"The Hat": A New 13-Sided Shape Solves Long-Standing Math Problem.

Mathematicians have created a new 13-sided polygon called "the hat" that can tile a plane without creating a repeating pattern, similar to the Penrose configuration. The hat is unique in that it only requires one prototile, called an "einstein," which was previously only theoretical. The shape is actually a polykite made up of eight kites connected at their edges. The researchers have pre-published their paper on Cornell University's arXiv repository and have a dedicated webpage with more information and sample images.