The components of this compound are eight-faced trapezohedra. Here’s what just one of them looks like:

I made these images using *Stella 4d*, which you can try for free right here.

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The components of this compound are eight-faced trapezohedra. Here’s what just one of them looks like:

I made these images using *Stella 4d*, which you can try for free right here.

To make this, I started with a dodecahedron, dropped the symmetry of the model from icosahedral to tetrahedral, then stellated it five times. Finally, I chose “color as a compound” for the color-settings. I did this using *Stella 4d*, software you can try for free right here: http://www.software3d.com/Stella.php.

I made this using Stella 4d, which you can try for free at this website.

I made this using *Stella 4d*, a program you can try for free right here.

I made this using *Stella 4d*, software you can try for free right here.

I made this using *Stella 4d: Polyhedron Navigator*, which you can try for free at this website.

I stumbled upon the compound above while playing with facetings, starting with the rhombic triacontahedron. Here’s the compound’s dual.

I made these rotating models using* Stella 4d*, a program you can try for free at this website.

I made this using *Stella 4d*, which you can try for free right here.

This was created using *Stella 4d: Polyhedron Navigator*. You may try this program for free at this website.

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.

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