Three Pentagrams (from 2011)

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I ran into this on Facebook, where I posted it in 2011. That was the year before I started this blog.

An Intermediate Form Between the Icosidodecahedron and the Rhombic Triacontahedron

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This polyhedron combines the faces of an icosidodecahedron (red and blue) with the those of a rhombic triacontahedron (green). The gaps between those two sets of polygons are the yellow rectangles. I made this using the “morph duals by expansion” function of Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.

Blues and Violets

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This was created using Geometer’s Sketchpad and MS-Paint.

At 53, My Age Is a Prime Number Again

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It has long been a tradition of mine to make star polygons to mark my birthdays. Since I’m 53 today, here’s a 53-pointed star.

A Tessellation for the New Year MMXXI

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Here’s another version, with different colors:

A Tessellation of Regular Hexagons and Squares, as Well as Equilateral and Elongated Hexagons

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Here’s the same tessellation, using different colors:

A Tessellation Featuring Regular Enneagons and Triangles, as Well as Equilateral Three-Pointed Stars

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Here’s a second version, with different colors:

A Tessellation Featuring Regular Octagons and Triangles, Together with Equilateral Four- and Six-Pointed Stars

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This tessellation started with a single equilateral triangle, surrounded by regular octagons. The one shown below is the same tessellation, but with different colors.

A Tessellation Featuring Regular Heptagons and Triangles, Together with Equilateral Four- and Six-Pointed Stars

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This started with the idea of attaching a regular heptagon to each side of an equilateral triangle. From there, it took on a life of its own.

Here’s another version, with different colors:

A Dodecahedron, with Mandalas

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The mandala used here first appeared in this blog-post. I then used Stella 4d: Polyhedron Navigator to put those images on the faces of a dodecahedron. If you’d like to try this program yourself, you can do so, for free, at http://www.software3d.com/Stella.php.