1. Introduction
2. Pavilion - angles of reflected rays
3. Pavilion - limits of reflected rays
4. Pavilion angle limits to reflect all incident rays
5. Best pavilion angle
6. Table size
7. Bezel angle
8. General method of determining bezel angle
9. Light entering the table
10. Central group of light rays
11. Group oblique from left
12. Group oblique from right
13. Mean light angle = bezel angle
14. Final angles and proportions
15. Girdle facets
16. Star facets
17. Comparison to actual cuts
19. Editors note

In 1919 Marcel Tolkowsky published "Diamond Design" in which he developed the angles and proportions of the brilliant cut which have become widely accepted as ideal.

Copies of this book are hard to find 2, so Tolkowsky's analysis is reiterated here for those who are curious to know how these 'magic numbers' came about.

This review follows Tolkowsky's logic but uses less awkward and more meaningful mathematics. It shows errors, omissions, and inconsistencies in his work, but none of these have a significant effect on the final results.

Tolkowsky was intimate with diamond-cutting and implies that he knew the answers before developing the theory. This is a common danger in research and it appears that some of his logic is tainted in an effort to arrive at these results.

Tolkowsky's first step involves a compromise of brilliance to get good dispersion, and all subsequent calculations are based on the results of this initial step 3. For this reason, and others, this method cannot be applied directly to studies of other gemstones; however, it is a good source of concepts for such efforts 4.

Certain limitations of this analysis must be pointed out:

  1. It applies to stones with nearly-constant pavilion and bezel slopes; this excludes step-cut stones.
  2. It considers only rays in planes parallel to the axis and perpendicular to the facets they hit; this is a small part of all the rays.
  3. It assumes that such rays have identical facets on opposite sides of the gem; this excludes fancy shape

    * 1 Never published. Submitted to GIA but declined by Richard Liddicoat, Pres. because it could undermine faith in the established cut-grading standards. Copy sent to Shinichi Minawa, Tokyo, Japan, 1976 Dec. 24.

    2 Most of this book has been re-produced by Moscow State University at Internet sites www.gemology.ru (Russian) and www.cutstudy.com (English).

    * 3 This analysis neglects partial reflections as rays are refracted. It cannot, therefore, be used for quantitative analysis of light returned.

    * 4 At that time this author was trying to discover criteria which governed the faceting of all transparent gemstones; this effort led to "Faceting Limits", published by GIA in 1975, presently being reproduced by Moscow State University at their web site.

  Author: Bruce L. Harding,
Holden, MA 1975 May 15 with footnotes by BLH 2001 Mar 19
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