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?