The orientation-dependence of the diffraction patterns of the transmission grating experiments have been systematically studied by rotating the 1D- and 2D-gratings around three axes. There are two kinds of gratings, transmission and reflective gratings. In this article, we show the novel phenomena: (1) the transmission grating creates simultaneously both the transmission diffraction pattern and the reflective diffraction pattern respectively, namely the transmission grating functions as both a transmission grating and a reflective grating in one experiment; (2) the reflective pattern is non-uniform, expanded, curved and inclined when the grating rotates, namely the reflective pattern has the same characteristics as that of the transmission patten in the same transmission grating experiment. We refer both as the “twin patterns” in the same experiment. We suggest to do the grating experiment with the experimental setups in this article by emitting photons one at a time.