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The twenty-eight patterns you’ve just seen are Regular tessellations — symmetrical, orderly, each one a mirror of itself in some direction. They are, in their way, perfect.

But perfection accounts for only twenty-eight of the five hundred and twelve possible patterns this system can generate.

What about the other four hundred and eighty-four?

They don’t follow the rules of mathematical symmetry. No rotation, reflection, or glide will map them onto themselves. By the strict definition, they are Irregular — imperfect.

And yet every one of them tessellates. Every one of them tiles a surface without gaps or overlaps, repeating endlessly in every direction. They are not lesser patterns. They are simply less constrained ones.

This is where things get interesting.

Rotate the lower right cell of the tile 90 degrees clockwise.

1-1-1-2 (6 downloads )