Category Archives: Mathematics

The dominant topic of my blog. You figured that out from the blog’s name, though, right?

The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part Two

Just like I did in the first part of this two-part post, I’m starting with the snub dodecahedron’s 43rd stellation. This time, though, this polyhedral exploration is going in another direction. In the image below, the yellow kites seen above … Continue reading

Posted in Mathematics | Tagged , , , | Leave a comment

The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One

If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi. Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the polyhedron shown above. Any chiral polyhedron … Continue reading

Posted in Mathematics | Tagged , , , , , , , , | 1 Comment

Selected Stellations of the Truncated Dodecahedron

This is the truncated dodecahedron. It is one of the Archimedean solids. This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation. Here is the 21st … Continue reading

Posted in Mathematics | Tagged , , , , , , , | Leave a comment

Nine Zonohedra

Software used to make these gifs: Stella 4d, available here.

Posted in Mathematics | Tagged , , , , , | Leave a comment

A Rhombic Dodecahedron, Made of Icosahedra, and Tall Triangular Antiprisms

Software used: Stella 4d, available at http://www.software3d.com/Stella.php.  

Posted in Mathematics | Tagged , , , , , | Leave a comment

Honeycomb Made of Cuboctahedra and Octahedra

This is the three-dimensional version of what is called a tessellation in two dimensions. It fills space, and can be continued in all directions. Software used: Stella 4d, available here.

Posted in Mathematics | Tagged , , , , , , , , , | Leave a comment

Spectral Circles on a Cuboctahedron

I used three programs to make this: Geometer’s Sketchpad, MS-Paint, and Stella 4d. The third of these may be tried for free at http://www.software3d.com/Stella.php.

Posted in Art, Mathematics | Tagged , , , , , , , , | 4 Comments