Brilliant (diamond cut)
A brilliant is a diamond or other gemstone cut in a particular form with numerous facets so as to have exceptional brilliance. The shape resembles that of a cone and provides maximized light return through the top of the diamond. With modern techniques, the cutting and polishing of a diamond crystal always results in a dramatic loss of weight; the round brilliant cut is preferred when the crystal is an octahedron, as two stones may be cut from one such crystal. Oddly shaped crystals such as macles are more to be cut in a fancy cut—that is, a cut other than the round brilliant—which the particular crystal shape lends itself to; the original round brilliant-cut was developed by Marcel Tolkowsky in 1919. The modern round brilliant consists of 58 facets, ordinarily today cut in two pyramids placed base to base: 33 on the crown, truncated comparatively near its base by the table, 25 on the pavilion, which has only the apex cut off to form the culet, around which 8 extra facets are sometimes added.
In recent decades, most girdles are faceted. Many girdles have 64, 80, or 96 facets. While the facet count is standard, the actual proportions are not universally agreed upon; some gem cutters refer to a Scandinavian brilliant cut. Quoting Green et al. 2001: Because every facet has the potential to change a light ray's plane of travel, every facet must be considered in any complete calculation of light paths. Just as a two-dimensional slice of a diamond provides incomplete information about the three-dimensional nature of light behavior inside a diamond, this two-dimensional slice provides incomplete information about light behavior outside the diamond. A diamond's panorama is three-dimensional. Although diamonds are symmetrical, light can enter a diamond from many directions and many angles; this factor further highlights the need to reevaluate Tolkowsky's results, to recalculate the effects of a diamond's proportions on its appearance aspects. Another important point to consider is that Tolkowsky did not follow the path of a ray, reflected more than twice in the diamond.
However, we now know that a diamond's appearance is composed of many light paths that reflect more than two times within that diamond. Once again, we can see that Tolkowsky's predictions are helpful in explaining optimal diamond performance, but they are incomplete by today's technological standards. Figures 1 and 2 show the facets of a round brilliant diamond. Figure 1 assumes that the "thick part of the girdle" is the same thickness at all 16 "thick parts", it does not consider the effects of indexed upper girdle facets. Figure 2 is adapted from Figure 37 of Marcel Tolkowsky's Diamond Design, published in 1919. Since 1919, the lower girdle facets have become longer; as a result, the pavilion main facets have become narrower. The relationship between the crown angle and the pavilion angle has the greatest effect on the look of the diamond. A steep pavilion angle can sometimes be complemented by a shallower crown angle, vice versa. Other proportions affect the look of the diamond: The table ratio is significant.
The length of the lower girdle facets affects whether Hearts and arrows can be seen in the stone, under certain viewers. Most round brilliant diamonds have the same girdle thickness at all 16 "thick parts". So-called "cheated" girdles have thicker girdles where the main facets touch the girdle than where adjacent upper girdle facets touch the girdle; these stones weigh more, have worse optical performance. So-called "painted" girdles have thinner girdles where the main facets touch the girdle than where adjacent upper girdle facets touch the girdle; these stones have less light leakage at the edge of the stone. Some diamonds with painted girdles receive lower grades in the GIA's cut grading system, for reasons given in a 2005 GIA article. Several groups have developed diamond cut grading standards, they all disagree somewhat on. There are certain proportions; the AGA standards may be the strictest. David Atlas has suggested; the HCA changed several times between 2001 and 2004. As of 2004, an HCA score below two represented an excellent cut.
The HCA distinguishes between brilliant and fiery cuts. The American Gem Society standards changed in 2005 to better match Tolkowsky's model and Octonus' ray tracing results; the 2005 AGS standards penalize stones with "cheated" girdles. They grade from 0 to 10; the GIA began grading cut on every grading report beginning 2006 based on their comprehensive study of 20,000 proportions with 70,000 observations of 2,000 diamonds. The single descriptive words are as follows: Excellent, Very Good, Good and Poor; the distance from the viewer's eye to the diamond is important. The 2005 AGS cut standards are based on a distance of 25 centimeters; the 2004 HCA cut standards are based on a distance of 40 centimeters. Polish and symmetry are two important aspects of the cut; the polish grade describes the smoothness of the diamond's facets, the symmetry grade refers to alignment of the facets. With
Gemology or gemmology is the science dealing with natural and artificial gemstone materials. It is considered a branch of mineralogy; some jewelers are academically trained are qualified to identify and evaluate gems. Rudimentary education in gemology for jewelers and gemologists began in the nineteenth century, but the first qualifications were instigated after the National Association of Goldsmiths of Great Britain set up a Gemmological Committee for this purpose in 1908; this committee matured into the Gemmological Association of Great Britain, now an educational charity and accredited awarding body with its courses taught worldwide. The first US graduate of Gem-A's Diploma Course, in 1929, was Robert Shipley, who established both the Gemological Institute of America and the American Gem Society. There are now several professional schools and associations of gemologists and certification programs around the world; the first gemological laboratory serving the jewelry trade was established in London in 1925, prompted by the influx of the newly developed "cultured pearl" and advances in the synthesis of rubies and sapphires.
There are now numerous gem laboratories around the world requiring more advanced equipment and experience to identify the new challenges - such as treatments to gems, new synthetics, other new materials. It is difficult to obtain an expert judgement from a neutral laboratory. Analysis and estimation in the gemstone trade have to take place on site. Professional gemologists and gemstone buyers use mobile laboratories, which pool all necessary instruments in a travel case; such so-called travel labs have their own current supply, which makes them independent from infrastructure. They are suitable for gemological expeditions. Gemstones are categorized based on their crystal structure, specific gravity, refractive index, other optical properties, such as pleochroism; the physical property of "hardness" is defined by the non-linear Mohs scale of mineral hardness. Gemologists study these factors while appraising cut and polished gemstones. Gemological microscopic study of the internal structure is used to determine whether a gem is synthetic or natural by revealing natural fluid inclusions or melted exogenous crystals that are evidence of heat treatment to enhance color.
The spectroscopic analysis of cut gemstones allows a gemologist to understand the atomic structure and identify its origin, a major factor in valuing a gemstone. For example, a ruby from Burma will have definite internal and optical activity variance from a Thai ruby; when the gemstones are in a rough state, the gemologist studies the external structure. The stone is identified by its color, refractive index, optical character, specific gravity, examination of internal characteristics under magnification. Gemologists use a variety of tools and equipment which allow for the accurate tests to be performed in order to identify a gemstone by its specific characteristics and properties; these include: Corrected 10× loupe Microscope Refractometer Polarising filter Magnifying eyepiece Contact liquid for RI up to 1.81 Polariscope Optic figure sphere Dichroscope Spectroscope Penlight Tweezers Stone cloth Color filter Immersion cell Ultraviolet lamp Gem identification is a process of elimination. Gemstones of similar color undergo non-destructive optical testing until there is only one possible identity.
Any single test is indicative, only. For example, the specific gravity of ruby is 4.00, glass is 3.15–4.20, cubic zirconia is 5.6–5.9. So one can tell the difference between cubic zirconia and the other two. And, as with all occurring materials, no two gems are identical; the geological environment they are created in influences the overall process so that although the basics can be identified, the presence of chemical "impurities" and substitutions along with structural imperfections create "individuals". One test to determine the gem's identity is to measure the refraction of light in the gem; every material has a critical angle. This can be measured and thus used to determine the gem's identity; this is measured using a refractometer, although it is possible to measure it using a microscope. Specific gravity known as relative density, varies depending upon the chemical composition and crystal structure type. Heavy liquids with a known specific gravity are used to test loose gemstones. Specific gravity is measured by comparing the weight of the gem in air with the weight of the gem suspended in water.
This method uses a similar principle to how a prism works to separate white light into its component colors. A gemological spectroscope is employed to analyze the selective absorption of light in the gem material; when light passes from one medium to another, it bends. Blue light bends more than red light. How much the light bends will vary depending on the gem material. Coloring agents or chromophores show bands in the spectroscope and indicate which element is responsible for the gem's color. Inclusions can help gemologists to determine whether or not a gemstone is natural, synthetic or treated. Institutes and laboratories American Gem Society - AGS Asian Institute of Gemological Sciences - AIGS Canadian Gemmological Association - CGA Canadian Institute of Gemmology - CIG European Gemological Laboratory - EGL Gemmological Association of Australia - GAA Gemmological Association of Great Britain - Gem-A Gemological Institute of America - GIA Gübelin
Diamond cutting is the practice of changing a diamond from a rough stone into a faceted gem. Cutting diamond requires specialized knowledge, tools and techniques because of its extreme difficulty; the first guild of diamond cutters and polishers was formed in 1375 in Nuremberg and led to the development of various types of "cut". This has two meanings in relation to diamonds; the first is the shape: square, so on. The second relates to the specific quality of cut within the shape, the quality and price will vary based on the cut quality. Since diamonds are one of the hardest materials, special diamond-coated surfaces are used to grind the diamond down; the first major development in diamond cutting came with the "Point Cut" during the half of the 14th century: the Point Cut follows the natural shape of an octahedral rough diamond crystal, eliminating some waste in the cutting process. Diamond cutting, as well as overall processing, is concentrated in a few cities around the world; the main diamond trading centers are Antwerp, Tel Aviv, Dubai from where roughs are sent to the main processing centers of India and China.
Diamonds are cut and polished in Surat and the Chinese cities of Guangzhou and Shenzhen. India in recent years has held between 19–31% of the world market in polished diamonds and China has held 17% of the world market share in a recent year. Another important diamond center is New York City; the diamond cutting process includes these steps. Diamond manufacturers analyze diamond rough from an economic perspective, with two objectives steering decisions made about how a faceted diamond will be cut; the first objective is that of maximum return on investment for the piece of diamond rough. The second is how the finished diamond can be sold. Scanning devices are used to get a 3-dimensional computer model of the rough stone. Inclusions are photographed and placed on the 3D model, used to find an optimal way to cut the stone; the process of maximizing the value of finished diamonds, from a rough diamond into a polished gemstone, is both an art and a science. The choice of cut is influenced by many factors.
Market factors include the exponential increase in value of diamonds as weight increases, referred to as weight retention, the popularity of certain shapes amongst consumers. Physical factors include the original shape of the rough stone, location of the inclusions and flaws to be eliminated; the weight retention analysis studies the diamond rough to find the best combination of finished stones as it relates to per carat value. For instance, a 2.20 carat octahedron may produce either two half carat diamonds whose combined value may be higher than that of a 0.80 carat diamond + 0.30 carat diamond that could be cut from the same rough diamond. The round brilliant cut and square brilliant cuts are preferred when the crystal is an octahedron, as two stones may be cut from one such crystal. Oddly shaped crystals, such as macles are more to be cut in a fancy cut—that is, a cut other than the round brilliant—which the particular crystal shape lends itself to. With modern techniques, the cutting and polishing of a diamond crystal always results in a dramatic loss of weight, about 50%.
Sometimes the cutters compromise and accept lesser proportions and symmetry in order to avoid inclusions or to preserve the weight. Since the per-carat price of a diamond shifts around key milestones, many one-carat diamonds are the result of compromising Cut quality for Carat weight. In colored diamonds, cutting can influence the color grade of the diamond, thereby raising its value. Certain cut shapes are used to intensify the color of the diamond; the radiant cut is an example of this type of cut. Natural green color diamonds most have a surface coloration caused by natural irradiation, which does not extend through the stone. For this reason green diamonds are cut with significant portions of the original rough diamond's surface left on the finished gem, it is these naturals. The other consideration of diamond planning is how a diamond will sell; this consideration is unique to the type of manufacturer. While a certain cutting plan may yield a better value, a different plan may yield diamonds that will sell sooner, providing an earlier return on the investment.
Cleaving is the separation of a piece of diamond rough into separate pieces, to be finished as separate gems. Sawing is the use of a diamond laser to cut the diamond rough into separate pieces. Bruting is the art of cutting a diamond round. In the modern era diamonds are rounded using either a laser. Industrial diamonds can be used for bruting a diamond round. Modern computer software measures the roundness of each diamond and "Ideal Cut" diamonds have to round within a 10th of a millimeter to qualify as an excellent cut diamond. Diamond polishing is the final polishing of the diamond. In a diamond factory one would find a diamond "Crossworker" who first places the main facets on a diamond; this is done to ensure maximum weight and best angles for the specific shape of diamond. After initial crossworking is complete, the diamond is finalized by smoothing the main facets by the crossworker, known as polishing the diamond. After the main facets have been polished by the crossworker, the final facets are polished onto the diamond by a "Brillianteer."
The facets added are the stars and bottom halves known as upper and lower girdle facets. The final stage
A gemstone is a piece of mineral crystal which, in cut and polished form, is used to make jewelry or other adornments. However, certain rocks and organic materials that are not minerals are used for jewelry and are therefore considered to be gemstones as well. Most gemstones are hard, but some soft minerals are used in jewelry because of their luster or other physical properties that have aesthetic value. Rarity is another characteristic. Apart from jewelry, from earliest antiquity engraved gems and hardstone carvings, such as cups, were major luxury art forms. A gem maker is called a gemcutter; the traditional classification in the West, which goes back to the ancient Greeks, begins with a distinction between precious and semi-precious. In modern use the precious stones are diamond, ruby and emerald, with all other gemstones being semi-precious; this distinction reflects the rarity of the respective stones in ancient times, as well as their quality: all are translucent with fine color in their purest forms, except for the colorless diamond, hard, with hardnesses of 8 to 10 on the Mohs scale.
Other stones are classified by their color and hardness. The traditional distinction does not reflect modern values, for example, while garnets are inexpensive, a green garnet called tsavorite can be far more valuable than a mid-quality emerald. Another unscientific term for semi-precious gemstones used in art history and archaeology is hardstone. Use of the terms'precious' and'semi-precious' in a commercial context is, misleading in that it deceptively implies certain stones are intrinsically more valuable than others, not the case. In modern times gemstones are identified by gemologists, who describe gems and their characteristics using technical terminology specific to the field of gemology; the first characteristic a gemologist uses to identify a gemstone is its chemical composition. For example, diamonds are made of carbon and rubies of aluminium oxide. Next, many gems are crystals which are classified by their crystal system such as cubic or trigonal or monoclinic. Another term used is habit, the form the gem is found in.
For example, which have a cubic crystal system, are found as octahedrons. Gemstones are classified into different groups and varieties. For example, ruby is the red variety of the species corundum, while any other color of corundum is considered sapphire. Other examples are the emerald, red beryl, goshenite and morganite, which are all varieties of the mineral species beryl. Gems are characterized in terms of refractive index, specific gravity, cleavage and luster, they may exhibit double refraction. They may have a distinctive absorption spectrum. Material or flaws within a stone may be present as inclusions. Gemstones may be classified in terms of their "water"; this is a recognized grading of the gem's luster, transparency, or "brilliance". Transparent gems are considered "first water", while "second" or "third water" gems are those of a lesser transparency. There is no universally accepted grading system for gemstones. Diamonds are graded using a system developed by the Gemological Institute of America in the early 1950s.
All gemstones were graded using the naked eye. The GIA system included a major innovation: the introduction of 10x magnification as the standard for grading clarity. Other gemstones are still graded using the naked eye. A mnemonic device, the "four Cs", has been introduced to help the consumer understand the factors used to grade a diamond. With modification, these categories can be useful in understanding the grading of all gemstones; the four criteria carry different weight depending upon whether they are applied to colored gemstones or to colorless diamonds. In diamonds, cut is the primary determinant of value, followed by color. Diamonds are meant to sparkle, to break down light into its constituent rainbow colors, chop it up into bright little pieces, deliver it to the eye. In its rough crystalline form, a diamond will do none of these things. In gemstones that have color, including colored diamonds, it is the purity and beauty of that color, the primary determinant of quality. Physical characteristics that make a colored stone valuable are color, clarity to a lesser extent, unusual optical phenomena within the stone such as color zoning and asteria.
The Greeks, for example valued asteria gemstones, which were regarded as powerful love charms, Helen of Troy was known to have worn star-corundum. Aside from the diamond, the ruby, emerald and opal have been considered to be precious. Up to the discoveries of bulk amethyst in Brazil in the 19th century, amethyst was considered a precious stone as well, going back to ancient Greece. In the last century certain stones such as aquamarine and cat's eye have been popular and hence been regarded as precious. Today such a distinction is no longer made by the gemstone trade. Many gemstones are used in the most expensive jewelr
In geometry, parallel lines are lines in a plane which do not meet. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel. Parallel planes are planes in the same three-dimensional space. Parallel lines are the subject of Euclid's parallel postulate. Parallelism is a property of affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines can have analogous properties that are referred to as parallelism; the parallel symbol is ∥. For example, A B ∥ C D indicates that line AB is parallel to line CD. In the Unicode character set, the "parallel" and "not parallel" signs have codepoints U+2225 and U+2226, respectively. In addition, U+22D5 represents the relation "equal and parallel to". Given parallel straight lines l and m in Euclidean space, the following properties are equivalent: Every point on line m is located at the same distance from line l.
Line m is in the same plane as line l but does not intersect l. When lines m and l are both intersected by a third straight line in the same plane, the corresponding angles of intersection with the transversal are congruent. Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, so, are "more complicated" than the second. Thus, the second property is the one chosen as the defining property of parallel lines in Euclidean geometry; the other properties are consequences of Euclid's Parallel Postulate. Another property that involves measurement is that lines parallel to each other have the same gradient; the definition of parallel lines as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements. Alternative definitions were discussed by other Greeks as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein.
Simplicius mentions Posidonius' definition as well as its modification by the philosopher Aganis. At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools; the traditional treatment of geometry was being pressured to change by the new developments in projective geometry and non-Euclidean geometry, so several new textbooks for the teaching of geometry were written at this time. A major difference between these reform texts, both between themselves and between them and Euclid, is the treatment of parallel lines; these reform texts were not without their critics and one of them, Charles Dodgson, wrote a play and His Modern Rivals, in which these texts are lambasted. One of the early reform textbooks was James Maurice Wilson's Elementary Geometry of 1868. Wilson based his definition of parallel lines on the primitive notion of direction. According to Wilhelm Killing the idea may be traced back to Leibniz. Wilson, without defining direction since it is a primitive, uses the term in other definitions such as his sixth definition, "Two straight lines that meet one another have different directions, the difference of their directions is the angle between them."
Wilson In definition 15 he introduces parallel lines in this way. Wilson Augustus De Morgan reviewed this text and declared it a failure on the basis of this definition and the way Wilson used it to prove things about parallel lines. Dodgson devotes a large section of his play to denouncing Wilson's treatment of parallels. Wilson edited this concept out of the third and higher editions of his text. Other properties, proposed by other reformers, used as replacements for the definition of parallel lines, did not fare much better; the main difficulty, as pointed out by Dodgson, was that to use them in this way required additional axioms to be added to the system. The equidistant line definition of Posidonius, expounded by Francis Cuthbertson in his 1874 text Euclidean Geometry suffers from the problem that the points that are found at a fixed given distance on one side of a straight line must be shown to form a straight line; this must be assumed to be true. The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles all transversals must do so.
Again, a new axiom is needed to justify this statement. The three properties above lead to three different methods of construction of parallel lines; because parallel lines in a Euclidean plane are equidistant there is a unique distance between the two parallel lines. Given the equations of two non-vertical, non-horizontal parallel lines, y = m x + b 1 y = m x + b 2
Cleavage, in mineralogy, is the tendency of crystalline materials to split along definite crystallographic structural planes. These planes of relative weakness are a result of the regular locations of atoms and ions in the crystal, which create smooth repeating surfaces that are visible both in the microscope and to the naked eye. Cleavage forms parallel to crystallographic planes: Basal or pinacoidal cleavage occurs when there is only one cleavage plane. Graphite has basal cleavage. Mica has basal cleavage. Cubic cleavage occurs on. Halite has cubic cleavage, therefore, when halite crystals are broken, they will form more cubes. Octahedral cleavage occurs. Fluorite exhibits perfect octahedral cleavage. Octahedral cleavage is common for semiconductors. Diamond has octahedral cleavage. Rhombohedral cleavage occurs when there are three cleavage planes intersecting at angles that are not 90 degrees. Calcite has rhombohedral cleavage. Prismatic cleavage occurs. Spodumene exhibits prismatic cleavage. Dodecahedral cleavage occurs.
Sphalerite has dodecahedral cleavage. Crystal parting occurs when minerals break along planes of structural weakness due to external stress or along twin composition planes. Parting breaks are similar in appearance to cleavage, but only occur due to stress. Examples include magnetite which shows octahedral parting, the rhombohedral parting of corundum and basal parting in pyroxenes. Cleavage is a physical property traditionally used in mineral identification, both in hand specimen and microscopic examination of rock and mineral studies; as an example, the angles between the prismatic cleavage planes for the pyroxenes and the amphiboles are diagnostic. Crystal cleavage is of technical importance in the electronics industry and in the cutting of gemstones. Precious stones are cleaved by impact, as in diamond cutting. Synthetic single crystals of semiconductor materials are sold as thin wafers which are much easier to cleave. Pressing a silicon wafer against a soft surface and scratching its edge with a diamond scribe is enough to cause cleavage.
Elemental semiconductors are a space group for which octahedral cleavage is observed. This means. Most other commercial semiconductors can be made in the related zinc blende structure, with similar cleavage planes. Cleavage Mineral galleries: Mineral properties – Cleavage
Facets are flat faces on geometric shapes. The organization of occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones have facets cut into them in order to improve their appearance by allowing them to reflect light. Of the hundreds of facet arrangements that have been used, the most famous is the round brilliant cut, used for diamond and many colored gemstones; this first early version of what would become the modern Brilliant Cut is said to have been devised by an Italian named Peruzzi, sometime in the late 17th century. On, the first angles for an "ideal" cut diamond were calculated by Marcel Tolkowsky in 1919. Slight modifications have been made since but angles for "ideal" cut diamonds are still similar to Tolkowsky's formula. Round brilliants cut before the advent of "ideal" angles are referred to as "Early round brilliant cut" or "Old European brilliant cut" and are considered poorly cut by today's standards, though there is still interest in them from collectors.
Other historic diamond cuts include the "Old Mine Cut", similar to early versions of the round brilliant, but has a rectangular outline, the "Rose Cut", a simple cut consisting of a flat, polished back, varying numbers of angled facets on the crown, producing a faceted dome. Sometimes a 58th facet, called a culet is cut on the bottom of the stone to help prevent chipping of the pavilion point. Earlier brilliant cuts have large culets, while modern brilliant cut diamonds lack the culet facet, or it may be present in minute size; the art of cutting a gem is an exacting procedure performed on a faceting machine. The ideal product of facet cutting is a gemstone that displays a pleasing balance of internal reflections of light known as brilliance and colorful dispersion, referred to as "fire", brightly colored flashes of reflected light known as scintillation. Transparent to translucent stones are faceted, although opaque materials may be faceted as the luster of the gem will produce appealing reflections.
Pleonaste and black diamond are examples of opaque faceted gemstones. The angles used for each facet play a crucial role in the final outcome of a gem. While the general facet arrangement of a particular gemstone cut may appear the same in any given gem material, the angles of each facet must be adjusted to maximize the optical performance; the angles used will vary based on the refractive index of the gem material. When light passes through a gemstone and strikes a polished facet, the minimum angle possible for the facet to reflect the light back into the gemstone is called the critical angle. If the ray of light strikes a surface lower than this angle, it will leave the gem material instead of reflecting through the gem as brilliance; these lost light rays are sometimes referred to as "light leakage", the effect caused by it is called "windowing" as the area will appear transparent and without brilliance. This is common in poorly cut commercial gemstones. Gemstones with higher refractive indexes make more desirable gemstones, the critical angle decreases as refractive indices increase, allowing for greater internal reflections as the light is less to escape.
This machine uses a motor-driven plate to hold a flat disk for the purpose of cutting or polishing. Diamond abrasives bonded to metal or resin are used for cutting laps, a wide variety of materials are used for polishing laps in conjunction with either fine diamond powder or oxide-based polishes. Water is used for cutting, while either oil or water is used for the polishing process; the machine uses a system called a "mast" which consists of an angle readout, height adjustment and a gear with a particular number of teeth is used as a means of setting the rotational angle. The angles of rotation are evenly divided by the number of teeth present on the gear, though many machines include additional means of adjusting the rotational angle in finer increments called a "cheater"; the stone is bonded to a rod known as a "dop" or "dop stick" and is held in place by part of the mast referred to as the "quill". The dopped stone is ground at precise angles and indexes on cutting laps of progressively finer grit, the process is repeated a final time to polish each facet.
Accurate repetition of angles in the cutting and polishing process is aided by the angle readout and index gear. The physical process of polishing is a subject of debate. One accepted theory is that the fine abrasive particles of a polishing compound produce abrasions smaller than the wavelengths of light, thus making the minute scratches invisible. Since gemstones have two sides, a device called a "transfer jig" is used to flip the stone so that each side may be cut and polished. Cleaving relies on planar weaknesses of the chemical bonds in the crystal structure of a mineral. If a sharp blow is applied at the correct angle, the stone may split cleanly apart. While cleaving is sometimes used to split uncut gemstones into smaller pieces, it is never used to produce facets. Cleaving of diamonds was once common, but as the risk of damaging a stone is too high, undesirable diamond pieces resulted; the preferred method of splitting diamonds into smaller pieces is now sawing. An older and more primitive style of faceting machine called a jamb peg machine used wooden dop sticks of precise length and a "mast" system consisting of a plate with holes placed in it.
By placing the back end of the dop into one of the many holes, the stone could