Cleaved surfaces of silicon carbide were investigated using low-energy electron diffraction (LEED) and core level photoelectron spectroscopy (PES). Despite the hardness of SiC, cleavage is possible for basal plane surfaces. On both the Si and the C face, i.e. SiC(0001) and SiC(000 (1) over bar) flat surfaces can be obtained with a sharp LEED pattern. The observed LEED pattern is interpreted as a 3-domain superposition of (2x1) reconstructions on the basis of spot intensity differences. Si 2p and C 1s photoemission results are interpreted in view of other, stable SiC surface reconstructions. A comparison is drawn to the Si(111)-(2x1) surface where the reconstruction has been interpreted by Pandey in terms of the pi-bonded chain model.