Impossible objects: shapes you can draw but never build.
The Penrose triangle and the never-ending stairs, the devil’s fork and the impossible cube; the Swedish artist who drew thousands of them, the three Escher prints built on them, why your brain falls for them, a 13.5-metre one you can visit, and how to draw your own. Every fact is linked to its source.
The short version
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
Your brain builds a 3D model of the world from the flat image on the back of your eye. Michael Bach
Cognitive scientists ask why we keep seeing an impossible figure as a real object even after we know it can’t exist. Illusions Index One standard answer is that parts of the visual system are “cognitively impenetrable”: knowing better doesn’t change what they output. Illusions Index
Sources don’t always agree on who drew what first, or on the details of the Perth sculpture. Where they differ, we show each version side by side.
Explore
Escher, in words
Belvedere, Waterfall and Ascending and Descending are based on three impossible figures: a cube, a triangle and a staircase. Escher in The Palace
We describe Belvedere, Ascending and Descending and Waterfall in words and link to the Escher museum’s own pages for the pictures.
A real one
The Impossible Triangle in East Perth, Western Australia, is by the artist Brian McKay and the architect Ahmad Abas. DENMAC The local art trail says the triangle was devised by Sir Roger Penrose in the 1950s, and that there are only two spots from which it looks complete. Claisebrook Art Trail
See it on the real impossible objects page.
Draw one, then play
A step-by-step guide to drawing an impossible triangle on dot paper, with a drawing pad that works on your phone; then a possible-or-impossible game, a 12-question quiz, myth or fact, and a toy where you turn a real object until it becomes impossible.
More from the family: lines that are the same length but refuse to look it, the moon illusion and the Ames room are on size.illusions.im; every illusion site is listed at illusions.im.