Possible or impossible?
Spot the impossible ones, turn a real object until it becomes impossible, then test yourself.
How to play. Pick an answer and the fact behind it appears, with a link to where it comes from. Without JavaScript, open “Show the answer” under each question.
Possible or impossible?
Eight drawings, all our own. Could each one be built as a real, solid object, seen just as it is drawn?
1 Possible or impossible?
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Impossible. Each corner is a normal right angle, but the bottom bar is drawn both in front of and behind the top corner. The impossible triangle could only exist if the rules of Euclidean geometry were broken: its bottom bar is drawn both in front of and behind the top corner. Illusions Index
2 Possible or impossible?
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Possible. This is the same shape you see as an impossible triangle, seen from a different spot. The gap shows: it is three joined struts. In 1968 Richard Gregory made a wooden object that looks like a real impossible triangle from one position only; from anywhere else it is clearly three joined struts. Illusions Index
3 Possible or impossible?
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Possible. A cube drawn with every edge showing can exist; here the front edges are drawn in front. 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
4 Possible or impossible?
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Impossible. A back edge crosses in front of a front edge: the impossible cube held by the man in Belvedere works like this. 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
5 Possible or impossible?
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Possible. Every beam sits where it should; a carpenter could make this one. Escher’s Belvedere cube is the impossible version. Of his three famous impossible prints, Escher invented the figure for Belvedere himself: an impossible cube. Escher in The Palace
6 Possible or impossible?
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Impossible. A back upright crosses in front of a front top beam. That only works on paper. Of his three famous impossible prints, Escher invented the figure for Belvedere himself: an impossible cube. Escher in The Palace
7 Possible or impossible?
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Impossible. Three prongs at one end, two at the other. At one end it seems to have three prongs; at the other, only two. Illusions Index
8 Possible or impossible?
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Impossible. Every step looks higher than the last, yet the loop closes. 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
Find the angle
This is a real object: three straight bars and a gap. Turn it with the slider and find the one viewpoint from which it becomes an impossible triangle. The minister said it can only be fully appreciated by moving around it to watch the shape change and the illusion appear. WA Government, 1999
Needs JavaScript: turn the slider to walk round the object.
The impossible objects quiz
1 Which is another name for the Penrose triangle?
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The tribar. The Penrose triangle is also called the tribar, the impossible tribar or the impossible triangle. MathWorld
2 In which journal did Lionel and Roger Penrose publish their impossible figures in 1958?
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The British Journal of Psychology. Lionel and Roger Penrose published it in the British Journal of Psychology, volume 49, in February 1958. Escher in The Palace
3 How old was Oscar Reutersvärd when he drew his first impossible triangle in 1934?
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18. In 1934, aged only 18, he drew an impossible triangle while sketching cubes in perspective. Escher in The Palace
4 Which projection did Reutersvärd always use?
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Isometric, with parallel lines. He always used the same isometric projection, where the lines of perspective stay parallel and never meet at a vanishing point. Escher in The Palace
5 What did Mad magazine call the devil’s fork?
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The poiuyt. Mad magazine made it a running joke, calling it the “poiuyt”: the third row of a keyboard typed from right to left. MathWorld
6 Which impossible figure did Escher invent himself, for Belvedere?
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The cube. Of his three famous impossible prints, Escher invented the figure for Belvedere himself: an impossible cube. Escher in The Palace
7 Waterfall’s water channel is built from which figure?
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Three Penrose triple bars. Waterfall’s water channel is built from three Penrose triple bars combined. Escher in The Palace
8 How often does a Necker cube typically flip, says Michael Bach?
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Every 3 to 5 seconds. Stare at a Necker cube and it suddenly flips between two orientations, typically every 3 to 5 seconds. Michael Bach
9 How tall is the Impossible Triangle in East Perth?
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13.5 m. It stands 13.5 metres high. DENMAC
10 In which film do the Penrose stairs appear?
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Inception. The Penrose stairs appear in Christopher Nolan’s 2010 film Inception. Escher in The Palace
11 Who made the 1754 engraving Satire on False Perspective?
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William Hogarth. Bach lists Josef Albers’s “Rolled Wrongly” from 1931 and Hogarth’s Satire on False Perspective from 1754. Michael Bach
12 Where was the Escher exhibition that Roger Penrose visited in 1954?
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The Stedelijk Museum, Amsterdam. Escher’s solo exhibition at the Stedelijk Museum ran from 27 August to 26 September 1954. Escher in The Palace The Penroses came up with the triple bar after Roger Penrose visited Escher’s one-man show at the Stedelijk Museum in 1954. Escher in The Palace
Myth or fact?
Eight statements. Some are true, some are myths.
1 Roger Penrose drew the impossible triangle before anyone else.
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Myth. Oscar Reutersvärd had drawn the shape earlier, though the Penroses didn’t know. Escher in The Palace In 1934, aged only 18, he drew an impossible triangle while sketching cubes in perspective. Escher in The Palace
2 Every corner of an impossible triangle makes sense on its own.
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Fact. 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
3 Once you know a figure is impossible, you stop seeing it as a solid object.
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Myth. 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
4 A real Penrose triangle sculpture has been built in Australia.
5 Escher was top of his class in mathematics.
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Myth. He did not excel at mathematics at school. Britannica
6 The devil’s fork seems to have three prongs at one end and two at the other.
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Fact. At one end it seems to have three prongs; at the other, only two. Illusions Index
7 The Necker cube is an impossible object.
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Myth. 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 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
8 Escher finished Ascending and Descending in 1960.
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Fact. Escher finished Ascending and Descending on 18 March 1960. Escher in The Palace
Want more? There is a Necker cube flip timer on the brain page and a drawing pad on the draw page.