Craig Kaplan's team finds "vampire" einstein

Wednesday, July 5, 2023

A 13-sided shape is tiled across a plane in a pattern of green and white

Just months ago, an international team of four that includes Cheriton School of Computer Science professor Dr. Craig Kaplan discovered a single shape that tiles the plane — an infinite, two-dimensional surface — in a pattern that can never be made to repeat.

The discovery mesmerized mathematicians, tiling enthusiasts and the public alike.

The shape, a 13-sided polygon they called “the hat,” is known to mathematicians as an aperiodic monotile or an “einstein,” the German words that mean “one stone.”

But the team’s most recent discovery has raised the bar once again. They found another shape, related to the first, that meets an even stricter definition. Dubbed the “spectre,” the new shape tiles a plane in a pattern that never repeats without the use of mirror images of the shape. For this reason, it has also been called a “vampire einstein” — a shape that tiles aperiodically without requiring its reflection.

Read the full story from Waterloo News.