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World 2 · Tiling the Plane · 14 min · PRO

The 17 wallpaper groups (and Penrose)

Every repeating pattern in the plane belongs to one of 17 types

PRO · Symmetry & Fractals

World 2: Tiling the Plane is part of PRO

The first world of Symmetry & Fractals is free. PRO opens the other 24 lessons in 6 worlds — simulations, quizzes and all.

  • Regular tilings: why only three?
  • Mixing shapes: semi-regular tilings
  • Escher-style tilings
  • The five Platonic solids
  • All the rotations of a cube
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← Escher-style tilingsThe five Platonic solids →

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