Friday, May 16, 2008

Naming Polygons

What do you call an 11-sided polygon? A 14-sided 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.pre-college 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.
John Conway
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 myriagon
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.

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