Formée Cross Rectangle(FORMEE_R.GEM)
by Robert W. Strickland
Revised 7/28/91, 5/10/92, 5/8/93
Angles for R.I. = 1.54
67 facets + 8 facets on girdle = 75
2-fold, mirror-image symmetry
96 index
L/W = 1.272 T/W = 0.795 T/L = 0.625
P/W = 0.649 C/W = 0.240
H/W = (P+C)/W+0.02 = 0.909
P/H = 0.714 C/H = 0.264
Vol./W^3 = 0.526
CAM PREFORM PF1 33.40 10-38-58-86 Cut to TCP PF2 35.00 24-72 Cut to TCP PF3 41.70 96-48 Cut to TCP G1 90.00 24-72 Cut to final length G2 90.00 10-38-58-86 Level false girdle G3 90.00 96-48 Level false girdle PAVILION 1 43.00 13-35-61-83 Cut to TCP of preform 2 46.00 10-38-58-86 Meet G1-G2-1 3 45.81 07-41-55-89 Meet G2-G3-2 4 62.00 24-72 Level girdle 5 54.00 23-25-71-73 Meet 2-4 at girdle line 6 70.00 96-48 Meet 2-3 at girdle line 7 60.00 01-47-49-95 " 8 42.20 10-38-58-86 Meet 1-2-3 9 45.00 96-48 Meet 8 at culet 10 47.31 03-45-51-93 Adjust angle if needed CROWN A 51.00 24-72 Leave some girdle B 42.50 23-25-71-73 Meet girdle line C 35.00 19-29-67-77 " D 44.00 10-38-58-86 Level girdle E 39.40 03-45-51-93 Meet girdle line F 42.19 02-46-50-94 " G 61.00 96-48 Level girdle H 38.31 07-41-55-89 Meet girdle line J 35.82 14-34-62-82 " T 0.00 Table Table
In this lesson, we will cut a rectangular design called the Formée Cross Rectangle. You might find it useful to print out the diagram above so you can see how the information on the diagram corresponds to the what you enter into GemCad.
For this design, we will need a Centerpoint Angle Method (CAM) preform. Briefly, this technique allows you to reproduce the girdle outline of the design without having to make any measurements. One cuts several facets to a common centerpoint, a meet point on the dop axis. This set of facets will be cut off later by the actual pavilion facets. One then cuts facets at 90°, making a level false girdle-line and establishing the outline of the stone.
Run GemCad. Change to the Parameter Menu and press the Index gear (g) key and set the index gear to 96. GemCad will ask you for the number of teeth and the bottom index position. Enter 96 for the number of teeth and 0 for the offset. This will make the 96 position at the bottom of the circle of numbers in the Top View. Next, change the symmetry to two-fold mirror-image with the Symmetry (y) command. Enter 2 and y in response to GemCad's questions about the symmetry. Now we are ready to cut the first four facets. Change to the Point Menu and use the Query user (q) command. GemCad will ask you for the coordinates of the point. Enter 0, 0, 1 for the x, y, and z coordinates, respectively. Enter y to tell GemCad you want to use the point. You will see 1pt displayed in the status box. (Recall that if you make a mistake and the information in the status box is incorrect, you can clear it with the Draw (d) key in either the Cut Facets Menu or Point Menu.) Next, change to the the Cut Facets Menu and press the Index (i) key. Enter 10. Now press the Angle (a) key and enter 33.4. GemCad will then cut four facets at index positions 10-38-58-86, and your display should look like Figure 20.
Figure 20. The start of the CAM preform
For many cuts, you can just enter the angle and index of the first set of facets, and GemCad will assume a “reasonable” cutting depth. Here, we typed in the coordinates of the centerpoint. Note also that it was necessary to enter this centerpoint before the angle and index. For some designs with high angle facets (about 50° or higher) the center point will be off the screen, and instead of a centerpoint you will see what looks like a facet at the top of the stone. GemCad starts off with a cube of rough a bit smaller than each view. The faces of this cube are not drawn, but all facets cut will be truncated at the faces of the cube.
The four facets meet at the exact center of the Top View. This is the centerpoint to which the other facets of the preform will be cut. Now, change to the Point Menu. Move your cursor near the centerpoint, as shown by the crosshairs in Figure 20. Press the Meet pt (m) key (or the left mouse button) and enter y to tell GemCad you want to use the point. Now change to the Cut Facets Menu, press the Angle (a) key and enter 35. Then, press the Index (i) key and enter 24. GemCad will then cut two facets at 24-72, making a total of 6 facets. Now let's cut the last pair of facets cut to the common centerpoint. Press the Index (i) key and enter 96 (or zero). Press the Angle (a) key and enter 41.7. Verify that you have a41.7,i0.0 displayed in the status box in the lower-left-hand corner of the screen. If so, change to the Point Menu. Move the cursor back to the centerpoint in the Top View, if it is not still there. Press the Meet pt (m) key. After you enter/tt yto tell GemCad you want to use the point, GemCad should cut two more facets at 96-48., and your display should look like Figure 21.
Figure 21. Facets cut to centerpoint for CAM preform
Now we are ready to cut the girdle facets at 90°. Move the cursor to the location of the crosshairs in Figure 21. Press the Pt on edge (e) key (or the right mouse button) and enter y to use the point. You should see 1pt in the status box. Change to the Cut Menu, and we will explore a new command. Move the mouse cursor inside one of the facets in the Top View and press the Jam index (j) key. You will see the index show up in the status box just as if you had entered the index with the Index (i) command. Try it with several of the facets. Now, find the facet cut at 24 index and use the Jam index (j) key to “jam” its index in the status box. You should see 1pt,i24.0 displayed in the status box. Then, press the Angle (a) key and enter 90. GemCad will then cut the two facets at 24-72. Your display should now look like Figure 22.
Figure 22. The length of the preform is now established
Now, move the cursor inside the facet at index 10. Use the Jam index (j) command to grab its index. (Keep trying until GemCad displays “i10.0” in the status box.) Now move the cursor inside the big facet at 90° in the Side View. Use the Jam angle (A) command to grab its angle. You should see a90.0,i10.0 displayed in the status box. Now change to the Point Menu, move your cursor to the point in the Side View as indicated in Figure 22. Press the Meet pt (m) key (or left mouse button) to pick the meet point and enter y to tell GemCad to use the point. GemCad will then cut the four facets at 10-38-58-86, and your display should look like Figure 23.
Figure 23. Corners cut off
Move the cursor to the point in the End View indicated by the crosshairs in Figure 23. Press the Meet pt (m) key (or left mouse button) to pick the meet point and enter y to use the point. Change to the Cut Facets Menu and move the cursor inside the facet at the 96 index position. (Just a bit up and to the left of the position in Figure 23.) Use the Jam index (j) command to grab its index. You should see 1pt,i0.0 in the status box. (Recall that index position 0 is the same as 96.) Now move the cursor inside the girdle facet at the 10 index position (just below the position in Figure 23). Use the Jam angle (A) command to jam in its angle of 90°, and GemCad will cut the final two girdle facets at 96-48. This completes the CAM preform. Your display should now look like Figure 24.
Figure 24. The completed CAM preform
Next we will cut the actual pavilion facets. These will cut off the preform facets that meet at the centerpoint. Now we shall cut facets at index positions 13-35-61-83. Press the Index (i) key and enter 13. Press the Angle (a) key and enter 43. You should now see/tt a43.0,i13.0in the status box. Change to the Point Menu and move the cursor to the centerpoint as shown in Figure 24. Press the Meet pt (m) key (or the left mouse button) and enter y to use the point. GemCad will cut 4 facets and tell you that 6 facets were cut off. You must press any key to acknowledge this warning. The 4 new facets cut off 6 of the CAM preform facets, and we will lose the other 2 later. Your display should look like Figure 25.
Figure 25. First four pavilion facets
Move the cursor to the location in the Side View shown in Figure 25. Press the Meet pt (m) key (or left mouse button) to enter the meetpoint and press enter y to confirm. Change to the Cut Facets Menu and enter an angle of 46 and an index of 10. GemCad will cut the four facets at 10-38-58-86. Your display should look like Figure 26. From now on, I'll assume you are now sufficiently familiar with changing back and forth between the Cut Facets Menu and the Point Menu and know how to use the Meet pt (m) key command, the Index (i) key command, and the Angle (a) key command. The remaining instructions will be in outline form.
Angle (a) 45.81
Index (i) 7
Move cursor as shown in Figure 26.
Figure 26.
Move cursor as shown in Figure 27.
Meet pt (m) and confirm with y
Angle (a) 62
Meet pt (m) and confirm with y
Four facets will be cut at 07-41-55-89, and display will look like Figure 27.
Figure 27.
Move cursor as shown in Figure 27.
Meet pt (m) and confirm with y
Angle (a) 62
Index (i) 24
Two facets will be cut at 24-72
Angle (a) 54
Index (i) 23
Move cursor as shown in Figure 27. (This is same point as used in the last step.)
Meet pt (m) and confirm with y
Four facets will be cut at 23-25-71-73, and your display will look like Figure 28.
Figure 28.
Move the cursor as shown in Figure 28.
Meet pt (m) and confirm with y
Angle (a) 70
Index (i) 96
Two facets will be cut at 96-48.
Move the cursor to the same point as before (Figure 28).
Meet pt (m) and confirm with y
Angle (a) 60
Index (i) 1
Four facets will be cut at 01-47-49-95, and your display will look like Figure 29.
Figure 29.
Angle (a) 42.2
Index (i) 10
Move cursor as shown in Figure 29.
Meet pt (m) and confirm with y
Four facets will be cut at 10-38-58-86. GemCad will warn you that these facets cut off the remaining CAM preform facets. Your display will look like Figure 30.
Figure 30.
Move cursor as shown in Figure 30.
Meet pt (m) and confirm with y
Angle (a) 45
Index (i) 96
Two facets will be cut at 96-48, and your display will look like Figure 31.
Angle (a) 47.31
Index (i) 3
Move cursor as shown in Figure 31.
Figure 31.
Meet pt (m) and confirm with y
Four facets will be cut at 03-45-51-93.
This completes the pavilion. Change to the Cut Menu and press the Xfer (x) key to transfer the stone. Your display should look like Figure 32.
Figure 32.
Now we need to establish the thickness of the girdle. Move the cursor to the point shown in Figure 32. The cursor should be on the horizontal line in the Side View a bit to the left of the girdle line. Press the Pt on edge (e) key (or the right mouse button) and confirm with y. There should now be a vertical dotted line in the Side View, and this line should define the girdle thickness. If the girdle thickness is not correct, redraw with the Draw (d) key, and set the point again.
Angle (a) 51
Index (i) 24
Two facets will be cut at 24-72, and your display should look like Figure 33.
Figure 33.
Angle (a) 42.5
Index (i) 23
Move the cursor as shown in Figure 33. This meet point will be used for the next 3 steps as well.
Meet pt (m) and confirm with y
Four facets will be cut at 23-25-71-73.
Move the cursor back to the point shown in Figure 33 if it is not already there.
Meet pt (m) and confirm with y
Angle (a) 35
Index (i) 19
Four facets will be cut at 19-29-67-77.
Angle (a) 44
Index (i) 10
Move the cursor back to the point shown in Figure 33 if it is not already there.
Meet pt (m) and confirm with y
Four facets will be cut at 10-38-58-86, and your display will look like Figure 34.
Figure 34.
Move cursor as shown in Figure 34.
Meet pt (m) and confirm with y
Angle (a) 39.4
Index (i) 3
Four facets will be cut at 03-45-51-93.
Angle (a) 42.19
Index (i) 2
Move the cursor back to the point shown in Figure 34 if it is not already there.
Meet pt (m) and confirm with y
Four facets will be cut at 02-46-50-94.
Move the cursor back to the point shown in Figure 34 if it is not already there.
Meet pt (m) and confirm with y
Angle (a) 61
Index (i) 96
Two facets will be cut at 96-48.
Angle (a) 38.31
Index (i) 7
Move the cursor back to the point shown in Figure 34 if it is not already there.
Meet pt (m) and confirm with y
Four facets will be cut at 07-41-55-89, and your display should look like Figure 35.
Figure 35.
Move the cursor to the location indicated by Figure 35. (If you don't see it, look again; it's in the Side View near the girdle line.)
Meet pt (m) and confirm with y
Angle (a) 35.82
Index (i) 14
Four facets will be cut at 14-34-62-82, and your display will look like Figure 36. Now we are ready to cut the table.
Figure 36.
Angle (a) 0 (There is no need to specify an index for the table.)
Move the cursor to the location shown in Figure 36.
Meet pt (m) and confirm with y
Figure 37.
GemCad will cut the table, and your display will look like Figure 37. The crown is now complete. The stone might appear too low in the End View, so let's move it up a bit. Change to the Cut Menu and move your cursor to the location shown in Figure 37. Press the Center (c) key, and GemCad will ask you whether you want to slide the stone along the x, y, or z axes. Enter z, and GemCad will scoot the stone up. (The z axis is the dop axis.) To use the Center (c) command, you place the cursor inside the stone in the End View at where you want the stone to be centered, press the Center (c) key, and enter z. If the cursor is below the center of the view, GemCad will move the stone up\/ to make the center of the view at the height on the stone where your cursor was. The stone should be positioned as in Figure 38.
Figure 38.
Now, change to the Diagram Menu and let's name (label) the facets. Move the cursor inside one facet and press the Name (n) key. GemCad will highlight the facet and ask you for its name. Do this for each facet in turn. (To name a girdle facet, you must be inside the girdle facet in the Side or End View. Its name will be shown in the Bottom View, however.) Now press the List to scrn (l) key to view the cutting sequence. Check to make sure each step has its name in the left column of the listing. If you wish, you may add cutting instructions for each step with the Gloss (inst) (G) key. The Heading (H) key command allows you to enter a heading of up to four lines. This is used to provide a title, designer, and date. The heading will show up at the top of the listing. The completed design should look like Figure 39.
Figure 39.
I suggest that you try to cut the Formée Cross Rectangle from the faceting diagram included in the center of this manual. Once you can cut the design from the faceting diagram without referring to the manual, you should be well prepared to cut from other published diagrams.
This completes the tutorial section of the manual. The next section is a reference manual that describes each GemCad command in detail.