The fluidized-bed vapour phase deposition of β-SiC on nuclear fuel granules can produce polygonal crystals. The examination of these and their etch figures by scanning electron microscopy indicates an internal structure composed of {111} planar sheets. The disposition of these sheets is discussed with the aid of three-dimensional models. It is concluded that a maximum of four sheet orientations can occur. From these, six families of sheet pairs can be made by appropriate combinations: these are labelled according to the [110] directions of the spines created by their intersections. The sheets produce traces on the external crystal faces, and the various possible juxtapositions of these traces are discussed.