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Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.

An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion. It consists of a two-dimensional figure which is instantly and subconsciously interpreted by the visual system as representing a projection of a three-dimensional object.

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.

The unsettling nature of impossible objects occurs because of our natural desire to interpret 2D drawings as three-dimensional objects. This is why a drawing of a Necker cube would be most likely seen as a cube, rather than "two squares connected with diagonal lines, a square surrounded by irregular planar figures, or any other planar figure." With an impossible object, looking at different parts of the object makes one reassess the 3D nature of the object, which confuses the mind.

Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline.

Notable impossible objects include:

1. Impossible cube — The impossible cube was invented by M.C. Escher for Belvedere, a lithograph in which a boy seated at the foot of the building holds an impossible cube.
2. Penrose stairs — The Penrose stairs was created by Lionel Penrose and his son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher.
3. Penrose triangle (Tribar) — The Penrose triangle was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form".
4. Impossible trident (or devil's tuning fork) — The Blivet has three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end.