Moon image from https://www.usgs.gov/news/national-news-release/usgs-releases-first-ever-comprehensive-geologic-map-moon. Polyhedron created using Stella 4d: Polyhedron Navigator, which you can try for free at this website.
First, the tetrahedron.
Next, the cube, with each square face augmented by a single rhombicosidodecahedron.
Next, this same operation is performed on an octahedron.
Next, the dodecahedron.
Finally, the last of the set, centered on an icosahedron. This one is my favorite.
I made these five models using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
The cluster below is formed by augmenting each face of the dodecahedron above with an icosidodecahedron.
Next, each triangular face is augmented with an icosahedron.
Now every pentagonal face is augmented with a dodecahedron.
Finally, the pentagonal faces in this cluster of polyhedra are augmented with icosidodecahedra. The resulting, new cluster has an overall icosahedral shape.
I did all of this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.
Here’s the icosidodecahedron — one of the Archimedean solids.
Next, here’s what this solid looks like, if you augment each pentagonal face with a dodecahedron, and each triangular face with an icosahedron.
Finally, here’s what happens if you augment each pentagonal face of this second solid with an icosidodecahedron.
I used Stella 4d: Polyhedron Navigator to create these images. You can try this program, for free, at http://www.software3d.com/Stella.php.
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