Scientists solve The Keller conjecture, posed by German mathematician Eduard Ott-Heinrich Keller,... has to do with tiling—specifically, how to cover an area with equal-size tiles without any gaps or overlap. The conjecture is that at least two of the tiles will have to share an edge and that this is true for spaces of every dimension
https://phys.org/news/2020-10-scientists-year-old-geometry-problem.html