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

Stellated Dual Morph 50.0%

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.

RD 5

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

A Compound of Three Elongated Octahedra

This compound is the 16th stellation of the tetrakis hexahedron, the Catalan solid which is the dual of the Archimedean truncated octahedron. I made it using Stella 4d, which you can try 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.

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.

Five Variants of the Compound of Two Tetrahedra

This is the compound of two tetrahedra, also known as Johannes Kepler’s Stella Octangula.

I found the five variations of this polyhedral compound shown below, located deep within the stellation-series of the great rhombicuboctahedron.

These .gif images were all made using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

The Third Stellation of the Pentagonal Icositetrahedron Is a Compound of Two Irregular Dodecahedra

Here’s the pentagonal icositetrahedron. It is the dual of the snub cube.

And here is its third stellation. As you can see, it’s a compound of two irregular dodecahedra.

I made these images using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.