A nonperiodic tiling is a tiling that is not invariant under any nonzero translation. Nonperiodicity is a property of a particular arrangement. An aperiodic tiling satisfies the stronger condition that arbitrarily large periodic patches do not occur. Thus, every aperiodic tiling is nonperiodic, but the converse need not hold. A nonperiodic tiling may contain arbitrarily large periodic patches, and its tiles may also form a periodic tiling.
The quaquaversal tiling is a three-dimensional nonperiodic tiling whose unmarked tile can also fill space periodically (Conway and Radin 1998, Radin 2021).
