face (noun), facet (noun): via French, from Latin facies “shape, form.” The Indo-European root is dhe- “to set, to put,” so a face means literally the shape put on something, and especially the shape taken on by the front of the head. In geometry, each of the polygonal shapes that bounds a polyhedron is called a face, by analogy with the face of a person. The word facet is a diminutive of French face. Each facet of a jewel, for example, is like a little face on the surface of the jewel. In mathematics a facet of a convex polytope is a face that is not contained in any larger face. [41, 57]

factor (noun, verb), factorize (verb), factorable (adjective): factor is a Latin word meaning “amaker, doer, performer, perpetrator,” from Latin factus, past participle of facere “to do, make,” with the addition of the agental suffix -or. A factor contributes to an act or process. Mathematically speaking, let the process in question be multiplication: each of the factors then contributes something toward the product. In early 19th century American textbooks, factors were called “component parts.” A nonmathematical borrowing related to factor is factory, a place where products are made. Some English-speaking countries use the verb factorize rather than factor. For the suffix in factorable, see -able. [41, 153, 69]

factorial (noun): from factor “a number that is part of a product” (see previous entry).