Never Repeating

Penrose tiles and the einstein

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

• Penrose tilings use two rhombi and never repeat, with five-fold symmetry.
• Quasicrystals are real materials with Penrose-like order (2011 Nobel Prize).
• In 2023, the single “hat” tile was shown to tile only aperiodically.

Steps

1. Penrose tiling
2. Penrose angles
3. Impossible crystals
4. Fat and thin
5. Why five is forbidden
6. One tile to rule them all