What is a polygon with 32 sides called?

Answer 1

32-triacontakaidigon, 33-triacontakaitigons, 34-triacontakaitetragon

Answer 2

Here is an excerpt from John Conway, a very famous mathematician in which he describes how he names the regular polygons.Conway says:"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."

Now using this we have: 1 monogon

2 digon

3 trigon, triangle

4 tetragon, quadrilateral

5 pentagon

6 hexagon

7 heptagon

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)

Having said this, if you cannot remember the term, it is safe to use the natural number, n and say an n-gon. So 32 sided polygon can be called a 32-gon and this terminology is widely used and understood among mathematicians. It is very nice to use the correct word, however, often times the price of using it is that many people do not understand what you mean.