Tetragon

The most common term in the USA for the polygon formed by sides connecting four points in a plane (with no three collinear) is quadrilateral from the Latin roots for "four sided". For many, this seems not in keeping with the common names for the other polygons; pentagon, hexagon, octogon... all of which combine Greek names for number with the Greek root gon for angle. For this reason many mathematicians extend this list down to "tetragon", for four-angled in Greek. This conforms to the use of tetrahedron for the solid with four faces. Although triangle is also not Greek, that name seems too well imbedded in language at such a low level that it does not seem wise to try to alter it.

John Conway posted a message to a discussion list that said the use of quadrilateral is fairly recent. "By the way, the term "quadrilateral" only came into routine use for a general four-sided polygon about a century ago, although there are some isolated early instance of its use in specialized senses. The older term was "trapezoid"; but (as I said here some time ago) this got confused with "trapezium", necessitating the introduction of a new word."

Many mathematicians also prefer the term quadrangle from the Latin for four-angled, which fits well with triangle. According to Jeff Miller's web sight on the first use of some math words, quadrangle dates back in English to at least the fifteenth century, and was used by Shakespeare