The impossible cube
A cube frame where a back edge passes in front of a front one.
How this site works. Every fact is in our own words and linked to its source, beside it. Where good sources disagree, we show each version in a “Sources differ” box. Every drawing is our own.
Escher’s own impossible figure
Of his three famous impossible prints, Escher invented the figure for Belvedere himself: an impossible cube. Escher in The Palace
Escher told the Penroses he had the idea for Belvedere before he read their article. Escher in The Palace
Escher also made a 1958 wood engraving of the same man with his impossible cube, Man with Cuboid. Escher in The Palace Man with Cuboid is tiny: 64 × 64 mm. EscherMath
Necker cube or impossible cube?
A Necker cube is a cube drawn with all its edges showing, so you can’t tell which face is at the front. It can exist on paper; the man’s cube can’t. Escher in The Palace
Sources differ: which cube is in Belvedere?
- In Belvedere, a drawing of a Necker cube lies on the floor; the man on the bench holds an impossible cube. Escher in The Palace
- A 2020 study instead names the Necker cube as the impossible structure in Belvedere. J. Imaging, 2020
- Michael Bach points out that an impossible figure is a different thing from the Necker cube’s flipping, though he finds his impossible version even less stable. Michael Bach
The Necker cube flips because it is ambiguous; the impossible cube can’t be built at all. There is more about the Necker cube on the brain page.
The trick, in words
In our drawing, eleven of the twelve beams sit where they should. Only one place is wrong: where a beam at the back crosses a beam at the front, we drew the back one on top. Your eye checks the corners one at a time, and each corner looks fine.
With an impossible object, every corner makes sense on its own. The trouble is that the corners combine viewpoints that can’t all be true at once. Michael Bach
Next: Oscar Reutersvärd →