A 15-hexagon shape reportedly covers 251 of 254 cells in a fifth ring

A post describes Heinrich Heesch’s 1968 question: How many rings of copies can surround a shape that cannot tile a floor forever? It says a 15-hexagon shape completes four rings and covers 251 of the fifth ring’s 254 cells, but a machine-checked proof rules out finishing that ring with this shape. Researchers and contributors are publicly testing candidates, with humans and AI agents taking shots at the problem, according to the post.