I made these two versions of the icosahedron, using rhombic triacontahedra and elongated prisms, and a program called Stella 4d. You can try this program yourself, for free, at http://www.software3d.com/Stella.php.
Happy Ludwig van Beethoven’s Birthday! For those keeping track, it’s his 253rd. A good way to celebrate is to listen to one or more of his symphonies, and I’ve chosen the Ninth to post here, as performed by the London Symphony Orchestra.
Charles Schulz’s Peanuts provided my earliest education regarding Beethoven. Here are some samples of this work.
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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