There are only 15 possible pentagonal tiles, research proves
(PHYSorg.com Mathematics)

Tiling the plane with a single pattern is a mathematical problem that has interested humans since Antiquity, notably for the aesthetic quality of tiles in mosaics or tiling. One of the unresolved problems in this field that has been puzzling the scientific community since 1918 has now been definitively resolved thanks to Michaël Rao of the Laboratoire d`informatique du parallélisme (CNRS/Inria/ENS de Lyon/Université Claude Bernard Lyon 1). Using computing tools he was able to demonstrate that there are only 15 five-sided patterns that can tile the plane. The research is now available on the Arxiv website.