A 24-gon would thus officially be an icositetragon.
There are variations in spelling and formation
(eg dekagon, endecagon, triskaidecagon,...)
(the "kai" here means "and")
The "gon" has an interesting etymology : it is ultimately derived from the Greek word "gonu" for "knee", which they transferred to "angle".
This word goes straight back to the Indo-European, and is essentially the same in lots of languages:
gonu (greek) genu (latin) k nee (english)
French is similar to Latin here, and German to English (except that the "K" is still pronounced.
3) The "hedron" in "polyhedron" is also an Indo-European word, meaning "seat". A "cathedral" church is one that contains a seat from which a bishop hands down authoritative opinions (cata = down, hedron = seat).
In accordance with Grimm's law, the "h" is Greek correesponds to "s" in English, while "d" may soften to "t" and "p" or "b" to "f" or "v". So look:
penta five hexa six hepta seven hedr seat ped foot
4) In summary, a "polygon" is a thing with many knees, and a "polyhedron" a thing with many seats.
I mentioned "ped" because it happens in that curious word "parallelepiped", which should really be pronounced parallel-epi-ped. Until about the middle of the 19th century this word was even longer - "parallelepipedon". It splits into parts thus
para - allele - epi - ped - on
beside other upon ground
(memo - "pedon", meaning the ground, is what you put your foot on)
Two things are "parallel" if one is beside the other - this was already used as a single word very early on. What the name means is that there's always a face that's parallel to the one upon the ground.
The term "allele" in modern biological use, is one of the "alternatives" that goes in a certain place along a chromosome.
5) The word "trapezium" has an interesting history. A Greek word for "table" was "tetrapedon" or "tetrapes", meaning "four legs". This then was used for "table-shaped", meaning quadrilateral. The particular kind of quadrilateral has changed around a bit over the years. Originally, it was used only for rectangles, but later for arbitrary quadrilaterals, and it is only quite recently that is has been specialized to those with two parallel sides. So in some scientific uses, "trapezoidal" refers to things with arbitrary quadrilateral faces, not just to those whose faces are trapeziums in the modern sense.
By the way, of course the circus "trapeze" is just a trapezium, in the sense of "rectangle".
I hope that someone else out there finds this nearly as interesting as I do.