Facets are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut into them in order to improve their appearance by allowing them to reflect light.

Cut Ruby
A cut ruby, with facets visible.

Facet arrangements

Of the hundreds of facet arrangements that have been used, the most famous is probably 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.[1][2] Later on, the first angles for an "ideal" cut diamond were calculated by Marcel Tolkowsky in 1919. Slight modifications have been made since then, but angles for "ideal" cut diamonds are still similar to Tolkowsky's formula. Round brilliants cut before the advent of "ideal" angles are often 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" which is similar to early versions of the round brilliant, but has a rectangular outline, and the "Rose Cut" which is a simple cut consisting of a flat, polished back, and 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 often have very large culets, while modern brilliant cut diamonds generally lack the culet facet, or it may be present in minute size.

Cutting facets

Spodumene oct faceted
A faceted spodumene, with reflecting internal inclusion.

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, strong and colorful dispersion which is commonly referred to as "fire", and brightly colored flashes of reflected light known as scintillation. Typically transparent to translucent stones are faceted, although opaque materials may occasionally be faceted as the luster of the gem will produce appealing reflections. Pleonaste (black spinel) and black diamond are examples of opaque faceted gemstones.

Facet angles

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 carefully 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.[3] 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", and the effect caused by it is called "windowing" as the area will appear transparent and without brilliance. This is especially common in poorly cut commercial gemstones. Gemstones with higher refractive indexes generally make more desirable gemstones, the critical angle decreases as refractive indices increase, allowing for greater internal reflections as the light is less likely to escape.

The faceting machine

This machine uses a motor-driven plate to hold a precisely flat disk (known as a "lap") for the purpose of cutting or polishing. Diamond abrasives bonded to metal or resin are typically used for cutting laps, and a wide variety of materials are used for polishing laps in conjunction with either very fine diamond powder or oxide-based polishes. Water is typically used for cutting, while either oil or water is used for the polishing process.

The machine uses a system generally called a "mast" which consists of an angle readout, height adjustment and typically a gear (called an "index 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, often called a "cheater". The stone is bonded to a (typically metal) rod known as a "dop" or "dop stick" and is held in place by part of the mast referred to as the "quill".

The modern faceting process

The dopped stone is ground at precise angles and indexes on cutting laps of progressively finer grit, and then 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 commonly 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 (the crown and pavilion), a device often called a "transfer jig" is used to flip the stone so that each side may be cut and polished.[3]

Other methods

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 often resulted. The preferred method of splitting diamonds into smaller pieces is now sawing.[2]

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 carefully placed in it. By placing the back end of the dop into one of the many holes, the stone could be introduced to the lap at precise angles. These machines took considerable skill to operate effectively.[3]

Another method of facet cutting involves the use of cylinders to produce curved, concave facets. This technique can produce many unusual and artistic variations of the traditional faceting process.

Natural faceting

Many crystals naturally grow in faceted shapes. For instance, common table salt forms cubes and quartz forms hexagonal prisms. These characteristic shapes are a consequence of the crystal structure of the material and the surface energy, as well as the general conditions under which the crystal formed.

The Bravais lattice of the crystal structure defines a set of possible "low-energy planes", which are usually planes on which the atoms are close-packed. For instance, a cubic crystal may have low-energy planes on the faces of the cube or on the diagonals. The planes are low-energy in the sense that if the crystal is cleaved along these planes, there will be relatively few broken bonds and a relatively small increase in energy over the unbroken crystal. Equivalently, these planes have a low surface energy. The planes with the lowest energy will form the largest facets, in order to minimize the overall thermodynamic free energy of the crystal. If the surface energy as a function of the planes is known, the equilibrium shape of the crystal may be found via the Wulff construction.

Growth conditions, including the surface the crystal is growing on top of (the substrate), may change the expected shape of the crystal; for instance, if the base of the crystal is under stress from the substrate, this may favor the crystal growing taller rather than growing outwards along the substrate. The surface energy, including the relative energies of the different planes, depend on many factors including the temperature, the composition of the surroundings (e.g. humidity), and the pressure.

See also

F-117 Nighthawk Front
Stealth, faceted F-117


  1. ^ Gems, 5th edition, Webster, 1995.
  2. ^ a b Gemstones of the world, Schumann, 1977.
  3. ^ a b c Faceting for Amateurs, 2nd Edition, Vargas, 1977.

External links

Chartered Institute of Library and Information Professionals

The Chartered Institute of Library and Information Professionals is a professional body for librarians, information specialists and knowledge managers in the United Kingdom. Since 2017, it has been branded CILIP: The library and information association (pronounced SIL-ip). CILIP in Scotland is an independent organisation which operates in Scotland on behalf of CILIP.

CILIP's 2020 goal is to "put information and library skills and professional values at the heart of a democratic, equal and prosperous society".

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn. Some authors use the terms "convex polytope" and "convex polyhedron" interchangeably, while others prefer to draw a distinction between the notions of a polyhedron and a polytope.

In addition, some texts require a polytope to be a bounded set, while others (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts treat a convex n-polytope as a surface or (n-1)-manifold.

Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming.

A comprehensive and influential book in the subject, called Convex Polytopes, was published in 1967 by Branko Grünbaum. In 2003 the 2nd edition of the book was published, with significant additional material contributed by new writers.In Grünbaum's book, and in some other texts in discrete geometry, convex polytopes are often simply called "polytopes". Grünbaum points out that this is solely to avoid the endless repetition of the word "convex", and that the discussion should throughout be understood as applying only to the convex variety.

A polytope is called full-dimensional if it is an n-dimensional object in Rn.

Diamond cut

A diamond cut is a style or design guide used when shaping a diamond for polishing such as the brilliant cut. Cut does not refer to shape (pear, oval), but the symmetry, proportioning and polish of a diamond. The cut of a diamond greatly affects a diamond's brilliance; this means if it is cut poorly, it will be less luminous.

In order to best use a diamond gemstone's material properties, a number of different diamond cuts have been developed. A diamond cut constitutes a more or less symmetrical arrangement of facets, which together modify the shape and appearance of a diamond crystal. Diamond cutters must consider several factors, such as the shape and size of the crystal, when choosing a cut. The practical history of diamond cuts can be traced back to the Middle Ages, while their theoretical basis was not developed until the turn of the 20th century. Design creation and innovation continue to the present day: new technology—notably laser cutting and computer-aided design—has enabled the development of cuts whose complexity, optical performance, and waste reduction were hitherto unthinkable.

The most popular of diamond cuts is the modern round brilliant, whose facet arrangements and proportions have been perfected by both mathematical and empirical analysis. Also popular are the fancy cuts, which come in a variety of shapes, many of which were derived from the round brilliant. A diamond's cut is evaluated by trained graders, with higher grades given to stones whose symmetry and proportions most closely match the particular "ideal" used as a benchmark. The strictest standards are applied to the round brilliant; although its facet count is invariable, its proportions are not. Different countries base their cut grading on different ideals: one may speak of the American Standard or the Scandinavian Standard (Scan. D.N.), to give but two examples.


Eyes are organs of the visual system. They provide organisms with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and convert it into electro-chemical impulses in neurons. In higher organisms, the eye is a complex optical system which collects light from the surrounding environment, regulates its intensity through a diaphragm, focuses it through an adjustable assembly of lenses to form an image, converts this image into a set of electrical signals, and transmits these signals to the brain through complex neural pathways that connect the eye via the optic nerve to the visual cortex and other areas of the brain. Eyes with resolving power have come in ten fundamentally different forms, and 96% of animal species possess a complex optical system. Image-resolving eyes are present in molluscs, chordates and arthropods.The simplest "eyes", such as those in microorganisms, do nothing but detect whether the surroundings are light or dark, which is sufficient for the entrainment of circadian rhythms. From more complex eyes, retinal photosensitive ganglion cells send signals along the retinohypothalamic tract to the suprachiasmatic nuclei to effect circadian adjustment and to the pretectal area to control the pupillary light reflex.

Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

In three-dimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face. To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes.

In polyhedral combinatorics and in the general theory of polytopes, a facet of a polytope of dimension n is a face that has dimension n − 1. Facets may also be called (n − 1)-faces. In three-dimensional geometry, they are often called "faces" without qualification.

A facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics.

Facet joint

The facet joints, (or zygapophysial joints, zygapophyseal, apophyseal, or Z-joints) are a set of synovial, plane joints between the articular processes of two adjacent vertebrae. There are two facet joints in each spinal motion segment and each facet joint is innervated by the recurrent meningeal nerves.

The biomechanical function of each pair of facet joints is to guide and limit movement of the spinal motion segment. In the lumbar spine, for example, the facet joints function to protect the motion segment from anterior shear forces, excessive rotation and flexion. Facet joints appear to have little influence on the range of side bending (lateral flexion). These functions can be disrupted by degeneration, dislocation, fracture, injury, instability from trauma, osteoarthritis, and surgery.

In the thoracic spine the facet joints function to restrain the amount of flexion and anterior translation of the corresponding vertebral segment and function to facilitate rotation. Cavitation of the synovial fluid within the facet joints is responsible for the popping sound (crepitus) associated with manual spinal manipulation, commonly referred to as "cracking the back."

The facet joints, both superior and inferior, are aligned in a way to allow flexion and extension, and to limit rotation. This is especially true in the lumbar spine.

Facet syndrome

Facet syndrome is a syndrome in which the facet joints (synovial diarthroses, from C2 to S1) degenerate to the point of causing painful symptoms. In conjunction with degenerative disc disease, a distinct but functionally related condition, facet syndrome is believed to be one of the most common causes of lower back pain.

Faceted classification

A faceted classification is a classification scheme used in organizing knowledge into a systematic order. A faceted classification uses semantic categories, either general or subject-specific, that are combined to create the full classification entry. Many library classification systems use a combination of a fixed, enumerative taxonomy of concepts with subordinate facets that further refine the topic.

Greater tubercle

The greater tubercle of the humerus is situated lateral to the head of the humerus and posterolateral to the lesser tubercle.

Its upper surface is rounded and marked by three flat impressions.

the highest of these gives ("superior facet") insertion to the supraspinatus

the middle ("middle facet") to the infraspinatus.

the lowest one ("inferior facet"), and the body of the bone for about 2.5 cm; below it, to the teres minor.The lateral surface of the greater tubercle is convex, rough, and continuous with the lateral surface of the body.

Between the greater tubercle and the lesser tubercle is the bicipital groove (intertubercular sulcus).

All three of the muscles that attach to the greater tubercle are part of the rotator cuff, a muscle group that stabilizes the shoulder joint. The fourth muscle of the rotator cuff (the subscapularis) does not attach to the greater tubercle, but instead attaches to the lesser tubercle.


Honesty is a facet of moral character that connotes positive and virtuous attributes such as integrity, truthfulness, straightforwardness, including straightforwardness of conduct, along with the absence of lying, cheating, theft, etc. Honesty also involves being trustworthy, loyal, fair, and sincere.

Honesty is valued in many ethnic and religious cultures.

"Honesty is the best policy" is a proverb of Benjamin Franklin, while the quote "Honesty is the first chapter in the book of wisdom" is attributed to Thomas Jefferson, as used in a letter to Nathaniel Macon. April 30 is national Honesty Day in the United States.

William Shakespeare famously describes honesty as an attribute people leave behind when he wrote that "no legacy is so rich as honesty" in act 3 scene 5 of "All's Well that Ends Well."Others have noted, however, that "[t]oo much honesty might be seen as undisciplined openness". For example, individuals may be perceived as being "too honest" if they honestly express the negative opinions of others, either without having been asked their opinion, or having been asked in a circumstance where the response would be trivial.


Hostility is seen as form of emotionally charged aggressive behavior. In everyday speech it is more commonly used as a synonym for anger and aggression.

It appears in several psychological theories. For instance it is a facet of neuroticism in the NEO PI, and forms part of personal construct psychology, developed by George Kelly.

Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same. More specifically, all faces must be not merely congruent but must be transitive, i.e. must lie within the same symmetry orbit. In other words, for any faces A and B, there must be a symmetry of the entire solid by rotations and reflections that maps A onto B. For this reason, convex isohedral polyhedra are the shapes that will make fair dice.Isohedral polyhedra are called isohedra. They can be described by their face configuration. A form that is isohedral and has regular vertices is also edge-transitive (isotoxal) and is said to be a quasiregular dual: some theorists regard these figures as truly quasiregular because they share the same symmetries, but this is not generally accepted. An isohedron has an even number of faces.A polyhedron which is isohedral has a dual polyhedron that is vertex-transitive (isogonal). The Catalan solids, the bipyramids and the trapezohedra are all isohedral. They are the duals of the isogonal Archimedean solids, prisms and antiprisms, respectively. The Platonic solids, which are either self-dual or dual with another Platonic solid, are vertex, edge, and face-transitive (isogonal, isotoxal, and isohedral). A polyhedron which is isohedral and isogonal is said to be noble.


A joint or articulation (or articular surface) is the connection made between bones in the body which link the skeletal system into a functional whole. They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally.

List of Empire ships (F)

Hundreds of Empire ships were employed by the Government of the United Kingdom. They were acquired from a number of sources: many were built for the government; others obtained from the United States; still others were captured or seized from enemy powers. Empire ships were mostly used during World War II by the Ministry of War Transport (MoWT), which owned the ships but contracted out their management to various shipping lines; however, some ships requisitioned during the Suez Crisis were also named as Empire ships. Most Empire ships have since been lost or scrapped; however a few still remain in active service or preserved.

Radiofrequency ablation

Radiofrequency ablation (RFA) is a medical procedure in which part of the electrical conduction system of the heart, tumor or other dysfunctional tissue is ablated using the heat generated from medium frequency alternating current (in the range of 350–500 kHz). RFA is generally conducted in the outpatient setting, using either local anesthetics or conscious sedation anesthesia. When it is delivered via catheter, it is called radiofrequency catheter ablation.

Two important advantages of radio frequency current (over previously used low frequency AC or pulses of DC) are that it does not directly stimulate nerves or heart muscle and therefore can often be used without the need for general anesthetic, and that it is very specific for treating the desired tissue without significant collateral damage.Documented benefits have led to RFA becoming widely used during the 21st century. RFA procedures are performed under image guidance (such as X-ray screening, CT scan or ultrasound) by an interventional pain specialist (such as an anesthesiologist), interventional radiologist, otolaryngologists, a gastrointestinal or surgical endoscopist, or a cardiac electrophysiologist, a subspecialty of cardiologists.

SLAC National Accelerator Laboratory

SLAC National Accelerator Laboratory, originally named Stanford Linear Accelerator Center, is a United States Department of Energy National Laboratory operated by Stanford University under the programmatic direction of the U.S. Department of Energy Office of Science and located in Menlo Park, California.

SLAC research centers on a broad program in atomic and solid-state physics, chemistry, biology, and medicine using X-rays from synchrotron radiation and a free-electron laser as well as experimental and theoretical research in elementary particle physics, astroparticle physics, and cosmology.

STL (file format)

STL (an abbreviation of "stereolithography") is a file format native to the stereolithography CAD software created by 3D Systems. STL has several after-the-fact backronyms such as "Standard Triangle Language" and "Standard Tessellation Language". This file format is supported by many other software packages; it is widely used for rapid prototyping, 3D printing and computer-aided manufacturing. STL files describe only the surface geometry of a three-dimensional object without any representation of color, texture or other common CAD model attributes. The STL format specifies both ASCII and binary representations. Binary files are more common, since they are more compact.An STL file describes a raw, unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. In the original specification, all STL coordinates were required to be positive numbers, but this restriction is no longer enforced and negative coordinates are commonly encountered in STL files today. STL files contain no scale information, and the units are arbitrary.

Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from



{\textstyle \mathbb {R} ^{d}}





{\textstyle \mathbb {R} ^{d-1}}

through a point beyond one of its facets or faces. The resulting entity is a polytopal subdivision of the facet in




{\textstyle \mathbb {R} ^{d-1}}

that is combinatorially equivalent to the original polytope. The diagram is named for Victor Schlegel, who in 1886 introduced this tool for studying combinatorial and topological properties of polytopes. In dimensions 3 and 4, a Schlegel diagram is a projection of a polyhedron into a plane figure and a projection of a 4-polytope to 3-space, respectively. As such, Schlegel diagrams are commonly used as a means of visualizing four-dimensional polytopes.


WeShow was an New York City-based online video aggregator that delivered tailored video content to viewers around the world. The WeShow editorial team selected videos found on the internet and organized them across 200 categories. User suggestions for content to be included were also entertained. Common video repositories used to source content included YouTube, Dailymotion, Metacafe, MySpace, and Google Video. WeShow did not serve as a social networking site, unlike some similar services, not supporting either video rating or comments. Voting for favorite videos, though, was supported through the WeShow Awards facet, which allowed voting on a selected set of videos each month leading to two top videos. WeShow TV was another facet, which highlighted daily new video content.Marcos Wettreich and Bruno Parodi founded WeShow in February 2007 and launched portals for the United States, the United Kingdom, and Brazil in July 2007.The premise on which the company was founded rests on findings from Kelton Research that American's viewing of online video was limited by the overwhelming volume available and the "dreaded" task of finding specific content in this mass, 96% of the time ending in failure. The company had financial backing from Bob Pitman via The Pilot Group, and Bill Sahlman. In September 2007, WeShow launched websites in France, Germany, and Spain. In December 2007 WeShow debuted in Japan, and in January 2008 a portal specially dedicated to China was created.

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