This approach of Pentagonal Persian Patterns is an alternative to the famous PIC theory. However, it turns out that the classification of pattern families and sets of tiles used is close to the one used by (at least some) masters of the art in Iran. A very simple transformation of one of these sets produce a new style of patterns. Then we dissect each tile of a specific set into rhombi, respecting the rules of the Binary tiling (not the Penrose tilling). Thus, applying the concept of X-Tiles to these rhombi, we get an equivalence relation between two families of traditional patterns.