Why Do Shapes Tile the Plane So Differently?

Imagine you're playing with building blocks. Some of them fit together like puzzle pieces, no gaps or overlaps, and they repeat to cover the whole floor. Other shapes don't do that, leaving spaces or causing piles. This is plane tiling, where certain shapes can cover a flat surface perfectly without any issues.

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Examples

  1. A kitchen floor with square tiles
  2. Bathroom tiles shaped like hexagons
  3. Puzzle pieces forming a big picture

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Categories: Math · geometry· tiling· patterns· mathematics