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Einstein Tiling

A tiling is a shape--or series of shapes--that repeats to fill space, such as a hexagon or square. An aperiodic tiling is a shape that does so without the pattern ever being the same.

This tiling, the first of its kind, is an "Einstein" tiling (cleverly meaning "one stone"). Called the "Hat" for its loose resemblance to a fedora; this shape, revealed by discoverer David Smith just a few days ago, is the first tiling ever discovered that:
A--doesn't repeat, and
B--is made from only one shape.

To make it work, some of the tiles have to be mirrored (the ones in green), meaning the search is still on for a true non-repeating, non-mirrored, one-shape tiling. Still, this is a major achievement for mathematics--and possibly other fields as well. The first 2-tile aperiodic tiling, the Penrose tiling, was later discovered to already exist in nature in the crystal structure of aluminum. Who knows where the Hat tiling could show up?

The Hat tiling is part of an infinite family of tilings with the same topology. The two endpoints of the family, called the Chevron and the Comet, can tile the plane periodically. The infinite series of Hats between them, however, MUST tile the plane aperiodically, making them a true Einstein tiling.

The 3-d shape in this workshop item features low friction and a tapered collision hull for easy assembly.