The crystallographic aspects of silicon/corundum epitaxy were investigated. Epitaxial deposition was carried out on corundum substrates of two orientations, and the observed crystallographic relationships were shown to be determined by three‐dimensional matching between the silicon structure and the sublattice of possible cation sites in corundum.Single‐crystal silicon layers were deposited onto (0001) and (8¯629) corundum substrates. For growth on (0001) corundum, (111) silicon is parallel to the interface with [1¯10] silicon parallel to [2¯110] corundum. For growth on (8¯629) corundum, the silicon plane parallel to the interface is irrational, but the epitaxial relationship closely approximates to the following: (001) silicon parallel to (0001) corundum with [1¯10] silicon parallel to [2¯110] corundum.These two epitaxial relationships are the only ones which permit three noncoplanar symmetry axes of the silicon to coincide with three such axes of the cation site sublattice of the corundum. They insure compatible surface symmetries and similar surface densities on an arbitrary deposit/substrate interface. In general, the silicon atom density on the interface does not exceed the cation site density. When it does so, however, the rational crystallographic relationship is modified slightly in order to lower the density of silicon atoms below that of the possible cation sites.