The nonrepeating Smith hat tile created twisting, pinwheel-like light patterns that ordinary quasicrystals do not produce. Its unusual effect comes from combining long-range order with a lack of ...

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 ...

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 ...