A Symmetrohedron Featuring Twenty Regular Enneagons, Twelve Regular Pentagons, and Sixty Isosceles Triangles

I made this using Stella 4d: Polyhedron Navigator. You can get a free trial download of this program at http://www.software3d.com/Stella.php.

A Symmetrohedron Featuring Six Regular Octagons, Eight Equilateral Triangles, and Twelve Pairs of Isosceles “Bowtie” Trapezoids

This 38-faced polyhedron has been bugging me for over a week. I have a gut feeling that I’ve blogged it before, but my repeated searches have not found it. Perhaps I’m wrong, and it isn’t a “rerun” after all.

I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Zonish Polyhedron Based on the Vertices of a Rhombicosidodecahedron

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Symmetrahedron Featuring Twelve Regular Pentagons

To make this, I stellated the dual of the tetrated dodecahedron over 200 times, and then applied Stella 4d‘s “try to make faces regular” function. This is probably not the easiest method to use, but I don’t know of any others. The quadrilaterals are all kites.

If you’d like to give Stella a try, for free, the website to visit is http://www.software.com/Stella.php/

A 1230-Faced Zonohedron Based On the Vertices of a Rhombic Enneacontahedron

The one below is in “rainbow color mode.”

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Polyhedron Featuring 18 Regular Octagons

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

A Zonohedron with 1,410 Faces

This version colors the faces by number of sides.

This one is in “rainbow color mode.”

I made these images using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

Truncating the Rhombic Triacontahedron

This is the rhombic triacontahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing twenty triangular faces.

Here’s what it looks like with only the twelve five-valent vertices truncated.

Finally, here’s the fully truncated rhombic triacontahedron.

I created these polyhedra using Stella 4d, a program you can try for free right here.

Truncating the Rhombic Dodecahedron

This is the rhombic dodecahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing eight triangular faces.

Here’s what it looks like with only the six four-valent vertices truncated.

Finally, here’s the fully truncated rhombic dodecahedron.

I created these polyhedra using Stella 4d, a program you can try for free right here.

A Non-Convex Polyhedron With Sixty Kites As Faces

I made this using Stella 4d, which you can find at this website.