One can easily devise a tiling with a single pentagon surrounded by triangles. While the complete set of tiles is aperiodic, the triangles can tile the plane periodically, so this example is not a valid aperiodic tiling. All known aperiodic tilings are based on shapes that can also tile the plane periodically. An obvious method of forcing tiles to go together in certain ways is to put notches and tabs of various shapes along the edges. The Robinson Tiles shown below use this approach.
Key tiles allow more versatility in matching tiles than notches and tabs.
The Ammann Tiling shown below under Composition uses this approach. In such cases, patterns can be drawn on the tiles, with the rule that patterns must match across tile edges. This approach is commonly used with Penrose Tilings. A variation on this technique is Ammann Bars, lines that continue straight across tile edges. For a long time it was believed that all sets of tiles that covered the plane must tile periodically, but in 1964 Robert Berger found a set of tiles that do not.