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Faceting limits

By Bruce L. Harding
Holden, Massachusetts, USA
Copyright GIA
Conclusions table of contents

     It is important to note that this analysis has three limitations:

  1. It assumes that pavilion and bezel slopes are constant: This is essentially true for brilliant cuts, but not for step cuts.
  2. It assumes that opposite facets have a common normal plane: This is true for round, square, and rectangular girdle shapes, but not for oval, pear, marquise, etc.
  3. It assumes that rays are in a plane through the gem axis: This is only a small part of all rays, but these are the only ones which can be analyzed simply.

     The first two assumptions are also inherent in the design slopes recommended by various references; such data were developed by trial-and-error on round brilliant cuts but may be used as approximate guides for other cuts.
     It is most significant, however, that the theoretical results show good correlation with those proven by trial-and-error, despite the third limitation described above. This indicates the validity of the method.
     The key to this study was the effect of the viewer`s head, which can be observed by close study of reflections in a cut gem. Other criteria which may have been overlooked will be added in later articles. Several sequels are already in process which probe specific aspects of the problem in more detail.
     As it stands, this is believed to be one of the better faceting guides to date. Comments from readers will be welcomed and reviewed toward making it even better.

Octonus Software & MSU Gemological Center.