Every Quadrilateral Tiles

Even the lopsided ones

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

• Every triangle and every quadrilateral (even a dart) tiles the plane.
• A quadrilateral’s angles add to 360°, so all four meet at each corner.
• Exactly 15 families of convex pentagons tile (complete in 2017); no convex 7-gon does.

Steps

1. Any triangle
2. Any quadrilateral
3. Why it works
4. The pentagon hunt
5. Seven sides
6. Corners of the tiling