A Truncated Icosahedron with Sixty Extra Hexagons


A Truncated Icosahedron with Sixty Extra Hexagons

I created this using Stella 4d, which is available (including a free trial download) at http://www.software3d.com/Stella.php. With adjustments in edge lengths to make the bond lengths correct, this would be the shape of a C180 fullerene molecule.

If the thirty-two faces of the truncated icosahedron are hidden, and only the sixty extra hexagons are visible, this polyhedron looks like this:

Dual of Geodesic Trunc Icosa

In “rainbow color mode,” it has an even more interesting appearance:

Dual of Geodesic Trunc Icosa

My name made the “Stella 4d” library discovery credits!


My name made the Stella library discovery credits!

Stella’s creator just came out with a new version of Stella 4d, and a discovery of mine made the built-in library that comes with that software. This is my blog, so I get to brag about that, right? My legal name appears in the small print on the right side, at the end of the first long paragraph. I added the red ellipses to make it easier to find.

You can see the earlier posts related to my discovery of this zonish truncated icosahedron here:



If you’d like to try (as a free trial) or buy this software (I recommend Stella 4d over the other available options), here’s the link for that: http://www.software3d.com/Stella.php.

Compound of a Slightly-Truncated Isocahedron and a Rhombic Triacontahedron


Compound of a Slightly-Truncated Isocahedron and a Rhombic Triacontahedron

Software used: Stella 4d, available at http://www.software3d.com/Stella.php (including a free “try it before you buy it” trial download).


Spinning Truncated Icosahedron

I don’t reblog things here, but I do appreciate getting e-mail from my followers, and I don’t mind posting an occasional link. One of them, a gentleman named Donald, sent me this link to an interesting video of a spinning truncated icosahedron, viewed from both the inside and outside, and set to music. To see it, simply follow the link above. Thanks for the tip, Donald — this is a really cool video!

An Expansion of the Truncated Icosahedron — and, Perhaps, a New Near-Miss


An Expansion of the Truncated Icosahedron -- and, Perhaps, a New Near-Miss

To create this using Stella 4d (see http://www.software3d.com/stella.php), I started with a truncated icosahedron, augmented each of its faces with a prism that was 1.5 times as tall as the base edge length, and took the convex hull of the result. It may qualify as a near-miss to the Johnson Solids — for that to be the case, all faces would have to be close to regular, but “close to” has no precise definition. I’ll have to consult with the experts on this one!

Twenty Hexagons with Heptagrammic Designs


Twenty Hexagons with Heptagrammic Designs

The design on the hexagons appeared in the last post here, and was created using Geometer’s Sketchpad and MS-Paint. After that, I used another program, Stella 4d, to place these images on the hexagons of a truncated icosahedron, render the pentagons invisible, and create this rotating .gif file.

Stella 4d may be tried and/or purchased at http://www.software3d.com/stella.php.