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Faceting limits

By Bruce L. Harding
Holden, Massachusetts, USA
Copyright GIA
Objectives table of contents
Figures 1
(click image for big view)
Figures 1 through 8 show a grid which represents all combinations of pavilion slopes from 35° to 45° and bezel slopes from 0° to 60°. Pavilion slopes greater then 45° are not considered in this initial discussion but will be described in future articles as they apply to certain facets.
     It is easier to define that which is bad about a gem than that which is good, so the object of this study is to delete areas of the grid which represent poor designs. Dark shading will be used for the worst conditions, medium shading for those which are less severe, and light shading for minor faults. "Best" designs will then lie in the areas of lightest shading.
Dead Center table of contents
     If the pavilion slope is less than the critical angle, no reflections can be seen through the table when looking into it perpendicularly; furthermore, reflections through the table cannot be seen from more then one side of the pavilion in other positions.
     This "dead" center condition is very undesirable so pavilion slopes less than the critical angle are shaded dark on the grid, as shown for peridot in Figure 1.
The Viewer`s Head table of contents
Figure 2
     Rays which are reflected to the viewer`s eye must come from directions which missed his head. Figure 2 shows that at a viewing distance of one foot, as when examining a stone prior to purchase, the angle (or divergence) between incident and reflected directions of the same ray must be at least 10°; otherwise the viewer will see reflections of himself.
Table-to-Table Rays table of contents
Figures 3a
Figures 3b
(click image for big view)

Figure 3A shows a ray entering and leaving the table, being reflected off both sides of the pavilion. For each pavilion slope P the internal divergence D (=180°-4P) is constant regardless of the ray angles. The corresponding external divergence is larger and varies according to the refractive index of the material and the ray angles; it is minimum when it is symmetrical as shown in Figure 3A.
     For this minimum external divergence to be 10°, the pavilion slope is about 1.5° more or less than 45°. Slopes between these values produce less divergence, so that they are shaded dark in Figure 3B.

Table-to-Bezel Rays table of contents
Figures 4a
Figures 4b
(click image for big view)
Figure 4A shows a ray entering the table perpendicularly, which returns to the bezel at an angle B-D to the bezel normal. By refraction, the corresponding external angle must be B10 to provide the required minimum divergence of 10°.
     Figure 4B shows plots of the two bezel slopes which satisfy this condition for each pavilion slope. Slope combinations between these plots produce divergence less than 10deg;. Because a large portion of returned light passes this way, this area is shaded dark.
Bezel-to-Table Rays table of contents
     Rays which enter the bezel and leave via the table follow paths identical to those described above, except in the opposite direction; accordingly, the shaded area of Figure 4B applies to these rays also.
Octonus Software & MSU Gemological Center.