Penrose Triangle

What is happening

Three square beams seem to join at right angles and close into a triangular loop. Cover the corners one at a time and each one looks like a perfectly ordinary solid. Look at the whole, though, and three right angles close a loop — something no real object can do.

Why it looks this way

The picture shows a solid that can actually be built. It is an L-shaped beam made of cubes laid out sideways, then backwards, then upwards, and the first and last cubes are really far apart. Seen from exactly one direction, diagonally from above, the last cube lands just below the first one in the picture, so the two ends seem to touch.

We read two surfaces that touch in a picture as surfaces that touch in space. A flat picture does not record distance in depth, so a near end and a far end that happen to overlap look the same. Each corner makes sense on its own; the contradiction only appears when you connect them all.

How to check

The answer view turns the same solid sideways. The two cubes painted orange are the ends that seemed to join in the normal view. Turned, they sit at different heights and depths, and the loop is open. The same trick also draws a staircase that climbs forever.

Try the Penrose stairs too

For reference: Penrose triangle (Wikipedia). The figure here is an original implementation.

First described

After Oscar Reutersvärd, 1934

The Swedish artist drew it first, out of stacked cubes. Lionel and Roger Penrose made it famous as an "impossible object" in 1958.

See it in the timeline