Made with *Stella 4d*, available as a free trial download at http://www.software3d.com/Stella.php.

# Category Archives: Mathematics

# Modifying a Snub Cube

This is the snub cube. It’s one of the thirteen Archimedean solids.

The first modification I made to this polyhedron was to stellate it once.

The next step was to augment each yellow face with a tall prism.

Next, I formed the convex hull of the above solid.

The software I use to manipulate polyhedra, *Stella 4d*, has a function called “try to make faces regular.” The last step of this short polyhedral journey was to use this function on the above convex hull.

If you would like to try *Stella 4d* for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.

# Modifying a Snub Dodecahedron

The polyhedron shown above is the snub dodecahedron, which is one of the Archimedean solids. The one shown below is its first stellation.

Next, each of the yellow faces was augmented with a tall prism.

The next step was to form the convex hull of the polyhedron above.

Finally, I used *Stella 4d*‘s “try to make faces regular” function on this convex hull. The result is below, and has 242 faces.

If you would like to try *Stella 4d*, the software I used to do all of this, simply visit http://www.software3d.com/Stella.php, and look for the free trial download.

# A Fractured Octahedron

Sometimes, when using *Stella 4d* (available here) to make various polyhedra, I lose track of how I got from wherever I started to the final step. That happened with this fractured version of an octahedron.

## Rings of Pentagons

### Image

# Eight Mandalas in Orbit

The mandalas on the eight hexagonal faces of this truncated octahedron were first seen in the blog-post immediately before this one. The six square faces have been hidden, creating holes in their places.

I used *Geometer’s Sketchpad* and *MS-Paint* to make this pattern, based on a ring of twenty-two hendecagons. The work of projecting this image onto a polyhedron, as well as making this rotating .gif image, was performed using another program,* Stella 4d: Polyhedron Navigator.* If you’d like to try* Stella* for yourself, there’s a free trial download available at http://www.software3d.com/Stella.php.