High Quality Content by WIKIPEDIA articles! In geometry, a tiling is a family of shapes – called tiles – that cover the plane (or any other geometric setting) without gaps or overlaps. Such a tiling might be composed from a single fundamental unit or primitive cell and is then called periodic. An example of such a tiling is shown in the diagram to the right (see the image description for more information). Every periodic tiling has a primitive cell that can generate it. A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles can be called aperiodic tilings.