sentences:  Most tiles have a unique pattern of girih inside the tile that are continuous and follow the symmetry of the tile.However, the decagon has two possible girih patterns one of which has only fivefold rather than tenfold rotational symmetry.In 2007, the physicists Peter J. Lu and Paul J. Steinhardt suggested that girih tilings possessed properties consistent with self-similar fractal quasicrystalline tilings such as Penrose tilings, predating them by five centuries.