Created with Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
I made these using Stella 4d, a program you can try for free at this website.
The stellation-series of the truncated dodecahedron contains some interesting polyhedra. Selections from this series appear below.
The polyhedron above is the 24th stellation of the truncated dodecahedron, while the one below is the 25th stellation.
The polyhedron immediately above is the truncated dodecahedron’s 27th stellation. The one shown below is the 29th stellation.
The last two polyhedra in this post are the truncated dodecahedron’s 36th stellation (above), and its 70th stellation (below).
These images were created using Stella 4d, software available here.
Stellation of a polyhedron involves extending its faces and/or edges into space to form other polyhedra, often with a star-like appearance, which is where the words “stellation,” “stellate,” and “stellated” originate. (“Stella” is Latin for “star.”)
Since this can be done repeatedly, long stellation-series exist for many polyhedra. In the case of the truncated dodecahedron, it was the 21st and 22nd stellations which I found the most aesthetically pleasing.
Here is the 21st stellation of this polyhedron:
And here is the 22nd:
Both of these polyhedra were created with Stella 4d, software you may try for yourself, right here.
This faceting of the truncated dodecahedron, one of many, was made with Stella 4d, software you can buy, or try for free, here. Here is its dual, below.
I made this using Stella 4d, which you can find at http://www.software3d.com/Stella.php.
I made this, using Stella 4d, by augmenting each decagonal face of the cluster in the previous post with a truncated dodecahedron. You can give this program a try yourself, for free, at http://www.software3d.com/stella.php.
This polyhedron has the twelve regular decagons and twenty regular triangles of the truncated dodecahedron, but they are moved outwards from the center, and rotated slightly, creating gaps. These gaps are then filled with thirty pairs of isosceles trapezoids in “bowtie” formation. That gives this polyhedron 92 faces in all.
Software credit: see http://www.software3d.com/stella.php
Geometer’s Sketchpad and MS-Paint were used to make the “Metapentagon” design shown in post before the last post. After that, I used Stella 4d (see http://www.software3d.com/stella.php) to project this image onto each face of a truncated dodecahedron, and create this rotating .gif file.
A flat version of the mandala on each decagonal face here may be seen in the previous post. I used Geometer’s Sketchpad and MS-Paint to make it.
To place the mandalas on the decagonal faces of a truncated dodecahedron, I used a program called Stella 4d, which you may try for yourself at http://www.software3d.com/stella.php.