What do you call an 11sided polygon? A 14sided polygon? Can you give me a list of names of polygons?This answer represents excerpts from contributions made by Prof. John Conway of Princeton University to the geometry.college and geometry.precollege newsgroups. For an etymological discussion in the Dr. Math archive, see "Naming Polygons."When naming polygons, for the "numerical" part of the name, we use the Greek prefixes: mono, di, tri, tetra, penta, hexa, hepta, octa, ennea, 1 2 3 4 5 6 7 8 9 deca, hendeca, dodeca, triskaideca, tetrakaideca, ..., enneakaideca, 10 11 12 13 14 19 icosa, icosikaihena, icosikaidi, icosikaitri, ..., icosikaiennea, 20 21 22 23 29 triaconta, triacontakaihena, ..., triacontakaiennea, tetraconta, ..., 30 31 39 40 pentaconta, hexaconta, heptaconta, octaconta, enneaconta, hecta 50 60 70 80 90 100 Prof. Conway writes:
Antreas Hatzipolakis and I worked out a complete system up to the millions from which this is taken, and which has also been "vetted" by several other scholars. The most important of the reasons which make me prefer the "kai" forms is that they permit these prefixes to be unambiguously parsed even when concatenated, as they are in Kepler's names for certain polyhedra; for example, the icosidodecahedron or (20,12)hedron, so called because it has 20 faces of one type and 12 of another. Kepler said "this particular triacontakaidihedron I call the icosidodecahedron", a remark showing that he also preferred the kai forms. Names of Polygons 1 monogon (Monogon and digon can only 2 digon be used in rather special 3 trigon, triangle circumstances. Trigon and 4 tetragon, quadrilateral tetragon are alternatives to 5 pentagon triangle and quadrilateral; 6 hexagon the adjectival forms trigonal 7 heptagon and tetragonal are more common.) 8 octagon 9 enneagon 10 decagon 11 hendecagon 12 dodecagon 13 triskaidecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ... 100 hectogon, hecatontagon 1000 chiliagon 10000 myriagonThe "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 IndoEuropean, 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.
Naming Polyhedra The "hedron" in "polyhedron" is also an IndoEuropean 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" in 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 footIn summary, a "polygon" is a thing with many knees, and a "polyhedron" a thing with many seats.
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