facet

n. one of the cut and polished surfaces of a gemstone; aspect, side (i.e. of a situation)

v. cut and polish the surface of a gemstone, cut facets on a gemstone

FACET is the acronym for the Faculty Colloquium on Excellence in Teaching, a program designed to recognize, support, and enhance outstanding teaching on the eight campuses of Indiana University.
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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.Of the many 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 arrangement of 57 facets was calculated by Marcel Tolkowsky in 1919. Slight improvements have been made since then, including the addition of a 58th facet (a culet) on the bottom of the stone. Since this is calculated to show maximum brilliance, round diamonds are rarely cut in any other arrangement, although recently the Princess cut is becoming popular. Other cuts, including "rose" cuts, are most typically found in antique jewelry. See diamond cuts for an in-depth discussion and diagrams of various shapes and ways of cutting faceted stones.
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n. facet, aspect, side (i.e. of a situation)

Noun
1. a distinct feature or element in a problem; "he studied every facet of the question"
(synonym) aspect
(hypernym) feature, characteristic
(hyponym) side
2. a smooth surface (as of a bone or cut gemstone)
(hypernym) subfigure