Symmetry axes of a diamond

In our opinion, most serious problems arise when one tries to reveal and grade such symmetry distortions as deviations of the table, culet, and the angles of crown and pavilion facets. In diamond grading systems, these deviations are measured with respect to either the «center» of the diamond or its «axis». However, there is no «center» in a diamond; and even if we are talking about the «axis», some further specification is needed. Indeed, the girdle surface is formed because of rotating a raw diamond. So, it is a reasonable approximation to assume that the girdle surface is a portion of a cylindrical surface and therefore has an axis of revolution. However, this axis may be not perpendicular to the table of the diamond. This occurs, for example, when the table of a cut diamond is not perpendicular to its girdle plane. The crown of a diamond consists of three tiers, namely – star facets, crown facets, and upper girdle facets. During the cutting process, each tier is formed by rotating the raw diamond about the axis of the stone-holder of the cutting dop. Strictly speaking, each tier has its own axis of revolution. However, since all the facets belonging to the crown are being cut without taking the diamond out of the cutting dop, one can assume (with a high degree of accuracy) that the whole crown has a single axis of revolution (symmetry axis), except for the table. The pavilion consists of two tiers: pavilion facets and lower girdle facets. However, similarly to the case of the crown, it can be assumed that the pavilion has the only axis of revolution. Thus, a round brilliant cut diamond has four principal axes: the table axis, crown axis, girdle axis, and pavilion axis (see Fig. 6). Of course, in an ideal, perfectly symmetric diamond, all these axes merge into one, and the term «diamond axis» becomes clear. However, if we are going to describe an asymmetric diamond, we cannot just say that some element of the stone is displaced with respect to an axis, because we need to clearly specify which axis we are talking about. Determining the facet inclination angles also becomes a problem for a non-ideal diamond, because of lacking specification which axis these angles are measured relative to.

Fig. 7. The axes of different cut elements of a diamond (table, crown, girdle, and pavilion) appear during certain diamond cutting steps. These axes may differ from each other. In such a case, various types of symmetry distortions arise in the diamond.

Thus, to correctly grade the asymmetry of a diamond, one needs a method capable of independently determining each of these axes and calculating their mutual deviation. Since there are four mutually independent axes in a diamond, the result of such a calculation can be conveniently represented by a matrix (Table 5)..