Regular Tilings

Why only three polygons work

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

• In a tiling, the angles meeting at each corner add up to 360°.
• Regular $n$-gon interior angle: $\frac{(n-2) \cdot 180°}{n}$.
• Only triangles, squares and hexagons tile on their own.

Steps

1. Meeting at a point
2. Interior angles
3. Which polygon?
4. Too little, too much
5. A twelve-sided corner
6. Why hexagons?