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.

# Category Archives: Mathematics

# A Tessellation for the New Year MMXXI

Here’s another version, with different colors:

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

Here’s the same tessellation, using different colors:

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

Here’s a second version, with different colors:

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

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

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

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.