1-1-1M-3M

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 270 degrees clockwise. [download id="15929"] Shape 16 Shape 54 Shape 68 Shape 200

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 the lower right cell of the tile. [download id="16108"] Shape 6 Shape 215 Shape 228 Shape 229

Rotate the upper right cell of the tile 90 degrees clockwise; mirror, then rotate the lower left cell of the tile 180 degrees; rotate the lower right cell of the tile 90 degrees clockwise. [download id="16029"] Shape 7 Shape 15 Shape 48 Shape 54 Shape 97

Mirror, then rotate the lower left cell of the tile 180 degrees; rotate the lower right cell of the tile 180 degrees. Shape 20 Shape 54 Shape 73 Shape 83

Rotate the upper right cell of the tile 90 degrees clockwise; mirror, then rotate the lower left cell of the tile 180 degrees; mirror, then rotate the lower right cell of the tile 90 degrees counterclockwise. [download id="16059"] Shape 27 Shape 126 Shape 222

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…