One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Tiles are a popular choice for many homeowners due to their durability and aesthetic appeal. Whether in the kitchen, bathroom, or living room, tile floors, backsplashes, and walls can provide a ...

Proving the “discrete” periodic tiling conjecture for high-dimensional lattices is a slightly different problem than proving the continuous version of the conjecture, as there are tilings that are ...