The vampire einstein

Researchers discover a single shape that tiles the plane aperiodically without reflection By Joe Petrik Cheriton School of Computer Science Just months ago, an international team of four that includes Cheriton School of Computer Science 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. "Our first paper solved the einstein problem, but as the shape required reflection to tile aperiodically people raised a legitimate question: Is there a shape that can do what the hat does but without reflection," Kaplan explains.