A Polyhedral Journey, Starting with the Compound of Five Dodecahedra

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.

A Dodecahedron, with Mandalas

The mandala used here first appeared in this blog-post. I then used Stella 4d: Polyhedron Navigator to put those images on the faces of a dodecahedron. If you’d like to try this program yourself, you can do so, for free, at http://www.software3d.com/Stella.php.

A Dodecahedron Made of Lux Blox . . . or Is It a Rhombicosidodecahedron?

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.

Spectral Dodecahedra

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.

A Dozen Dodecahedra, Surrounding an Icosahedron

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.

Two Images of a Toroidal Rhombic Triacontahedron Made of 212 Dodecahedra

I made these using Stella 4d, a program you can try as a free trial download at http://www.software3d.com/Stella.php.

A Twice-Zonohedrified Dodecahedron

If one starts with a dodecahedron, and then creates a zonohedron based on that solid’s vertices, the result is a rhombic enneacontahedron.

If, in turn, one then creates a new zonohedron based on the vertices of this rhombic enneacontahedron, the result is this 1230-faced polyhedron — a twice-zonohedrified dodecahedron. Included in its faces are thirty dodecagons, sixty hexagons, and sixty octagons, all of them equilateral.

Stella 4d: Polyhedron Navigator was used to perform these transformations, and to create the rotating images above. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

Two Rhombic Polyhedra with Tessellated Faces

These polyhedra are the rhombic dodecahedron (above), and the rhombic triacontahedron (below).

I made both of these using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. The tessellation on the faces of these polyhedra first appeared right here on this blog, in the post just before this one.