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  Naming Polygons and Polyhedra  

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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.



Naming Polyhedra

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" 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
                                      foot

In summary, a "polygon" is a thing with many knees, and a "polyhedron" a thing with many seats.



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