EXAMPLE 4 Tiling Using a Triangle

How can you make an Escher-like tiling by starting from a triangle?

Modify half of one side of the triangle, then rotate that modified half side around the midpoint of the side to extend the modification to the rest of the side, thereby making the new side centrosymmetric. Then you can do the same to the second and third sides (Figure 20.18).

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Figure 20.18: Figure 20.18 How to make an Escher-like tiling by translations and halfturns, using a scalene triangle base.