Mathematicians Discover New Shapes and Patterns

Mathematicians have identified a 13-sided shape called "the hat" that can tile a surface without repeating, making it an aperiodic monotile. The hat is a polykite shape consisting of eight kites connected at their edges. The existence of an aperiodic monotile was purely theoretical until a research team led by mathematician David Smith and colleagues proved its existence in a preprint paper posted online this month. The discovery appears to answer a long-standing question in the field of geometry.