A 24-gon is possible
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Just call it a "24-sided polygon".
An n-sided polygon or n-gon, just like it sounds, has n sides. For example, a 13-sided polygon has 13 sides. A 24-gon has 24 sides.
There is no formula for how many sides there are in a polygon; the name of the polygon shows how many sides it has.
Providing that it's a regular polygon then: 360/15 = 24 sides
There is not a name for such a polygon. A polygon with one million sides is called a megagon though..