What is polygon with the longest name?

Answer 1

Beyond 100-sided polygons, mathematicians generally resort to using the number, i.e., a 123-sided polygon would be called a 123-gon. In this respect, there is no limit to the length of the name of a polygon, as there is no limit to the number of sides a polygon can have.

However, for named polygons, if considering the number of letters in the name, there are 16 that are tied, with 21 letters. The one with the smallest number of sides is the tetracontakaitetragon (44 sides). The one with the largest number of sides is the enneacontakaienneagon (99 sides). Any polygon with a two-digit number of sides, such that both digits are either 4, 5, 7, or 9 (but the two digits need not be the same) will have a name with 21 letters. This derives from the fact that the prefixes for 4, 5, 7, and 9 (tetra, penta, hepta, and ennea) have more letters than those for the other prefixes.

However, if you consider the number of syllables in the name, the winner is enneacontakaienneagon (99 sides), with 10 syllables, because the ennea prefix (which appears twice in this name) has 3 syllables as opposed to two for all the other prefixes, even the ones that have 5 letters.