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When people talk about patterns that repeat, they usually mean one of the 17 wallpaper groups (https://en.wikipedia.org/wiki/Wallpaper_group). And people are interested in patterns that do tile the grid completely, but don't match one of those patterns. Originally it took thousands, but people had gotten it down to 2 shapes that together tiled the grid completely, but not in one of those 17 groups.

Now, people have gotten it down to a single shape that—by itself—tiles the pattern infinitely, but not in one of those 17 groups.




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