Major and minor symmetry distortions

Not all of the symmetry distortions that arise during manufacturing a diamond are accidental. In some cases, the manufacturer purposely distorts the symmetry of the stone being cut. For example, he may get rid of an inclusion by changing the tilt angle of a single facet. This distorts both the shape of the adjacent facets and pointing of the adjacent edges. In such a case, to analyze the asymmetry on the basis of the scheme suggested, it is necessary to determine the position of the corresponding axis, the tilt angle of each facet with respect to this axis, and the maximum deviation of these tilt angles. This would allow one to reveal the «minor symmetry flaws», that is, minor distortions of the symmetry of the diamond. Thus, each cell of the matrix discussed above should be filled in with two figures: the first is the mutual deviation of the axes, characterizing the «major symmetry», while the second is the deviation of a particular facet from its position yielding the perfect symmetry. This figure characterizes the «minor symmetry».
When determining the parameters of a diamond facet, a single angle is conventionally measured (for example, the angle between the facet and the girdle plane). However, each facet is a part of a plane, and to unambiguously define the orientation of a plane, two angles are required, for example – the tilt angle and the azimuth. Many symmetry distortions are due to different azimuth inclinations of facets. For example, this can be a mutual tilt of opposite pavilion facets. These deviations may seem insignificant since they are not striking when the stone is examined with a loupe, but they are very important when one performs ray-tracing for the diamond.

The method suggested describes only a portion of those phenomena conventionally considered as symmetry distortions (for example, it does not describe additional facets). Therefore, it must not be used instead of the symmetry analysis methods existing so far. However, the data being the output of our approach characterize main symmetry distortions, both major and minor, allow one to understand the reason of these distortions, and provide a link between the output of a scanner, the diamond cut parameters considered by the existing diamond grading systems, and the appearance of the diamond whose symmetry is being analyzed. Therefore, we think that adding the suggested matrix to a diamond certificate (a gemological conclusion on the quality of the diamond) would inform the dealers and customers about some important features of the diamond cut quality.