In his free time, David Smith designs tiles. More specifically, the retired print technician and recreational mathematician pieces together as many tiles as he can (no gaps allowed) before the pattern either repeats or cannot continue.
Until recently, every shape anyone had ever tested met one of those two fates — despite the scrutiny of many brilliant minds over the past 50 years. Then, one day last November, Smith found the only known exception.
Using an app called PolyForm Puzzle Solver, Smith constructed a jagged, 13-sided shape. Vaguely reminiscent of a top hat, he began filling the screen with copies of it. They joined seamlessly and, to his surprise, without repeating.
“The tessellations were something I had not seen before,” he says.
Keen to investigate further, he cut out dozens of paper copies and started fresh. One after another, the tiles kept falling into place. They invited him deeper into ...
