Star Polygon Enumeration

For any given regular convex polygon, how many star polygons exist?

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That’s the beginning. Here are two more:

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Since the pattern continues in this manner, it is easy to find the number of possible star polygons for a regular polygon with n sides. First, if (and only if) n is odd, add one. Next, divide by two. Lastly, subtract two, and you have your answer.

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