Compound of Five Rhombic Dodecahedra

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Compound of Five Rhombic Dodecahedra

These images were created with software you can find at http://www.software3d.com/stella.php.

If you make the faces invisible, and just view a wire-frame model, this compound looks like this:

Cuboctahedra 5

This second image will get larger if you click on it.

Star Polygon Enumeration

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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.