Before 2023, the question, “Is there a single tile that only tiles the plane non-periodically?” had no known answer.

We now know the answer is “Yes!” and you can hold an example in your hands.

These tiles are laser cut from solid American walnut, stained a lovely blue on one side, and protected with a layer of clear coat. They are beautiful to look at, and satisfying to hold.

Discovered by an international team of professional and amateur mathematicians (Smith, Myers, Kaplan, and Goodman-Strauss), the tiling made by the hat tiles grows in stages, from one tile (stage 0), to four (stage 1), then thirty-one tiles at stage 2. This set includes enough tiles to build stage 2.

You can learn much more about these aperiodic monotiles by reading the published paper, and you can learn even more by pairing these gorgeous tiles with the beautiful ideas laid out there.