Variety of problems that arise when using the current symmetry grading systems

Example 1. Tilted table. Consider a scanner, such as a Sarin one, which measures the facet tilt angles with respect to the table plane of the diamond being scanned. Should this plane be tiled with respect to the pavilion axis, the angles will be measured incorrectly. That is, instead of revealing that the pavilion is properly cut, all its facets making equal angles with the pavilion axis, and only the table is not good, the report will «claim» that the pavilion facets all have different tilt angles, that the cut is faulty, and that the stone should be either marked down or re-cut. Meanwhile, the right conclusion of the device would be the following: «all the pavilion facets make the same such-and-such angle with the pavilion axis, but the table is not perpendicular to the pavilion axis».
Let us see at the two tilted table diamonds. The diamond No.1 is taken form Internet (www.diamonds.net), and has the Sarin Report, see Fig 1.

Fig. 1. The Sarin report for this diamond reveals the considerable difference for the pavilion angles (from 40.8 to 42.6 degrees). Source: www.diamonds.net

Fig. 2 and Table 3 show the result of angle measurements on the base of the table plane for the first diamond example. Pavilion angles have variation 1.8 (from 40.8 to 42.6 degrees).

Fig. 2. The tilt angles of the pavilion facets measured by a Sarin scanner relatively to the table are 40.8 and 42.6 degrees, difference is 1.8 (minimum is marked in red, maximum in green color). Taking into account 0.8° displacement of the table axis and pavilion axis, we introduce the corresponding correction that changes the tilt angles to 41.7 and 41.8 degrees.

Table 3. Diamond No. 1 measurements. Rows 1 and 2 – angles measured by a Sarin scanner; row 3 – the sums of the angles of opposite facets; row 4 – the average values of these angles.

If one calculated the facet tilt angles on the basis of dihedral angles between opposite facets, the variations of the angles would be much smaller than those appearing in a Sarin report. According to such a report, the stone might get a low grade in symmetry. At the same time, the dihedral angle between opposite facets is what strongly affects the diamond cut quality. These dihedral angles are formed by pairs of the pavilion facets 1and 5, 2 and 6, 3 and 7, 4 and 8. If one has an intention to see such a tilted table diamond in an instrument like “Hearts and Arrows Viewer” the axis of the diamond should be combined with the axis of the instrument.
The diamond No.2 is owned by one of the authors (G.H). The parameters of this diamond with tilted table are shown in the Table 4. The crown and pavilion axes are tilted from table axis at the different angles. As the result the significant (approximately 1 degree) difference will be obtained if the angles will be measured in the base of the table plane. Meanwhile a good quality of such a stone is confirmed by «hearts and arrows» patterns obtained with structural illumination after its position was corrected on order to match the viewer’s axis (Fig. 3)

Table 4. Rows 1 and 2 – angles measured by a Sarin scanner; row 3 – the sums of the angles of opposite facets; row 4 – the average values of these angles.

Fig. 3. a) Snapshot of the diamond No.2, made by means of an Idealscope. The diamond is positioned so that its table is perpendicular to the optical axis of the camera. An off-axis displacement of the culet and pale regions of partial light leakage through the pavilion can bee seen. b) Snapshot of the same diamond slightly rotated in order to compensate for the table tilt. The degree of optical symmetry became much higher, as a result. c) and d) Snapshots of the diamond made by means of a “Hearts and Arrows viewer” device, which demonstrate perfect «hearts and arrows» patterns.

Example 2. Distorted girdle shape. Among the symmetry distortions considered major in all the grading systems mentioned, the one being easiest to measure is, probably, the degree of girdle non-roundness (the deviation of its shape from a perfect circle). This is because the diameter of a diamond is quite easy to accurately measure at a sufficiently large number of places. Even if a diamond grading certificate does not mention this kind of symmetry distortion and its grade, the document anyway contains the minimum and the maximum diameter of the stone. These data allow one to calculate the variation of the girdle diameter on the basis of the difference between these two values.

However, there is a geometrical figure different from the circle, which has the same diameter no matter what a direction it is measured along (the blue contour in Fig.4). If the girdle contour is something intermediate between this figure and a circle, the certificate of the diamond will contain no data prompting the consumer to suspect that the stone is not symmetric. However, such a shape of the girdle distorts the facet arrangement. First of all, it makes opposite facets non-parallel to each other, which dramatically changes the paths of light rays inside the diamond (See below the «Major and minor symmetry distortions» section to find more about the two angles that define the orientation of each facet).

Fig. 4. The girdle of a «triangular» diamond (green contour) weakly differs from a circle (red contour). According to expert conclusions and certificates, such a stone is «good» (any diameter of the girdle is the same), but, as a matter of fact, its symmetry is poor.

Example 3. Non-constant girdle thickness. The girdle of a round brilliant cut diamond has 16 thinner regions and 16 thicker ones. All the thinner regions are of the same kind, while the thicker ones can be divided into two types: main facet junctions and edge junctions. There are some diamonds in which the girdle thickness differs from one thicker region to another. For example, at the main facet junctions the girdle is thicker than at the edge junctions (see Fig. 4). This occurs when the upper and lower girdle facets are slightly tilted not with respect to the girdle plane but with respect to the diamond axis (azimuth angle deviation). Since many laboratories measure girdles at their thinner regions, their cut grades are not affected by the increase in the girdle thickness at its thicker region. This fact can be used to increase the average thickness of the girdle and therefore to increase the stone weight by 2-3%, sacrificing the optical properties of the diamond. (Increasing the girdle thickness not at the facet junctions but at the edge junctions, on the contrary, does not increase the weight but improves the optical properties of the stone. This idea is used, for example, by Eightstar Diamonds company).
 

Fig. 5. The girdle of this diamond is perfectly made in the thinner regions in order to allow it to be graded as AGS 0. However, the thickness of the thicker regions of the girdle is increased in order to increase the weight yield of the stone. 46.2° tilt angle of twin upper girdle facets compensates for the thickened girdle. The inset shows a diamond with a usual girdle, in which the tilt angle of twin upper girdle facets is 41.3 degrees.

Fig. 6 illustrates real examples of two diamonds with the girdle shape as it described above.

Of course, we could give more such examples, but our goal is not to list all of these but to demonstrate the breadth of the problem. The problem is that in some cases those stones looking good are graded poorly, because they lack symmetry in accordance with the chosen symmetry grading system. On the other hand, some stones look bad and their actual symmetry is poor, but the current symmetry grading systems conclude that they are good.