A note on aperiodic Ammann tiles (Q715004)

The Ammann Tiles A2, also known as Ammann Chairs, are a well known example of an aperiodic prototile set with two tiles. The tiles, together with some local (or matching) rules, allow tilings of the plane that everywhere obey the local rules, but none of these tilings possesses a non-trivial translation symmetry. In fact, there are several local rules known that make the Ammann Chairs into an aperiodic prototile set. Some of them are just edge-to-edge rules, formulated via some artificial vertices on the tiles. All of them had to use `potential' vertices so far, which might be there or not, depending on the local configuration. Strictly speaking, this increases the number of prototiles needed. Here, the author introduces pseudo-vertices (which are always there) and gives a simple edge-to-edge rule that turn the Ammann Chairs into an aperiodic prototile set by just requiring that tiles have to meet edge-to-edge (and vertex-to-vertex).