Priebe Frank non PV
A plane substitution tiling which does not possess flc. It arises from the 1-dimensional substitution a -> abbb, b -> a, which inflation factor is not a PV-number. In the last sentence, ‘arises’ is to be understood as follows: Whenever one has a 1-dimensional substitution, it defines a d-dimensional substitution just by taking the Cartesian product. For an example, see Fibonacci times Fibonacci. Then, a 1-dimensional cut through each such d-dimensional tiling along a direction of some edge is the 1-dimensional tiling itself.

Polytopal Tiles
Parallelogram Tiles
Self Similar Substitution