High-resolution transmission electron microscopy (HRTEM) images of the [11-20] and [11-20] zones of cubic and hexagonal SiC layers grown by molecular beam epitaxy (MBE) often reveal regions of material exhibiting an unusual periodicity. We describe the identification of 3 and 4-fold periodicities. The 3-fold contrast was found in earlier works of Jepps and Page to appear in HRTEM images of polycrystalline SiC when it was attributed to the 9R-SiC polytype. In this paper we demonstrate by HRTEM image simulations that the models of the 9R and the 12H polytypes can fit qualitatively the experimental HRTEM images. However, by comparison of the FFT patterns of the experiments and the simulations, we demonstrate that the periodical structures disagree with the 9R and 12H polytypes. We show unambiguously that the model of overlapping crystals does fully match the experiments.