Let’s Tessellate

One of the things I enjoy about parquetry is the challenge that comes with client requests for new patterns. This is usually in the form of a diagram of something that someone has seen and thinks is cool. One challenge is confirming that the design will work.  Is it practical to manufacture? All makers know that just because someone can render it, doesn’t mean that it can be made. There are things that won’t work, so it is necessary to discuss with the client, usually through a third party in our case, necessary modifications to facilitate manufacture.

A more interesting challenge it to make sure the pattern can be tessellated.  Nobody can afford to have people on site fitting together small pieces of wood. Can the pieces be made into a practical sized tile that fits together and can be tiled infinitely? I usually do this on CAD. Normally it is not difficult, but sometimes it is a challenge to find a nice repeating pattern within the floor than can be made and which will fit together easily at installation. In this case I was too busy and had Xiao May in my office put this together and then cut up some duplicates to make sure it would work.

Tile tessellations are a very ancient art and some aspects are also a difficult mathematical challenge. A question that has puzzled geometers for centuries is whether there is a tile shape that can fit together, but never repeats? Put another way, if you were to continue to tile in a plane using one basic unit, is it possible that no larger units would emerge? This is known as the Einstein Tile Problem. Einstein in this case is not referring directly to Albert, but rather to “One Stone”, cleverly using Albert’s surname to suggest a high level of difficulty. Incredibly, the Einstein Problem was solved a couple of years ago by a retired postal worker in the UK, whose very ordinary name, David Smith, deserves to be remembered. His tile is a hat-shaped object that fits together and does the trick of never forming into a second repeatable unit. Look it up!