The surfaces of gems, pastes, and most other substances worked by the lapidary, are, as is well known, cut into facets to improve their brilliancy, by multiplying the number of reflecting surfaces, in order that the play of light may be proportionally increased. Facets are principally cut upon transparent and semi-transparent stones, but sometimes also upon opake stones, such as carnelian; and speaking generally, it may be said that the greater the natural brilliancy of the stone, the fewer facets are necessary to produce the required play of light; and with valuable gems it is always desirable to produce the brilliancy with as few facets as possible, in order to avoid confusion in the rays of light.

Opake stones are cut on the face only, and the stone is in general thin, and flat on the back; but transparent stones are, if possible, left thick, and so cut as to make the back, or lower part of the stone that is enclosed in the setting, of about double the thickness of the front or face that is exposed. The back of the stone is cut into facets or squares that exactly correspond in plan with the position of the principal facets on the front of the stone; and the angles which the squares at the back make with the axis of the stone, are required to be such, that all the light reflected from their surfaces, may fall within the central flat surface on the front of the stone, called the table.

The facets are arranged upon the stones in a great variety of methods, but they may nearly all be considered as modifications of three principal varieties, namely, the trap cut, the brilliant cut, and the rose cut, one of the two latter forms being always employed for diamonds.

The trap cut, or trapping, as it is called by lapidaries, consists of parallel planes nearly rectangular, arranged round the contour of the stone, as shown in figs. 1151 to 1156. This cut is always used for emeralds, and sometimes also for the fronts of other gems, but it is principally employed for the backs of stones, the fronts of which are cut in one of the modifications of the brilliant cut.

The brilliant cut consists of lozenge-shaped facets alternated with triangles, as shown in figs. 1157 to 1167, and is used for the fronts of most transparent stones that are sufficiently thick to allow of being cut into facets on both the front and back. The different modifications of this form of facetting, are known as the half brilliant, or single cut; the full brilliant; the split brilliant, or trap brilliant; and the double brilliant, or Lisbon cut; according to the arrangement of the principal facets.

The rose cut consists of triangular facets arranged upon and around a central hexagon, as in figs. 1169 to 1173. This cut is employed upon such stones as are thin, and large on the surface, or, as it is called, much spread, as the rose cut is applied only on the front of the stone, and the back is left flat. The rose cut is considered to give the greatest lustre that can be obtained from cutting the front only, as the surface is entirely covered with facets, and on this account the rose cut is sometimes applied to opake stones, but its principal application is to the diamond, or to other colourless gems employed as fictitious diamonds, such as the jargoon.

In all cases of cutting valuable gems, the principal object of the lapidary is to fashion the stone so as to produce as much display as can be attained without materially reducing the size of the gem, and this circumstance in great measure determines the manner in which it is cut. This is especially the case with the diamond, which is always found in the form of an octahedron, more or less perfect in form; and unless the diamond has defects, it is always cut as a brilliant, with an octagonal base, that being the largest regular figure that can be inscribed within the octahedron.

Diamonds that have defects are split by cleavage, and the pieces are cut into rose diamonds, and which form is also adopted for those whole diamonds that are too thin to be cut into brilliants. Other valuable gems are in like manner cut into the largest regular forms they will respectively produce.

With less valuable stones and pastes, the reduction of the material is of less importance, and the form of cutting is rather a matter of choice than otherwise; but in order that they may the more nearly resemble valuable gems, they are usually cut into corresponding forms; this is especially the case with pastes, which are cut on the front in exactly the same manner as the gems they are intended to represent, and the cutting at the back is only modified, so as to cause the play of light to assimilate to that of the gems themselves.

In all cases of cutting gems or pastes into facets, the general contour of the stone is first produced by roughly grinding it into form, much the same as for a rounded stone. Generally the first step is to grind a flat face upon the stone, in order to judge of its quality, and ascertain whether it contains any imperfections, and, if so, the cutting is modified accordingly. If the stone proves to be tolerably perfect, and it is to be cut into facets upon both the front and back, the flat surface first cut is made to constitute the table of the stone, and the edges are corrected to bring it to a regular figure, generally a circle or ellipsis, but sometimes a square, or rectangle, with the corners rounded off, according to the shape that can be produced with the least waste of material. The edge thus ground forms the girdle, or extreme margin of the stone by which it is retained in the setting. The part between the girdle and table, called the top of the stone, is then rounded or bevelled off to about the extent that the facets are desired to extend. The back of the stone is afterwards rounded in the same manner to the general shape, leaving a small central plane called the cullet, or cullasse.

If the stone is to be cut into facets on the front only, the flat face first cut is mostly made to constitute the back of the stone, the edges are corrected for the girdle, and the front is prepared by cutting, first, a flat face for the table, and afterwards rounding or bevelling the top. So far the stones are prepared in the same manner to the general shape, whatsoever form of facetting is to be adopted.