# Impossible cube

An impossible cube that defies the laws of geometry.

The impossible cube or irrational cube is one of several impossible objects. The impossible cube draws upon the ambiguity present in a Necker cube illustration. Ambiguous figures like the Necker cube are those that, for the viewer, flip back and forth between equally possible perspectives of the object represented. Impossible figures, such as the Penrose triangle and blivet, are a special class of ambiguous figures in which parts of the picture that are not ambiguous are drawn in incompatible perspectives.

Impossible figures like the impossible cube provide opportunities both for valuable research into human perceptual processes and to bring joy and fascination to many through their inclusion in works of art. Such artworks reveal humankind's endless fascination with the creative and unusual. These instances can also help us realize that our own perceptions may be limited or different from those of another person viewing the same thing, but from a different angle.

## Discovery

The origins of the impossible cube are often attributed to artist M. C. Escher, whose work often featured optical illusions and impossible objects. The impossible cube can be seen in the 1958 lithograph Belvedere, in which a seated man appears to be constructing an impossible cube from the drawing of a Necker cube.

## Description

Drawing of the Necker cube and impossible cube.

An impossible cube is usually rendered as a Necker cube in which the edges are depicted as solid beams. This apparent solidity gives the impossible cube greater visual ambiguity than the Necker cube, which is much less likely to be perceived as an impossible object. When viewing the impossible cube, all the corners appear to be correct, but the edges of the cube overlap in ways that are not physically possible.

A three dimensional construction that, when viewed from a specific angle, can appear to be a three dimensional impossible cube.

## Explanation

The illusion plays on the human eye's interpretation of two-dimensional pictures as three-dimensional objects. Visual perspective is used to create the illusion of depth, but the three edges on the back of the cube are placed in the foreground.

## Applications

The impossible cube holds a great deal of fascination for viewers. Variations on the impossible cube have been published and "constructed." One famous example of an impossible cube constructed from wood is a photograph published by C. F. Cochran in the June 1966 issue of Scientific American, where it was called a "Freemish Crate" to be used for shipping impossible objects. In reality, the Freemish Crate, as well as all three dimensional impossible cubes, was not actually an impossible cube. The form is constructed to look like an impossible cube from one very specific angle only, as shown in the drawing to the right.

Other impossible objects, such as those utilized by M. C. Escher in his fascinating drawings and lilthographs, can also be created to look like the two dimensional representation from a certain viewing direction only.[1] Interestingly, even when the viewer has seen the object from other angles and so is fully aware that the figure is not "impossible," perception from the critical viewing angle does not change—the figure is still seen as impossible.[2]

## Notes

1. Escher for Real Gershon Elber, 2002-2007. Retrieved January 3, 2008.
2. Richard L. Gregory, Eye and Brain. (Princeton, NJ: Princeton University Press, 1997, ISBN 0691048371) p. 239.

## References

• Bool, F.H., J.R. Kist, and F. Wierda. M.C. Escher: His Life and Complete Graphic Work (With a Fully Illustrated Catalogue) September 1992. Harry N. Abrams, Inc. ISBN 0810981130
• Gregory, Richard L. 1997. Eye and Brain. Princeton, NJ: Princeton University Press. ISBN 0691048371
• Robinson, J. O. 1998. The Psychology of Visual Illusion. Dover Publications. ISBN 978-0486404493
• Schattschneider, Doris and Michele Emmer. M.C.Escher's Legacy: A Centennial Celebration. September 2005. Springer. ISBN 3540201009
• Seckel, Al. Optical Ilusions: The Science of Visual Perception. September 2006. Firefly Books. ISBN 1554071720

## Credits

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchers here:

The history of this article since it was imported to New World Encyclopedia:

Note: Some restrictions may apply to use of individual images which are separately licensed.