Author Archives: RobertLovesPi

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

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.