Impossible object
two-dimensional figure representing a projection of a three-dimensional object that cannot exist
An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object but cannot exist as a solid object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline.
Notable examples
Notable impossible objects include:
Explanations
Impossible objects can be unsettling because of a human tendency in many cultures to interpret 2D drawings as three-dimensional objects. This is why a drawing of a Necker cube would most likely be seen as a cube, rather than "two squares connected with diagonal lines", "a square surrounded by irregular planar figures" or any other planar figure. Looking at different parts of an impossible object makes one reassess the 3D nature of the object, which confuses the mind.
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.
Roger Penrose wrote about describing and defining impossible objects mathematically using the algebraic topology concept of cohomology.
History
An early example of an impossible object comes from Apolinère Enameled, a 1916 advertisement painted by Marcel Duchamp.
“Impossible object” enters the record as two-dimensional figure representing a projection of a three-dimensional object that cannot exist. Crown Archives preserves that source wording while asking what Impossible, object and two-dimensional can confirm, complicate or overturn.
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The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Jun 24, 2026. The linked authority identifier is Q601362. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1916.
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This entry incorporates text from “Impossible object” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.