Draw an impossible triangle
Four steps, a sheet of dot paper and a pencil. Or use the drawing pad below.
Why dot paper?
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
Isometric dot paper has its dots in a triangle grid, so the three directions of a cube’s edges are already laid out for you. Our drawings on this site are made the same way: every edge of the triangle runs along a line of dots.
Draw the outline
Step 1: the outline. Every edge follows the dots.Drawing: our own Draw the hole
Step 2: the triangular hole in the middle.Drawing: our own Add the face lines
Step 3: the lines that split each bar into faces. Each corner is a normal right angle.Drawing: our own Shade three tones
Step 4: shade the faces: light on top, mid and dark on the two sides. Done.Drawing: our own
Our drawing points sideways to fit the dot grid. Turn your paper round and it points up.
The drawing pad
Tap a dot to start a line, then tap where it ends. Keep tapping to carry on from there; tap the same dot twice to lift your pencil.
Tap a dot to start a line. (Needs JavaScript.)
Now try these
- A longer triangle. Make each bar one dot longer. It still works: the trick is in the corners, not the length.
- Four sides. There are impossible figures with four sides and more, too. Illusions Index
- A cube chain. Draw it as a row of small cubes, as Reutersvärd did. In 1934, aged only 18, he drew an impossible triangle while sketching cubes in perspective. Escher in The Palace
- A devil’s fork. Follow Michael Bach’s three steps on the fork page.
Our tip: draw lightly first. The outline is easy; the face lines are where most people go wrong, and an eraser is your best friend. Useless agrees.
Next: play the games →