Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets

Simple quasiperiodic tilings with 8-fold and 12-fold symmetry are presented that possess local de-/inflation symmetry and perfect matching rules. The special feature of these tilings is that the full information is already derivable from the set of vertex sites alone. This means that the latter is a valid representative of the corresponding equivalence class of mutual local derivability