Necker Cube


The necker cube is an illusion in which a two-dimensional drawing of an array of cubes appears to simultaneously protrude from and intrude into the page.

A Necker cube appears on the banner shown in Escher's lithographs "Metamorphosis I" (Bool et al. 1982, p. 271; Forty 2003, p. 39), "Cycle" (Bool et al. 1982, p. 274), and "Convex and Concave". It is also the basis for the arcade game Q*bert.

Depending on the view point chosen for projection, the cubes may be composed of one, two, or three types of rhombi.

Necker cube in Pompeii, courtesy of S. Jaskulowski

The Necker cube is also a tiling that was used in ancient times, including as a mosaic on the floor of one of the houses in Pompeii, as illustrated in the photograph above (courtesy of S. Jaskulowski).

Necker cube quilt created by Janice Ewing

The image above shows a Necker cube pattern emblazoned on a quilt created by Janice Ewing using a pattern by Karen Combs.

See also

Cube, Rhombus, Schroeder Stairs, Tiling

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Bool, F. H.; Kist, J. R.; Locher, J. L.; and Wierda, F. M. C. Escher: His Life and Complete Graphic Work. New York: Abrams, 1982.Cromwell, P. R. Polyhedra. New York: Cambridge University Press, p. 155, 1997.Escher, M. C. "Metamorphosis I." Woodcut on two sheets. 1937., M. C. "Cycle." Lithograph. 1938., M. C. "Convex and Concave." Lithograph. 1955., M. The Nature of Visual Illusion. New York: Dover, pp. 25 and 118, 1996.Forty, S. M.C. Escher. Cobham, England: TAJ Books, 2003.Jablan, S. "Impossible Figures.", M. "Animated Necker Cube.", M. Graphica 1: The World of Mathematica Graphics. The Imaginary Made Real: The Images of Michael Trott. Champaign, IL: Wolfram Media, pp. 12 and 84, 1999.

Referenced on Wolfram|Alpha

Necker Cube

Cite this as:

Weisstein, Eric W. "Necker Cube." From MathWorld--A Wolfram Web Resource.

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