A Polyhedron Featuring Sixty Heptagons, a Dozen Decagons, Thirty Octagons, and 120 Rectangles, Split Between Two Types at Sixty Each

I made this using Stella 4d: Polyhedron Navigator. This program is available as a free trial download at http://www.software3d.com/Stella.php.

Dual of Geodesic Rhombicosidodecahedron

This polyhedron has, as faces, a dozen regular pentagons, thirty rhombi, and sixty irregular heptagons. I made this using Stella 4d, which is available as a free trial download at http://www.software3d.com/Stella.php.

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.