Mathematicians have finally discovered an elusive ‘einstein’ tile

A 13-sided shape called ‘the hat’ forms a pattern that never repeats

An image of several dark blue, gray, white, and light blue, 13-sided tiles interconnected.

A 13-sided tile called “the hat” forms a pattern that covers an infinite plane yet it cannot repeat, making it a long-sought shape known as an “einstein.” A sample of that pattern is shown here.

D. Smith, J.S. Myers, C.S. Kaplan and C. Goodman-Strauss (CC BY 4.0)

A 13-sided shape known as “the hat” has mathematicians tipping their caps.