(reprinted from the December 1994 issue of the USFG Newsletter with permission from the author and the USFG)
In our last newsletter I said that the sequencing of facets is determined by the order in which points on the stone must be made, and that the two most common starting places were either a culet point or a set of girdle points. Now we will look at a couple of actual examples to illustrate just how one analyzes a design to determine the cutting order.
First we’ll take the El Diablo pavilion; I have received an inquiry about it. It seems my list of facet sets was taken as a cutting sequence. On my own designs I seldom give a cutting sequence. The list is just a list for you to sequence your own way. The facets set numbers are only for handy reference. You should recognize the El Diablo as a barion style pavilion. “What is a Barion” was in the June 94 issue. Most oblong barion pavilions have an angular bend along the side between steep break facets and the shallower culet facets; this design is no exception. The meetpoints along this bend must be derived from the cutting sequence; they cannot be used for starting meetpoints. This design can be cut from one of the preforms given, or meetpoint style starting at the culet. Let’s analyze it both ways. Starting with a preform, we first want to make a level girdle line around the stone, so we will cut the girdle breaks, sets 1 and 2. This line should be high enough up the stone to make room for the culet. But why guess; why not cut set 7 first so we know where to make the girdle line to begin with. You can see on the plan view that only on the ends is there a facet connecting the girdle and the culet. This link between the girdle and the culet is very important, and should be established on your stone as early as possible. So cut set 7, then girdle the stone at 70 degrees. By girdling the stone I mean to cut a level line of break facets around the stone at a single mast height setting, using the highest break facet angle. In this case it is 66.360 for P1, but we set it a few degrees higher so we can later fit P1 to meet Point 2-4-6 (Point 2-4-6 is the point created by cutting facets 2, 4, and 6).
On nearly all oblong barion pavilions you have to start at the ends and chain toward the middle of the sides. Once the end points are made, sets 2 and 4 can be cut to meet at the end, and set 6 can be cut to meet at the culet. This makes Point 2-4-6 to which sets 1 and 3 are cut. It would be premature to cut set 5 along with set 6, because if set 5 is already cut when we chain from corner to the side, then how are we going to fit set 3 in? Sets I and 5 would create a meetpoint on the Y axis, and when you go to cut set 3 you would probably fall short of that meetpoint or overrun it, unless you cheated, and we don’t want to do any unnecessary cheating. It wastes time and leads to complications. So we leave set 5 to the last.
Next we cut sets 1 and 3 to Point 2-4-6, and sets 1 and 3 make a new meetpoint on the Y axis. Now we cut set 5 to fit between this new meetpoint and the culet. Set 5 may not be exactly 41 degrees but it will be close; nobody will know the difference, and no cheating will be necessary. Whenever you chain around the stone, look for a point at or near the end of the chain where you can make an adjustment which will bury any accumulated errors.
Usually the sequence starting from the culet is the reverse of that starting at the girdle. Since the connection between the girdle and culet is through set 7, we should cut that set first and make the culet point. Since we have to start our chaining from the end girdle points, we should make those two points next by cutting 4 facets at 90 degrees on set 2 indices, using a constant mast height so both ends are the same. From the two end points cut sets 2 and 4, and from the culet cut set 6. As before this makes the meetpoint to which sets 1 and 3 are cut. Now sets 1 and 2 make the meetpoint to which the 90 degrees girdles at set l’s indices are cut. Again, set 5 is cut last and to fit.
The other example is the pavilion of the Backgammon #2, as shown on the official diagram for the 1996 Australian Cup Challenge. At first glance it appears that the shape is indeterminate; no method is given for determining the size of the cut corner. I had a call about this. In our Sept. [1994] Newsletter the article about Gemstone Geometry discussed how three facets make a point and two facets make a line, and that the Slope of a line is determined by the angles of the two adjacent facets and their index numbers. Look at this pavilion. Do you see that sets 1 and 2 both extend from girdle to culet, and the line between them hits a corner? That’s your answer.
This pavilion is a natural CLAM Preform (Corner Locator Angle Method), which means that two facets meeting at the culet make a line which locates a corner point. In this design they are facets 1 and 2. If you make a rectangle at 90 degrees to the required L/W which is 1.422, then cut sets 1 and 2, you will have a point on the sides of the stone to which the G2 facets at 90 degrees can be cut, completing the preform. Most CLAM preforms are not naturals, and the two facets coming off the culet are temporary, used only to locate the corner point.
For a third example, the crown of the Backgammon #2 cut offers another lesson in sequencing points made on the stone. Here we have a rather complicated group of facets on the ends of the stone.
This crown brings us to yet another thing to look for in analyzing a design — Step Facets. Always look for pairs of step facets; they can help you immensely in deciding the order of cutting. Here we have four pairs of them: d and e are at index 2, f and g are at index 4, k and m are at index 22, and j and h are at index 24. Working from girdle to table, the lower-angled facet of each stepped-pair can be put off until its higher-angled companion is cut. You should also be aware that the three girdle break facets a, b, and c are the upper members of a step pair with the 90 degree girdle facets, and if they terminate at a single upper point, they too are flexible. We will use this advantage to cut the correct angle of facet “a” last.
So here you will first make a level girdle line around the stone using the highest angled break facet which is c at 66.24 degrees on the ends, but you can let the angle be whatever it wants when you move to index 12 at the corner and index 96 on the side, as long as it doesn’t go below a or b’s angle. After girdling there’s a couple of ways to go, you could work up the side with the large zig-zag facets and adjust the end facets to fit, or you could work up the ends and adjust the large zig-zag facets to fit. Working from the end is best. Why? Because the large zig-zags are at lower angles and harder to cut accurately. Facet f is already down to 17 degrees–an angle where you should start using a 45 degree dop, and it’s a waste of time changing to a 45 degree dop and back.
So starting at the ends, cut b and c, then d and k. Then facets j and m, followed by i, will finish up the ends of the stone. Now you have the two points to which facet f should be cut. The upper steps–g and h can then be cut in that order without any problem, then cut set e to fit, and then set a is cut last and to fit. This sequence takes the most advantage of the steps. When you have pairs of steps as on this crown, the upper one of the pair can usually be postponed to your advantage, because its angle is flexible. If you can let your accumulation of small errors end up on a step facet, you can often save yourself the necessity of cheating. It’s much easier to make an adjustment in an angle instead of an index number (cheating).
I hope you see from this little exercise how in sequencing the order of facets cut we are also sequencing the order in which points are made on the stone, and that is the important consideration.