Escher’s Tricks

Design your own tile

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Translation trick: deform a pair of opposite edges with the same curve.
• Rotation tricks: S-curves about edge midpoints, or curves rotated about corners.
• A tile made this way keeps the area of the original lattice cell.

Steps

1. Bump and dent
2. Opposite sides
3. Turning tricks
4. How many lizards?
5. Which base shape?
6. Area never changes