Mixing Polygons

Semi-regular tilings

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Semi-regular tilings use several regular polygons with the same arrangement at every corner.
• Notation like 4.8.8 lists the polygons around a corner.
• There are exactly 8 semi-regular tilings. Angles summing to 360° is necessary, but not sufficient.

Steps

1. Octagons and squares
2. Check the corner
3. Fill the gap
4. Build a corner
5. How many?
6. Complete the vertex
7. Triangles and 12-gons