The impossible cube or irrational cube is an impossible object that draws upon the ambiguity present in a Necker cube illustration. An impossible cube is usually rendered as a Necker cube in which the edges are apparently solid beams. This apparent solidity gives the impossible cube greater visual ambiguity than the Necker cube, which is less likely to be perceived as an impossible object. The illusion plays on the human eye's interpretation of two-dimensional pictures as three-dimensional objects.

In M. C. Escher's lithograph Belvedere, the figure of a boy seated at the foot of the building is holding an impossible cube; the rest of the scene is based on the same principle that makes the impossible cube. In the scene, a ladder from the inside of the first story leads to the outside of the second. However, this is not appreciated by the prisoner in the basment cell because the basement is a possible cuboid and he is unambiguously on the inside.

A doctored photograph purporting to be of an impossible cube was published in the June 1966 number of Scientific American, where it was called a "Freemish Crate".

See also: Penrose triangle.