Impossible cube

In Escher's Belvedere a man seated at the foot of a building holds an impossible cube. A drawing of the related Necker cube (with its crossings circled) lies at his feet, while the building itself shares some of the same impossible features as the cube.^[1][2] Another Escher print, Man with Cuboid, shows the same man and impossible cube, without the Necker cube drawing.^[3] In Escher's version, the beams in the top half of the drawing are drawn as if viewed from above, with a crossing consistent with that point of view, while the beams in the bottom half are drawn as if viewed from below, again with a crossing consistent with that point of view.^[4] This internal consistency of the top and bottom halves of the drawing is a reflection of the impossible tower that forms the main subject of Escher's print, whose interlaced pillars again look consistent if one views only a single floor at a time.^[5]

Other artists than Escher, including Jos De Mey, have also made artworks featuring an impossible cube.^[3] A doctored photograph purporting to be of an impossible cube was published in the June 1966 issue of Scientific American, where it was called a "Freemish crate".^[6][7] An impossible cube has also been featured on an Austrian postage stamp, honoring the 10th Congress of the Austrian Mathematical Society in Innsbruck in 1981.^[8] The Austrian stamp shows Escher's version, but some of these alternative versions draw all beams with a single viewpoint from above, reversing one or both of the crossings of the Necker cube from the way the beams of a standard cube would cross with that viewpoint.^[9]