 1934 he drew the Penrose triangle, some years before the Penroses. In Reutersvärd's version 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 referred to Escher, whose work had sparked their interest in the subject, but not Reutersvärd, of whom they were unaware. The article was only published in 1958.
From the 1930s onwards Dutch artist M.C. Escher produced many drawings featuring paradoxes of perspective gradually working towards impossible objects. In 1957 he produced his first drawing containing a true impossible object: Cube with Magic Ribbons. He produced many further drawings featuring 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 contemporary artists 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.
See also 
- Four-dimensional space
- Multistable perception
- Necker cube
- Non-Euclidean geometry
- Optical illusion
- Strange loop
- Three hares
- M.C. Escher
- Mathematical Circus, Martin Gardner 1979 ISBN 0-14-022355-X (Chapter 1 – Optical Illusions)
- Optical Illusions, Bruno Ernst 2006 ISBN 3-8228-5410-7
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