These images of Jupiter, Saturn, Uranus, and Neptune were all acquired by NASA. I placed them on this polyhedron, and created this rotating .gif, using Stella 4d, which you can try for free at this website.
This is one of many possible facetings of the dodecahedron. It’s colored by face type above, and is shown in “rainbow color mode” below. I made both rotating images using Stella 4d, which you can try for free at this website.
This zonish polyhedron has 162 faces, and is based on the faces and the vertices of a dodecahedron. I made it using Stella 4d, which you can try for free at this website.
Here’s a single dodecahedron.
A new “cluster polyhedron” can be made by augmenting each pentagonal face with another dodecahedron.
If you can do it once, you can do it again, augmenting each pentagon with a new dodecahedron.
I made these polyhedral clusters using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
I made this .gif, of two dodecahedra orbiting a common center of mass, using a program called Stella 4d: Polyhedron Navigator. This program may be tried for free at http://www.software3d.com/Stella.php.
This is the compound of five dodecahedra, a shape which is included in the built-in polyhedral library of Stella 4d, a program you can try for yourself, free, right here.
I wanted to see what I could make, starting from this compound. My first modification to it was to create its convex hull, which is shown below.
The next move was to use Stella‘s “Try to Make Faces Regular” function, which produced this:
Next, I augmented this figure’s thirty yellow rhombi with prisms.
I then created the convex hull of this augmented polyhedron.
Next, I used the “Try to Make Faces Regular” function again, producing a solid that looks, to me, like a hybrid of the rhombicosidodecahedron and the rhombic triacontahedron.
This polyhedron has yellow faces that are almost squares. Careful inspection reveals that they are actually isosceles trapezoids. The next thing I did was to augment each of these trapezoids with a tall prism.
The next step was to, again, create the convex hull.
That was the end of this polyhedral journey, but I am confident there will be others.
This is the third polyhedral model I’ve built with Lux Blox, and the first to use the Lux trigons (the black pieces) which were added to the Lux system in 2017. If you view this polyhedron as having orange pentagonal faces, white edges, and black vertices, it’s a dodecahedron. On the other hand, it can be seen as having orange pentagonal faces, white square faces, and black triangular faces, in which case this is a rhombicosidodecahedron.
Lots of us are stuck inside because of COVID-19, and a set of Lux Blox is the perfect tool (or toy, if you prefer) to avoid boredom while we wait this thing out. You can find Lux for sale at www.luxblox.com, and delivery is fast.
Stella 4d: Polyhedron Navigator has a “put models on vertices” function which I used to build this cluster of 101 dodecahedra. If you’d like to try this software for yourself, there is a free trial download available at http://www.software3d.com/Stella.php.
I made these virtual models using Stella 4d: Polyhedron Navigator. If you’d like to try this program for yourself — free — the website to visit is http://www.software3d.com/Stella.php.