above the middle or girdle of the stone) and 25 on the pavilion (the lower half below the girdle). The girdle may be frosted, polished smooth, or faceted. In recent decades, most girdles are faceted; many have 32, 64, 80, or 96 facets; these facets are excluded from the total facet count. Likewise, some diamonds may have small extra facets on the crown or pavilion that were created to remove surface imperfections during the diamond cutting process. Depending on their size and location, they may hurt the symmetry of the cut and are therefore considered during cut grading. Figure 1 assumes that the "thick part of the girdle" is the same thickness at all 16 "thick parts". It does not consider the effects of indexed upper girdle facets. Figure 2 is adapted from the Tolkowsky book, originally published in 1919. Since 1919, the lower girdle facets have become longer. As a result, the pavilion main facets have become narrower. Proportions While the facet count is standard, the actual proportions—crown height and crown angle, pavilion depth and pavilion angle, and table size—are not universally agreed upon. There are at least six "ideal cuts" that have been devised over the years, but only three are in common use as a means of benchmarking. Developed by Marcel Tolkowsky in 1919, the American Standard (also known as the American Ideal and Tolkowsky Brilliant) is the benchmark in North America. It was derived from mathematical calculations that considered both brilliance and fire. The benchmark in Germany and other European countries is the Practical Fine Cut (, also known as the Eppler Cut), introduced in 1939. It was developed in Germany by empirical observations and differs only slightly from the American Standard. Introduced as part of the Scandinavian Diamond Nomenclature (Scan. D. N.) in 1969, the Scandinavian Standard also differs slightly. Other benchmarks include: the Ideal Brilliant (developed in 1929 by Johnson and Roesch), the Parker Brilliant (1951), and the Eulitz Brilliant (1968) The Ideal and Parker brilliants are disused because their proportions result in (by contemporary standards) an unacceptably low brilliance. The Eulitz cut is the only other mathematically derived benchmark; it is also historically the only benchmark to consider girdle thickness. A more modern benchmark is that set by Accredited Gem Appraisers (AGA). Although their standard generally makes a modern ideal cut it has been criticised for being overly strict. A summary of the