In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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.
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. 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.
In psychology, a facet is a specific and unique aspect of a broader personality trait. Both the concept and the term "facet" were introduced by Paul Costa and Robert McCrae in the first edition of the NEO-Personality Inventory (NEO-PI) Manual. Facets were originally elaborated only for the neuroticism, openness to experience, and extraversion traits; Costa and McCrae introduced facet scales for the agreeableness and conscientiousness traits in the Revised NEO-PI (NEO PI-R). Each of the Big Five personality traits in the Five Factor Model contains six facets, each of which is measured with a separate scale. The use of facets and facet scales has since expanded beyond the NEO PI-R, with alternative facet and domain structures derived from other models of personality. Examples include the HEXACO model of personality structure,psycholexical studies, circumplex models (e.g., Goldberg's Abridged Big-Five Dimensional Circumplex), the Multidimensional Personality Questionnaire (MPQ), and the California Psychological Inventory.
A facet is a flat surface of a geometric shape, e.g., of a cut gemstone.
Facet may also refer to:
Facets may refer to:
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.
Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.
In his review for AllMusic, Alex Henderson says that "this CD doesn't quite fall into the 'essential' category... Nonetheless, Geometry is an enjoyable release that Perelman's more-devoted followers will want."
The Penguin Guide to Jazz notes that "Bergman is wily enough to find ways of both supporting and undercutting the mighty sound of the tenor."
In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.
In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:
If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.
Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.