Vertical nanorod assembly over three dimensions is shown to result. In the formation of Moire interference patterns arising from rotational offsets between respective monolayer sheets. Six distinct patterns are observed in HRTEM and angular dark-field STEM (DF-STEM) images, allowing the exact angle of rotation to be determined from their respective size and repeat order. At large rotation angles approaching 30 degrees, the aperiodicity in the structure of the nanorod supercrystals becomes apparent, resulting in 12-fold ordering characteristics of a quasicrystal. The rotational offsets are further elucidated from Fourier transform and small angle electron diffraction, allowing interpretation of several multilayers when combined with DF-STEM and SEM. Pattern formation owing to angular rotation is differentiated from those occurring from a lateral shift, providing an important insight into the complex multilayered structures in assembled rods that may have an impact on their collective electronic or photonic properties. We also show how random tetrapods when present at low concentrations in colloidal nanorod solutions act as termination points for 2D sheet crystallization, impacting the size and shape of the resultant assemblies. The occurrence of Moire patterns in rod assemblies demonstrates the extra-ordinary order achievable in their assembly and offers a nondestructive technique to precisely map the placement of each nanorod in this important nanoarchitecture.