Dodecahedron with Mandalas

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Dodecahedron with Mandalas

This rotating image took three different programs to create. First, I made the mandala (seen in the previous post) using Geometer’s Sketchpad. Next, I used MS-Paint to complete the colorization of it. Finally, I used Stella 4d (see http://www.software3d.com/stella.php if you’d like to try or buy it) to put this mandala on each face of a dodecahedron, and then create the rotating .gif you see here.

I find both Stella 4d and Geometer’s Sketchpad to be indispensable tools for mathematical investigations and the creation of geometrical art, and highly recommend both programs.

Stars and Flowers

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Stars and Flowers

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:

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

Circles, Triangles, and Hexagons

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Circles, Triangles, and Hexagons

Nine Circles and Their Inscribed Octagrams

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Nine Circles and Their Inscribed Octagrams

128 Semicircles

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128 Semicircles

52 Triangles Inscribed in 13 Circles

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39 Squares Inscribed in 13 Circles

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39 Squares Inscribed in 13 Circles

Star Polygon Enumeration

Posted on 17 February 2013 by RobertLovesPi

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

That’s the beginning. Here are two more:

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.