Crystals and pastes employed as fictitious diamonds, are generally cut as in figs. 1177 to 1179. The front is cut as a full brilliant of eight principal squares, upon a regular octagonal base like the diamond. The back is first cut with a row of eight squares, somewhat like fig. 1176; a row of double skill facets are then arranged around the girdle, as in fig. 1162; and, lastly, a row of eight facets are arranged around the culasse. These facets are cut upon the angles joining the principal back squares, the points are extended until they meet the double skill facets, and the back facets intersect each other near the culasse, giving the appearance of a star, whence this form of facetting for the back is known as the star cut. The row of facets around the culasse materially increases the brilliancy, and causes the play of light more nearly to approach that of the diamond. Figs. 1180 to 1182 represent the same form of cutting applied to a hexagonal stone.
The form of facetting called the x cut, shown in figs. 1183 to 1186, is considered to be a very perfect style of cutting for stones having a square or a regular octagon for their base, as it allows of a considerable number of triangular facets being cut upon the top, and at the same time the table and girdle may be retained of one regular figure. In cutting this form, the front is trapped in two heights, and the squares thus produced are converted into triangles by cutting one pair of triangular facets upon every angle of the square or octagon. As seen in the figures, these facets extend from the table to the girdle, and meet in the center of the sides. The x cut is seldom applied to other than square or octagonal stones, and for these shapes the back is generally facetted with the star cut, but sometimes octagonal stones are trapped at the back.
Figs. 1187 and 1188 represent the dental cut, which consists of two rows of triangular facets cut on the top of the stone. The two rows are interposed, so that the bases of one row of triangles form the margin of the table, and the bases of the second row are placed on the line of the girdle, each row extending from the girdle to the table, as seen in the figures, which show the application of this cut to an elliptical stone having eight principal sides. In cutting this form, the front is first trapped in one height with eight squares, and the figure is completed by cutting eight triangular facets around the table, every facet being placed, as usual, upon one of the angles formed by the foundation squares. The back is generally trapped.
All the different forms of facetting are usually cut by practical lapidaries, without any other guide than the gim peg, and cement stick, as shown in fig. 1150. The more difficult cases of cutting valuable gems, arise from the irregular forms of the rough gems, or slight imperfections in their substance, and these difficulties require to be combated rather by judgment and dexterity of hand, than by mechanical guides. This dexterity once acquired, renders the employment of guides less necessary, when the forms of the rough gems are more favourable, especially as the adjustments can be effected more rapidly by the practised fingers, than by mechanical means.
In the comparatively slow process of polishing the facets on diamonds, a very simple form of guide is adopted, as alluded to at page 176, Vol. I.; but this instrument only serves to retain the stone in position, and all the adjustments of angle are effected by hand, in order that the operator may be enabled to place every facet flat upon the skive, without reference to the particular angle at which it was cut.
Fig. 1189 shows a modification of this instrument, contrived by a Geneva lapidary, to adapt it to the cutting of facets at definite angles, and published in the Dictionnaire Technologique. The instrument, called a cadrans, has two jaws, a, which are closed like a vice by a screw passing through them, each of the jaws has on the inside a hemispherical cavity, into which is fitted a brass ball; a tube passes through the ball, and carries at its upper end a small flat disk, b, having on the upper side several concentric circles divided into equal parts. Every circle has a different number of divisions, which are so arranged as to include all the numbers usually required in cutting facets. The cement stick, carrying the stone to be cut, is made cylindrical, and fits within the tube sufficiently tight to retain its position during the cutting of the stone, and the upper end of the stick is made square to carry a small index point, by which the divisions on the disk are read off.
The vertical angle of the tube is determined by the quadrant c, fixed on one side of the jaws, a, and the tube is retained at any angle by closing the jaws upon the ball. The center of the quadrant is supposed to be in the center of the ball, and the arc is divided as usual into 90 degrees, the upper division is marked 0, and the lower 70, the remainder of the arc being hidden by the jaw. When the tube is fixed at 0, the cement stick is vertical, and this position serves for cutting the table or the culasse; on fixing the tube at 20 degrees, all the facets cut in this position will be inclined at that angle, and the number of facets around the stone will be determined by twisting the cement stick in the tube, until the index marks the required division on the disk, b.