In an effort to identify low-surface-energy, close-packed, conducive-to-growth hexagonal semi-polar planes on which micropipe free SiC crystals and/or hetero-epitaxial AlGaN structures with a reduced piezoelectric field and a smaller lattice mismatch can be grown, an orientation relationship between the cubic 3C and nH hexagonal structures was developed. Specific hexagonal planes corresponding to the (10 0)c and (1 11)c cubic planes were found, and equations were developed to determine the planar structure and packing density of these planes to assess whether there is a good chance that high-quality material can be grown on these surfaces, and, if so, whether it is likely that stacking faults will be formed. It is shown that stacking faults will likely form in SiC crystals grown on the hexagonal nH (3 (3) over bar 0 2n)(H) and (3 (3) over bar 0 (n) over bar)(H) planes, which correspond to the (1 0 0)(C) and (1 (1 1) over bar)(C) cubic 3C planes. It is also shown that good epitaxy of AlGaN films should be possible on these planes although it is likely stacking faults will be formed. The % Al for which there is no lattice mismatch in the direction containing a component parallel to the c-axis is 95.4 and 83.3 for growth on the 4H (3 (3) over bar 0 8) and (3 (3) over bar 0 (4) over bar) planes, and 88.3 and 76.9 for growth on the 6H (1 (1) over bar 0 4) and (1 (1) over bar 0 (2) over bar) planes. Published by Elsevier B.V.