Ah, a polygon with 31 sides is called a "triacontakaihenagon." Isn't that a lovely name? Just imagine all the beautiful angles and lines you can create with a shape like that. Remember, there's no mistakes in geometry, just happy little shapes waiting to be discovered.
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The formal name is tricontakaihenagon. Most people, including mathematicians, will use 31-gon since that effectively communicates the size of the polygon. But, if you want to appear pretentious or be obfuscatory, by all means use the Greek prefices.
The name of a polygon with 15 sides is a pentadecagon
A pentagon is the polygon with 5 sides.
A polygon with seven sides is a heptagon.
A regular polygon
A polygon can have any number of sides above three. The name of a three-sided polygon is a triangle.