Fundamental aperiodic tesselations
Here are diagrams of some of the most basic aperiodic tesselations
Most of the work on aperiodic tesselations has ignored the basic tesselations -
apparently on the grounds that finding tiles that can cover the plane
periodically (as well as aperiodically) is trivial.
However, these are the sorts of tiling patterns that are more likely to be
on interest to those involved with crystal structures.