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Reading and Understanding Faceting Diagrams

A faceting diagram, also referred to as a faceting pattern, or a "cut", is a graphical representation and set of instructions providing the information needed cut a particular gemstone design. Learning to read, understand and apply faceting diagrams is an essential and fundamental skill that all faceters need to acquire. Faceting diagrams present the instructions for various gemstone designs in a manner that may appear somewhat cryptic to the uninitiated, but which are compact, concise, and readily understood by faceters fluent in the language and format of modern faceting diagrams.

The way gemstones are designed and diagrammed has undergone a profound revolution over the last several decades. Perhaps the most significant and fundamental advancement in contemporary faceting is the development and widespread adoption of meetpoint faceting methodology and techniques. An understanding of meetpoint faceting technique is essential to reading and using the wealth of modern faceting diagrams to facet gemstone designs.

The general idea of a meetpoint is derived from basic geometry. You may recall from geometry that the intersection of two non-parallel planes forms a line containing all the points shared in common by both planes. You may also recall that when the lines of intersection of three planes are not parallel, they meet at a single, unique point shared in common by the intersecting planes. One probably familiar example of this is the origin (0,0,0) in the three-dimensional Cartesian coordinate system, where the X-Y, X-Z and Y-Z planes and X,Y,Z axes (lines) intersect at the sole, unique point they share in common. Extending these mathematical concepts to faceted stones, facet faces are analogous to plane surfaces, facet edges are analogous to line segments formed at the intersection of two plane surfaces, and meetpoints are analogous to unique points formed at the intersection of line segments. Meetpoints are those unique points on facet edges that are shared in common by three or more adjacent facet faces.

Figure 1: Illustration of Meetpoints on a Standard Round Brilliant
3-View Meetpoint Diagram

Figure 1 serves to illustrate the concept of meetpoints. This gemstone design, a standard round brilliant, has a total of 57 meetpoints:
1 meetpoint where its eight pavilion main facets (P2) all converge and meet at the culet
8 meetpoints where pairs of pavilion main facets (P2) and pairs of pavilion break facets (P1) meet
8 meetpoints where pairs of pavilion break facets (P1) and pairs of girdle facets (G1) meet
8 meetpoints where pairs of pavilion break facets (P1), a pavilion main facet (P2) and pairs of girdle facets (G1) meet
8 meetpoints where pairs of girdle facets (G1) and pairs of crown break facets (C1) meet
8 meetpoints where pairs of girdle facets (G1), pairs of crown break facets (C1) and a crown main facet (C2) meet
8 meetpoints where pairs of crown break facets (C1), pairs of crown main facets (C2) and a crown star facet (C3) meet
8 meetpoints where a crown main facet (C2), pairs of crown star facets (C3) and the table (T) meet

The placement of facets about a stone during the cutting process was generally more of a time consuming, trial-and-error sort of affair prior to popularization and adoption of meetpoint technique, particularly so for lower symmetry shapes such as ovals, navettes, pears and hearts. Mechanical preformers were sometimes employed as aids in generating girdle outlines, but these devices did not eliminate a great deal of estimating, interpolating, cut and try, and "looks about right" work and frustration on the part of the faceter when cutting pre-meetpoint technique designs.

This is not to infer that pre-meetpoint technique designs did not employ meetpoints - most did. However, the instructions provided by gemstone designers for faceting pre-meetpoint technique designs were necessarily vague and imprecise, because the exact placements and angles required to join facet faces at the intended meetpoints on these designs hinged on variable girdle outlines and indeterminate facet placements at the beginning of the faceting sequence.

Contemporary meetpoint technique differs from older ways of faceting in the manner meetpoints are generated and used as stones are faceted. This difference is primarily one of emphasizing ordered cutting and polishing sequences during the faceting process that employ meetpoints as precise targets to determine the placement of succeeding facets.

Another profound and sweeping advancement in contemporary faceting has been the development and widespread adoption of the personal computer and the adaptation and application of computer aided drafting and optical ray tracing software to the processes of gemstone design and the generation of modern faceting diagrams. Prior to the revolution spawned by the availability of contemporary computer tools, the application of mathematics to the process of gemstone design involved very tedious and demanding manual calculations requiring applications of trigonometry and analytical geometry beyond the inclination and dedication of most faceters and gemstone designers.

Prior to the advent of personal computers, the process of gemstone design was largely much more an on-the-dop, cut-and-try, recut-and-retry affair. After a design was developed and refined by test cutting, the information needed for other faceters to reproduce it could be recorded and incorporated into a faceting diagram. Pre-computer era faceting diagrams varied widely between designers and publishers in their format, and in all too many cases, the veracity and accuracy of the published cutting instructions.

The GemCad gemstone design and ray-tracing software developed by Robert Strickland was first released to the faceting community as DOS software in 1989, and eventually updated to a Microsoft Windows compatible version in 2002. Other pioneers of note involved in the application of personal computers and analytical processes to gemstone design include Norman Steele, Robert Long and Fred Van Sant. Robert Strickland's GemCad is now ubiquitously employed by contemporary gemstone designers, and GemCad's .gem file format has emerged as digital lingua franca for the exchange of gemstone designs among contemporary faceters.

GemCad software facilitates personal computer users in making printed copies of faceting diagrams. The GemCad diagram format has been almost universally adopted and embraced by the contemporary faceting community as a de facto standard for the publication and presentation of faceting diagrams. A GemCad generated faceting diagram for a standard round brilliant gemstone design is presented below and referenced in the ensuing discussion explaining its interpretation.

Figure 2: GemCad Rendered Diagram of a Standard Round Brilliant
GemCad Rendered Diagram of a Standard Round Brilliant

A GemCad rendered and generated faceting diagram groups and conveys information about the design in three major sections. The first section, highlighted in yellow in the above diagram, consists of a geometric CAD-style drawing of the gemstone from four different perspectives or points of view. The second section, highlighted in red in the above diagram, consists of a table of dimensions summarizing overall parametric data for the particular design. The third section, highlighted in blue in the above diagram, consists of a table of cutting instructions specifying numeric protractor angles and index settings for cutting related sets (tiers) of facets. Each of the diagram sections provide information germane to cutting the design and are used together by the faceter to interpret the diagram and apply it to the faceting process.

The 4-view drawing consists of a crown planview, a pavilion planview, and side and end views of the finished stone. Together these four views provide an overview of the general layout and overall shape of the gemstone. The 4-view drawing also provides a number of labeled dimension lines. The dimensions usually labeled are:

W - the width of the stone
L - the length of the stone
C - the height of the crown
P - the depth of the pavilion
T - the length of the table
U - the width of the table

These dimensions are unitless and related to each other in the table of dimensions as ratios based on W, the width of the stone.

Individual facets are also labeled in the 4-view drawing. The designer typically applies a unique label to one facet in each tier of the design. The concept of a tier is fundamental to understanding faceting diagrams and the faceting process in general. A tier is a set of facets that are cut at the same protractor angle and elevation, but at different index settings as they a placed about a stone. The standard round brilliant design rendered in the example diagram above consists of 6 tiers of related facets:

Figure 3: Illustration of Facet Tiers on a Standard Round Brilliant
Illustration of Facet Tiers on a Standard Round Brilliant

The P1 tier (16 pavilion break facets)
The P2 tier (8 pavilion main facets)
The G1 tier (16 girdle facets)
The C1 tier (16 crown break facets)
The C2 tier (8 crown main facets)
The C3 tier (8 crown star facets)
The table facet (T) can be conceptualized as an additional tier consisting of a single facet, and is listed as such by GemCad in the table of cutting instructions.

Once the elevation and protractor angle of the faceting head has been adjusted as specified to cut a particular tier, all the facets in that tier are typically cut together on their respective index settings as a sequential step in the faceting process. Then the protractor angle of the faceting head is set as specified to cut the next specified tier, the elevation of the faceting head is adjusted, and then all the facets in that tier are typically cut together on their respective index settings as the next sequential step in the process. An more fully elaborated example and description of this process is presented in the step-by-step directions for cutting the "Simple Jack" design presented in the chapter Cutting Your First Stone.

The table of dimensions provides parametric information about the design. Among these parameters are the refractive index of the material upon which the design is predicated, the total number of facets in the design, the symmetry of the design, and the index gear specified to cut the design. A number of unitless dimensions are also provided in the table of dimensions, which are expressed as ratios based upon the width of the stone. These are:

L/W = length of the stone:width of the stone
T/W = length of the table:width of the stone
U/W = width of the table:width of the stone
P/W = the depth of the pavilion:width of the stone
C/W = the height of the crown:width of the stone
Vol./W3 = the volume of the stone:cube of the width of the stone

The use of unitless ratios to express dimensions of the stone facilitates the process of scaling the diagram to cut any particular size stone.

The dimensions P/W and C/W can be particularly germane and useful for gauging whether a stone of a given width can be cut from a particular piece of rough without running out of sufficient material to cut the pavilion or crown. Once the location of the girdle and width of the stone are established, the rough can be gauged with calipers to determine if there is sufficient material to cut the crown and pavilion at the specified angles. As an example, to cut a 10mm diameter standard round brilliant using the example diagram above, the crown will require a minimum of 1.95mm material above the girdle and the pavilion will require a minimum of 4.66mm material below the girdle because:

C/W = .195
C/10mm = .195
C = .195 x 10mm
C = 1.95mm

P/W = .466
P/10mm = .466
P = .466 x 10mm
P = 4.66mm

The table of cutting instructions specifies the protractor angle and index settings required to cut each tier of facets on the design. Each tier listed in the table of cutting instructions is identified with a label corresponding to the labels provided on the 4-view drawing. On elaborated diagrams presented for beginning faceters, each facet in a tier may be individually labeled for the sake of clarity, as has been done on the "Illustration of Meetpoints" diagram above. However, typically only one facet of each tier is labeled on the 4-view drawing to minimize clutter on more complex designs.

There are no hard and fast rules for naming and labeling tiers and facets on a faceting diagram, but many designers employ the convention of labeling pavilion tiers P1,P2,P3,etc., girdle tiers G1,G2,G3,etc., and crown tiers C1,C2,C3, etc. On more complex diagrams a convention of labeling tiers 1,2,3,4,5,6,7,etc. or a,b,c,d,e,f,g,etc. is sometimes employed to help minimize label clutter and overlap on the geometric rendering. Yet another convention may employ acronyms for labels such as PM, PB, G, CB, CM, CS and T for the pavilion mains tier, pavilion breaks tier, girdle tier, crown breaks tier, crown mains tier, crown stars tier and table respectively.

The diagram section containing numerical cutting instructions is often (but not always) elaborated upon with textural remarks providing additional step-by-step explanations and clarifications. There is a bit philosophy and differences of style and opinion at play between gemstone designers regarding the extent and scope of adequate explanatory remarks. The late Fred Van Sant, who is held in high esteem as a talented gemstone designer by many in the faceting community, was notorious for a lack of explanatory textural remarks included on his published gemstone diagrams. I once queried Fred as to why he didn't elaborate his diagrams with explanatory remarks. Fred's frank and uncompromising response was that the numerical information presented in his diagrams contained the information necessary to cut his designs. Fred contended that a workable cutting order and meetpoint sequence was the responsibility of and at the discretion of the faceter, and that if they weren't up to the task of figuring that out on their own, they had no business faceting in the first place...

Fred's point that the nuclear information required to replicate and cut a specific design is contained within its kernel of numeric index settings and protractor angles is illustrative. However, my own philosophy is that the purpose of publishing a faceting diagram is to communicate how to cut a particular design to other faceters. There are merits to presenting more than the bare minimum of necessary information when it comes to communicating how-to. Those merits include clarity and comprehensibility, merits that I have found to be particularly appreciated by beginning faceters.

On properly thought-out and presented faceting diagrams, the label order should correspond to a recommended cutting order or sequence on the part of the designer, especially so with diagrams presenting designs suitable and recommended for less experienced faceters. Thus the P1 tier is cut before the P2 tier, the P2 tier is cut before the P3 tier, and so forth.

On some meetpoint designs there may be only one cutting order or sequence conforming to the methodology of meetpoint technique, where the locations of facets on a particular tier are precisely determined by meetpoints created during the process of cutting preceding tiers. On other designs there may be more than one tier order or sequence that can be employed to determine the locations of facets on a particular tier by preceding meetpoints. Cutting and polishing sequences are in fact ultimately at the faceter's discretion, but it is suggested that the presented tier sequence and cutting order be followed by beginning faceters until enough experience is gained to know where and why a deviation to the diagram sequence may be warranted.

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