Amman has cut up the Penrose Rhombs to make 3 convex tiles that tile aperiodically. Recall that the kite and dart, as well as the rhombs, are only forced to tile aperiodically if they are either altered or if some sort of matching rules are applied.
It is unknown whether there is an aperiodic convex set with fewer than three tiles. Perhaps a related question is whether there are any undiscovered tilings by convex pentagons.
Aperiodic Tiling and Penrose Tiles Tiling Plane and Fancy Tiling references Tiling links