Date: 30 May 1995 10:09:38 -0400 From: Trevor Ratcliff Newsgroups: local.dr-math Subject: Naming Polygons Dr. Math: Could you please give me a complete list of polygon names, from 3 - 100, if such a list exists? Thanks Martial and Ratman
Date: 30 May 1995 22:52:57 -0400 From: Sarah Seastone Subject: Materials for Naming Polygons For a full list of polygon names, see "Names of polygons and polyhedra" in the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.polygon.names.html Following are some of the contributions that were made by Prof. John Conway to the newsgroup geometry.pre-college on the subject of naming polygons. The full discussions are archived at http://mathforum.org/kb/message.jspa?messageID=1076464&tstart=0 _____________________________________________________________ From: "John Conway" Subject: Re: 11-gon Date: Mon, 24 Oct 94 20:10:39 EDT I have obviously missed an interesting discussion on names for polygons! Anyway, I'll throw in what I know, since such things have always interested me. 1) For the "numerical" part of the name, one should use the Greek prefixes: mono, di, tri, tetra, penta, hexa, hepta, octa, ennea, deca, hendeca, dodeca, trideca, etc, icosa, triaconta, hecta .. 10 11 12 13 20 30 100 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 corresponds 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. John Conway ______________________________________________ From: "John Conway" Subject: Re: 11-gon Date: Mon, 24 Oct 94 21:16:16 EDT I see someone asked about the 24-gon, 48-gon, 96-gon. The "official" names are icositetragon tetracontaoctagon enneacontahexagon if anyone cares. A "myriagon" would be a polygon with 10000 sides. The word "macaronic" is usually used for a word made of pieces from several languages - one doesn't need "linguistic heteromorph"! John Conway ______________________________________________ From: "John Conway" Subject: Re: 11-gon Date: Mon, 24 Oct 94 21:21:28 EDT By the way, "icositetrahedron" appears in some dictionaries. The dual of the rhombicuboctahedron has been called either a trapezoidal or tetragonal icositetrahedron, while the dual of the snub cube is a pentagonal icositetrahedron. I saw the word "tetrakaidecahedron" in a recent "press release" from the Minneapolis Geometry Center, so you can see that people DO occasionally use such words. John Conway ______________________________________________ From: "John Conway" Subject: Re: 11-gon Date: Mon, 24 Oct 94 21:35:08 EDT I'm working my way back through all this email. I see that "undecagon" and "duodecagon" have been rearing their ugly heads again. The full set is monogon, digon, trigon, tetragon, pentagon, hexagon, heptagon, octagon (of which monogon and digon can only be used in rather special circumstances; it's digon not "bigon"; and trigon and tetragon are alternatives to "triangle" and "quadrilateral" - the adjectival forms "trigonal" and "tetragonal" being more common), then enneagon, decagon, hendecagon, dodecagon, triskaidecagon, tetrakaidecagon,... not nonagon undecagon duodecagon but tridecagon and tetradecagon (&c) are OK. The (synonymous) words "triskaidecaphobia" and "tridecaphobia" appear in dictionaries (occasionally spelled with a "k" instead of that "c"). I was reminded of them in O'Hare airport yesterday, as I passed gates 10,11,12,14,15,... ! John Conway
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