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For each set of patterns I had to start with a regular polygon, and divide it up into several smaller shapes. I then used these shapes as tiles to construct six different patterns, demonstrating maximum diversity from a minimum inventory.
Yawn.
For this pattern, I had to create a non-repeating (or aperiodic) tiling, made from only two shapes, a 'kite' and a 'dart', using a set of very specific construction rules.
The pattern might look like it repeats, but trust me, it doesn't.