The proper name is icositetragon. Most people, including mathematicians, will use 24-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.
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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.
Providing that it's a regular polygon then: 360/15 = 24 sides
A 24-gon is possible
It has 360/24 = 15 sides.