Challenge

Build Tilings & Tessellations

Graphic of Penrose aperiodic pentagonal tiling in black, white and turquoise
Penrose aperiodic pentagonal tiling. ExaPlex Image CC BY-NC

Build connected shapes that fill the plane with no gaps or overlaps.

  • How many different tiling patterns can be made with regular polygons? How many categories of tilings are there?
  • Who is Johannes Kepler? How did he connect tessellation to other patterns he saw in nature?
  • What are Girih tiles? Where are the earliest surviving examples of this form of decoration?
  • Who is Roger Penrose? How did he tile the plane with pentagonal shapes?
  • What is aperiodicity? What are quasicrystals and what properties do they have?
  • What are emergent systems? How is Penrose tiling an example of an emergent system?

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