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

# Tag Archives: polyhedral

# 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 Compound of the Rhombic Triacontahedron and a Truncation of the Icosahedron

In the compound above, the yellow hexagons are not quite regular, which is why I’m calling the yellow-and-orange polyhedron *a* truncation of the icosahedron, rather than simply *the* truncated icosahedron. I stumbled upon it while playing with *Stella 4d*, which you may try for free at http://www.software3d.com/Stella.php.

# The Compound of Five Rhombic Dodecahedra

This is the compound of five rhombic dodecahedra, with each component shown in a different color. This is one of the few well-known polyhedral compounds which is actually more attractive with the faces hidden, and that’s what’s shown in the next image.

I made these images using *Stella 4d: Polyehdron Navigator*, which you can try for free at http://www.software3d.com/Stella.php.

# A Rhombic Triacontahedron, Vertices Surrounded By Smaller Rhombic Triacontahedra, and Its Interesting Dual

The first image shows a central yellow rhombic triacontahedron, with smaller, blue rhombic triacontahedra attached to each of its thirty-two vertices. The second polyhedron shown is the dual of the first one, with colors chosen by the number of sides per face in the second image — pentagons red, and triangles yellow. The convex hull of this second polyhedral complex shown would be an icosidodecahedron, itself the dual of the rhombic triacontahedron.

I use software called *Stella 4d: Polyhedron Navigator* to make the rotating polyhedral images on this blog. You can try *Stella *for yourself, for free, at http://www.software3d.com/Stella.php.

# A Compound of Six Pentadecagonal Prisms

This chiral polyhedral compound was generated from a partial faceting of the polyhedron shown in the last post here, using *Stella 4d*‘s faceting function, plus its “try to make faces regular” operation afterwards. Making the six-prism compound in the first place was suggested by Tony Hartley, on Facebook, where I posted a link to that last post in a mathematical group for discussion. Thanks, Tony!

If you’d like to try *Stella* for yourself, the site to visit for a free trial download is http://www.software3d.com/Stella.php.

# Compound of Three Elongated Octahedra

This was created using *Stella 4d*, software you may try for free at this website.

# A Compound of the Icosahedron and the Small Stellated Dodecahedron

I found this by further stellation of the polyhedra shown in the two posts right before this one, using a program called *Stella 4d: Polyhedron Navigator*. You can try* Stella* for free at http://www.software3d.com/Stella.php.

# A Compound of the Great Rhombicosidodecahedron and the Small Stellated Dodecahedron

I made this, using *Stella 4d* (available here), by multiple stellation of the faceted great rhombicosidodecahedron shown in the post immediately before this one.

# A Dozen Truncated Icosahedra, Surrounding a Central Dodecahedron

Created using *Stella 4d*, which you can try for yourself, for free, at http://www.software3d.com/Stella.