The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. In mid-November of ...

The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, ...