Penrose Triangle
Make the Penrose triangle, also called the impossible triangle or tribar: three straight bars that seem to meet at right angles in a loop that cannot exist. Set the bar width and the exact size in inches or centimetres, pick the three face colours or print the outline to colour in, choose the classic right-hand twist or its mirror, and print one big triangle, a sheet of small ones or a 4-step how-to-draw sheet. 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). Measure the bar at the bottom of the page to check the size. The width is the length of the bottom side, tip to tip.
Triangle
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 make and print a Penrose triangle
- Set the bar width as a percentage of the side.
- Pick the twist, the look (shaded or outline) and the three face colours.
- Choose one triangle, a sheet of them or the how-to-draw steps.
- Set the width in inches or cm and the paper.
- Download the PDF and print at 100% (Actual size), or the SVG for a cutter or a print shop.
What you can use it for
- Art class: drawing and shading an impossible figure
- Optical illusion displays and science fair posters
- Colouring pages and maths club handouts
- Logos, stickers and laser-cut or vinyl-cut designs (SVG)
- Tattoo and embroidery outlines
- Puzzle and escape room props
How the figure is built
Each side of the triangle gets three lines: the outside edge, a middle line and the inside edge. Every face starts on the outside of one bar and, at the corner, turns onto the inside of the next bar. The three faces fit together with no gap and no overlap, and our tests check that every face is a closed outline that never crosses itself and that every line is drawn once.
| Step | What to draw |
|---|---|
| 1 | Draw the outer triangle (the outside edges). |
| 2 | Draw the inside edges: a small triangle with each side running on past one corner. |
| 3 | Draw the middle lines that switch beams at every corner. |
| 4 | Shade each face by the way it points: light, middle, dark. |
Bar width
| Bar width (% of the side) | At 6 in wide | |
|---|---|---|
| 10 % | 15.2 mm | 0.6 in |
| 14 % | 21.3 mm | 0.84 in |
| 18 % | 27.4 mm | 1.08 in |
| 22 % | 33.5 mm | 1.32 in |
| 26 % | 39.6 mm | 1.56 in |
Sizes
| Paper | Largest triangle, portrait | Landscape |
|---|---|---|
| US Letter | 7.5 in (19 cm) | 8 in (20.6 cm) |
| A4 | 7.25 in (18.4 cm) | 7.75 in (19.9 cm) |
| Width | Triangles per US Letter page | Per A4 page |
|---|---|---|
| 1.5 in (38.1 mm) | 24 | 24 |
| 2 in (50.8 mm) | 12 | 15 |
| 3 in (76.2 mm) | 6 | 6 |
| 4 in (101.6 mm) | 2 | 2 |
Every page has a 1 in (or 2 cm) bar at the bottom to check the print is at 100%. For a giant triangle over several sheets, download the SVG and use the Poster Tiler.
What prints
| Download | What is in it |
|---|---|
| Every page at real size, vector: faces, lines 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 |
Which tool to use
| You want | Use |
|---|---|
| The impossible triangle | Penrose Triangle (this page) |
| Shapes drawn on an isometric grid by hand | Isometric Drawing Tool |
| The Penrose kite and dart or rhombus tiling | Penrose Tiling Generator |
| Wavy and warped optical patterns | Op Art Generator |
Different Penrose: the Penrose Tiling Generator makes the aperiodic tiling, not this figure. To draw your own cube figures, try the Isometric Drawing Tool or print Isometric Graph Paper.
More free tools
Geometry, illusions and drawing?
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Frequently asked questions
What is a Penrose triangle?
A drawing of three square bars joined end to end at right angles that seems to form a closed triangle. Each corner looks right on its own, but the three corners cannot all be true at once, so the object cannot be built. It is also called the impossible triangle or tribar.
Is it the same as the impossible triangle?
Yes. Penrose triangle, impossible triangle, Penrose tribar and impossible tribar all name the same figure.
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 do I draw a Penrose triangle?
Draw an equilateral triangle. Draw the inside edges: a smaller triangle the same distance in from every side, with each side running on past one corner. Then draw the middle lines, halfway between: each runs along one side and stops at the next. Shade the three faces light, middle and dark. Choose How to draw to print these steps, each drawn from the finished figure.
Why does it look possible at every corner?
Your eye reads each corner as a normal 90° joint between two bars. Only when you follow a face all the way round do you find it ends on a different face from where it began.
Can a real Penrose triangle be built?
Only as a trick: a sculpture with a gap or a bent bar that looks like the triangle from one exact viewpoint. The Impossible Triangle sculpture in East Perth, Australia (1999) works this way.
What does the bar width change?
How thick the three bars are, as a percentage of the side. Thin bars (10 %) look like a wire frame; thick bars (22 to 26 %) leave a small hole in the middle. The table below gives the bar width at 6 in.
What is the twist?
Right-hand is the usual figure. Left-hand is its mirror image: the faces wrap round the other way.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. The figure is drawn by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.