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Math · Intermediate

Tilings & Patterns

Bathroom floors, honeycombs, Islamic mosaics and Escher prints all solve the same puzzle: covering a flat surface with no gaps or overlaps. Discover why only three regular polygons tile, why five-fold symmetry can't repeat, the seven kinds of frieze, the astonishing tilings that never repeat at all, and how to design your own Escher tile.

7 lessons~35 min0/7 complete
1

Covering the Plane

Regular and semi-regular tilings.

  1. Regular TilingsWhy only three polygons work
  2. Mixing PolygonsSemi-regular tilings
2

Symmetry and Surprise

Repeating and non-repeating patterns.

  1. Symmetries of PatternsWhy there is no five-fold symmetry
  2. Never RepeatingPenrose tiles and the einstein
3

Shapes That Tile

Any quadrilateral, Escher’s tricks and tiling puzzles.

  1. Every Quadrilateral TilesEven the lopsided ones
  2. Escher’s TricksDesign your own tile
  3. Tiling PuzzlesDominoes, colourings and counting