# Eleven Times Two Times Three is Sixty-Six

The pink hendecagons are regular, and there are twenty-two of them.

## Some Polygons with Irritating Names

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These polygons are known to virtually all speakers of English as the triangle and the quadrilateral, but that doesn’t mean I have to like that fact, and, the truth is, I don’t. Why? There are a couple of reasons, all involving lack of consistency with the established names of other polygons.

Consider the names of the next few polygons, as the number of sides increases: the pentagon, hexagon, heptagon, and octagon. The “-gon” suffix refers to the corners, or angles, of these figures, and is derived from Greek, The end of the word “triangle” also refers to the same thing — but not in Greek. For the sake of consistency, triangles should, instead, be called “trigons.”

In the case of the quadrilateral, the problem is twofold. The suffix “-lateral” refers to sides, not angles. For the sake of consistency, “-gon” should be used instead. The prefix “quadri-” does mean four, of course, but is derived from Latin, not Greek. We use the Greek prefix “tetra-” to refer to four when naming polyhedra (“tetrahedron”), so why not use it for polygons with four sides, also? The best name available for four-sided polygons requires a change in both the prefix and suffix of the word, resulting in the name “tetragon” for the figure on the right.

When I listed the names of higher polygons above, I deliberately stopped with the octagon. Here’s the next polygon, with nine sides and angles:

I’m guilty of inconsistency with the name of nine-sided polygons, myself. All over this blog, you can find references to “nonagons,” and the prefix “nona-” is derived from Latin. Those who already know better have, for years, been calling nine-sided polygons “enneagons,” using the Greek prefix for nine, rather than the Latin prefix, for reasons of consistency. I’m not going to go to the trouble to go back and edit every previous post on this blog to change “nonagon” to “enneagon,” at least right now, but, in future posts, I will join those who use “enneagon.”

Here’s one more, with eleven sides:

I don’t remember ever blogging about polygons with eleven sides, but I have told geometry students, in the past, that they are called “undecagons.” I won’t make that mistake again, for the derivation of that word, as is the case with “nonagon,” uses both Latin and Greek. A better name for the same figure, already in use, is “hendecagon,” and I’m joining the ranks of those who use that term, derived purely from Greek, effective immediately.

With “hendecagon” and “enneagon,” I don’t think use of these better names will cause confusion, given that they are already used with considerable frequency. Unfortunately, that’s not the case with the little-used, relatively-unknown words “trigon” and “tetragon,” so I’ll still be using those more-familiar names I don’t like, just to avoid being asked “What’s a trigon?” or “What’s a tetragon?” repeatedly, for three- and four-sided polygons. Sometimes, I must concede, it is necessary to choose the lesser of two irritations. With “triangle” and “quadrilateral,” this is one of those times.