Stairs that never end
Climb all the way round and you arrive back where you started, still climbing.
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.
Up for ever
The Penroses’ 1958 article included a drawing and a 3D model of a continuous flight of stairs that seems to lead up, or down, for ever. Escher in The Palace
Roger’s father Lionel, an expert in genetics and mathematics, built some models from Roger’s drawings. Escher in The Palace
Who drew them first?
He designed an impossible staircase in 1937. Escher in The Palace His early discoveries stayed hidden for decades: Roger Penrose only found out in 1984 that Reutersvärd had drawn the triangle and the stairs first. Escher in The Palace
Escher’s monks
The Penrose article sparked the idea, and he started work in late 1959. Escher in The Palace Escher finished Ascending and Descending on 18 March 1960. Escher in The Palace
In a letter to his son Arthur, Escher described the staircase as a sealed ring, “like a snake eating its own tail”. Escher in The Palace
In his own book, Escher imagined the people on the stairs as monks of some unknown sect, climbing for a few hours a day as a ritual duty. Escher in The Palace Two “recalcitrant individuals” refuse to take part. Escher in The Palace
Read more on our Escher page, where we describe the print in words.
How the drawing works
In our drawing every step is a real block, and every block is a little lower than the one before. The ring of steps is not closed in 3D: it is a spiral, and we chose a viewpoint from which its two ends line up exactly, one behind the other. That is the same trick as the open triangle on the triangle page.
Our view: the stairs are the most “lived-in” impossible object. You can imagine climbing them, which is exactly why they feel so wrong.
On screen
The Penrose stairs appear in Christopher Nolan’s 2010 film Inception. Escher in The Palace
Lionel Penrose sent Escher their Christmas puzzle page, “Puzzles for Christmas”. Escher in The Palace
Next: the devil’s fork →