1-1-3-3M

Rotate the upper right cell of the tile 90 degrees clockwise; mirror, then rotate the lower left cell of the tile 270 degrees counterclockwise; rotate the lower right cell of the tile 90 degrees clockwise. [download id="16089"] Shape 6 Shape 7 Shape 8 Shape 227

Rotate the upper right cell of the tile 90 degrees clockwise; mirror, then rotate the lower left cell of the tile 270 degrees counterclockwise; mirror, then rotate the lower right cell of the tile 90 degrees counterclockwise. [download id="16116"] Shape 50 Shape 126 Shape 230 Shape 231 Shape 232

Rotate the lower right cell of the tile 270 degrees clockwise. Shape 7 Shape 54 Shape 59 Shape 60

Rotate the upper right cell of the tile 90 degrees clockwise; mirror the lower left cell of the tile; rotate the lower right cell of the tile 180 degrees. [download id="15923"] Shape 27 Shape 126 Shape 184 Shape 192

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…