Polygons: why are three and four different from other "sidegons"

A few past Questions almost get to my query but even this about "name-gons" doesn't quite do it. Please don't even trouble to read on unless you're interested in what might seem totally trivial…

Why are three- and four-sided figures not called "trigons" and "tetragons", or indeed any-kind of "…gon"?

Above seven, it would be very odd to deviate from the standard list of names for polygons: octa…, nona…, deca… etc.

For six and seven it might not seem so strange to see "sex…" and "sept…" instead of "hex…" and "heptagon" but those are still "sidegons".

Three and four seem to be exceptions and I'm wondering whether there's any rule for that, linguistic or mathematical, or it's just traditional.

Is "trigon" seriously used for "triangle", except broadly as in "trigonometry"?

Is "tetragon" really used for "quadrangle"? Quad itself seems to be the special preserve of academia and even "rectangle" is often usurped by "oblong" or "square".

This might well seem wholly pointless yet on a different level, three and four-sided figures, when they're equilateral, are physically different.

That is, squares and equilateral triangles are the only shapes any old bodger can construct with a single measurement and almost no skill; unexpectedly useful in many practical applications - and that's apart from the triangle being the only rigid shape. Is that wholly irrelevant, or could it somehow bleed across into the nomenclature?

• You can add dictionary definitions for tetragon and trigon, together with caveats ('archaic' for the latter). Sep 13, 2021 at 18:00
• If you can construct all three sides of an equilateral triangle from scratch with your single measurement, you can certainly make another such triangle on one of those sides. Keep repeating that around a common point and you have a hexagon. Sep 13, 2021 at 18:37
• @DjinTonic Quite… which is one reason hexagons tessellate as well as triangles or squares and nothing else but specially selected oblongs/quadrangles/rectangles Sep 13, 2021 at 19:58
• @RobbieGoodwin There are irregular pentagons that can tile the plane Sep 13, 2021 at 20:16
• @DjinTonic That might be but here, it has no relevance. Sep 13, 2021 at 20:23

According to the OED's citations, square was first used 1300-1400; triangle 1398; quadrangle 1398; rectangle 1560;

then hexagon 1560; polygon 1560; pentagon 1570; octagon 1594; trigon 1600 (basically all around the same time) It looks like we adopted a neat Latin naming convention as we found interest and practical use for more figures with an increasing numbers of sides:

-gon, comb. form

1652 News from Lowe Countreys 2 For 'tis not..Trigonall, or Pentagonall, Or any of the Gones at all OED

Etymology: < classical Latin -gōnon (in e.g. octagōnon octagon n.), -gōnum (in e.g. trigōnum trigon n.) ...

Compare French -gone.

It's unreasonable to think we'd rename our three- and four-sided shapes—triangles, quadrangles, squares, and rectangles. We just "gone" off after that: new shapes need new names.

The OED has this telling early citation for hexagon:

1570 H. Billingsley tr. Euclid Elements Geom. iv. f. 124 We may in a Hexagon geuen either describe or circumscribe a circle.

I think architectural and scientific interest in geometry (and Euclid in particular) played a role in adopting -gone.

An interesting early -angle "exception" is the five-pointed star, a pentangle (1390):

A pentagram; a talisman or magical symbol in the shape of or inscribed with a pentagram OED

In other words, a pentangle isn't a pentagon.

• My mistake-- edited. The -gon comes from the greek for knee, so also angle. Sep 13, 2021 at 22:22
• Jolly good. and remembering that the only point here is the difference, how does that address the difference between three- and four- or five- or more-angled figures. Sep 19, 2021 at 21:10
• Thanks and how does that address the Question? I was not asking about what the difference is, but why there is a difference… If I failed to make that clear, where did I go wrong? I didn't bother to contrast pentagram to pentagon because here, that difference seems irrelevant; In other words, a pentangle is a pentagon when the shape is what matters. If the reason for drawing that shape is what matters, you're moving outside language and into philosophy… Sep 19, 2021 at 21:53