Impossible Shapes
Print impossible shapes: figures that look solid but could never be built. Pick one of our 12 figures: the impossible triangle, square, pentagon, hexagon, heptagon and octagon, their left-hand mirror twins, a triangle of cubes in the style of Oscar Reutersvärd, and the impossible cube in two looks. Print it shaded in three tones or as an outline to colour in, at an exact size, as a sheet of copies, as a 4-step how-to-draw worksheet, or all figures on one page. Download a PDF on US Letter or A4, a 300 DPI PNG or an SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). The how-to-draw sheet builds the figure in four steps, each drawn from the finished figure, so you can copy it line by line.
Figure
Colours and lines
Page
Runs in your browser with our own code: nothing you type is uploaded or saved. The figures are our own drawings. You may use what you make here, including commercially, with no credit needed.
How to print impossible shapes
- Pick a figure.
- For the flat figures, set the bar width.
- Choose shaded or outline, and the three colours.
- Choose one figure, how-to-draw steps, a sheet or all figures on one page.
- Download the PDF and print at 100% (Actual size).
What you can use it for
- Art lessons on shading and perspective
- Drawing practice: copy each step
- Optical illusion colouring pages
- Maths and psychology class handouts
- Posters, stickers and SVG designs for cutters
- Puzzle hunts and escape rooms
The 12 figures
| Figure | Drawn as | Faces | Lines | Lines in steps 1 / 2 / 3 |
|---|---|---|---|---|
| Impossible triangle (Penrose triangle) | Flat bars, three tones | 3 | 9 | 3 / 6 / 9 |
| Impossible triangle, left-hand twist | Flat bars, three tones | 3 | 9 | 3 / 6 / 9 |
| Impossible square | Flat bars, three tones | 4 | 12 | 4 / 8 / 12 |
| Impossible square, left-hand twist | Flat bars, three tones | 4 | 12 | 4 / 8 / 12 |
| Impossible pentagon | Flat bars, three tones | 5 | 16 | 5 / 11 / 16 |
| Impossible pentagon, left-hand twist | Flat bars, three tones | 5 | 16 | 5 / 11 / 16 |
| Impossible hexagon | Flat bars, three tones | 6 | 19 | 6 / 13 / 19 |
| Impossible heptagon | Flat bars, three tones | 7 | 21 | 7 / 14 / 21 |
| Impossible octagon | Flat bars, three tones | 8 | 24 | 8 / 16 / 24 |
| Triangle of cubes (after Reutersvärd) | Isometric cubes | 30 | 31 | 9 / 18 / 31 |
| Impossible cube | Isometric cubes | 18 | 41 | 26 / 36 / 41 |
| Impossible cube of blocks | Isometric cubes | 95 | 81 | 27 / 51 / 81 |
All are our own drawings, built by our own code. Our tests check every face: a closed outline that never crosses itself, no two faces overlapping, one shade per face direction, and every line drawn exactly once.
What prints
| Download | What is in it |
|---|---|
| Every page at real size, vector: faces, lines, step captions and the size bar | |
| PNG 300 DPI | One picture per page (a ZIP when there are several) |
| SVG | The page on screen at real size, with faces and lines in separate groups |
Layouts
| Layout | What you get |
|---|---|
| One figure | Centred at the width you type |
| How to draw | Four panels, each step adding lines, the last one shaded |
| As many as fit | A sheet of copies at the width you type |
| All figures | Every figure with its name on one page |
Every page has a 1 in (or 2 cm) bar at the bottom to check the print is at 100%. To build your own cube figures, use the Isometric Drawing Tool, or print Isometric Graph Paper to practise.
Which tool to use
| You want | Use |
|---|---|
| Ready impossible figures and drawing steps | Impossible Shapes (this page) |
| Your own cube drawings | Isometric Drawing Tool |
| Flat optical illusion patterns | Op Art Generator |
| The Penrose kite and dart tiling | Penrose Tiling Generator |
More illusions and geometry: the Op Art Generator, the Penrose Tiling Generator and the Tessellation Maker.
More free tools
Geometry, illusions and drawing?
Drawing and print tools that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What are impossible shapes?
Drawings of solid objects that cannot exist in three dimensions. Every part looks correct, but the parts contradict each other: a face that turns into another face, or a beam that is in front at one end and behind at the other.
Which impossible shapes are here?
12 figures: the impossible triangle (Penrose triangle), square, pentagon, hexagon, heptagon and octagon, mirror twins of the triangle, square and pentagon, a triangle of cubes after Oscar Reutersvärd, and the impossible cube drawn with beams and with blocks. The table below lists them.
Who invented the impossible triangle?
The Swedish artist Oscar Reutersvärd drew the first one in 1934, as a triangle of cubes. Lionel Penrose and his son, the mathematician Roger Penrose, found it again on their own and published it in 1958 in the British Journal of Psychology, in a paper called Impossible objects: a special type of visual illusion. That is why it is also called the Penrose triangle or tribar.
How does an impossible polygon work?
Each side is a bar showing two faces. At every corner, the face on the outside of one bar turns onto the inside of the next bar. Going round, you never get back to the face you started on, so the frame cannot be solid.
How does the impossible cube work?
It is a cube frame drawn in isometric view, with one upright beam drawn in front of the beams it should pass behind. Every corner looks normal; the crossing is what cannot happen.
How do the how-to-draw steps work?
Each step adds lines to the one before, and the last step is the finished figure, line for line. For the flat figures: the outside edges, then the inside edges, then the middle lines that switch beams, then the shading.
Why are Penrose stairs and the impossible fork not here?
We only print figures whose every face we can draw and test exactly. Those two need curved or hand-faked parts, so we left them out for now.
Can I colour them in?
Yes. Choose Outline only: the faces print white with black lines.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. The figures are drawn by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.