The symmetry of diamond is still sometimes questioned. Most people agree that diamond belongs to the space group Fdm and therefore to point group . Some however, on account of the existence of a few natural tetrahedral diamonds, have assigned diamond to the point group 3m. We report here on an X-ray topographic investigation, using both conventional and synchrotron sources, of eleven natural tetrahedral diamonds. Two large specimens (from the Alpheus Williams' collection) were studied and found to consist of two portions, unequal in size, that were twinned on a (111) plane. Another diamond (from Professor R. A. Howie's collection) was found to contain two non-parallel (111) twin planes with the diamond filling the space between them, giving the crystal a tetrahedral morphology. Four tetrahedral diamonds (selected by Tolansky) were shown to be either twinned on a (111) plane, or cleavage fragments consisting of one component of a made or single crystals that had been plastically deformed. Similar results were found for some diamonds from the Argyle Mine. Our findings are consistent with diamond belonging to the holosymmetric class () rather than to the hemihedral class (3m).