A Starry Icosidodecahedron

The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

An Excavated Tetrahedron

Polyhedral excavation is the opposite of augmentation. In this excavated tetrahedron, short pyramids have been removed from each face. I made this using Stella 4d, which can be tried for free at this website.

Four Octahedra

There’s a tetrahedron in the center of this figure, but you can’t see it because it is covered on all sides by octahedra. I made this using Stella 4d, which you can try for free at this website.

Here’s another version, with a different coloring-scheme.

Two Versions of a Fifty-Faced Symmetrohedron

The first version of this polyhedron was created by zonohedrification of a tetrahedron, based on that solid’s faces, edges, and vertices. All of its faces are regular polygons, except for the red hexagons.

I used Stella 4d: Polyhedron Navigator to make these (and you can try that program for free at this website). The next thing I did was to apply Stella‘s “try to make faces regular” function to the solid above, producing the one shown below. In this second version, the only irregular faces are the yellow isosceles trapezoids.

Augmenting, then Reaugmenting, the Octahedron

The blue figure above is an octahedron. The next image shows what happens if red octahedra are used to augment each of the blue octahedron’s faces.

The third image shows what happens if yellow octahedra are used to augment each red face in the second figure.

These polyhedral images were created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

An Augmented Great Dodecahedron

To make this polyhedron, I started with a great dodecahedron, and then augmented each of its facelets with a prism, using a program called Stella 4d. You can try this program for free at this website.