Selections from the First Hundred Stellations of the Rhombicosidodecahedron

Since shortly after I learned of their existence, I have found the rhombicosidodecahedron to be the most attractive of the Archimedean solids. That’s a personal aesthetic statement, of course, not a mathematical one.

Rhombicosidodeca

This solid has a long stellation-series. With Stella 4d, the program I used to make these images, it’s easy to simply scroll through them. The stellation of this polyhedron follows these stellation-diagrams; I used Stella 4d to make them as well. You may research, try, or buy this program at this website. The first of these stellation-diagrams is for the planes of the twelve pentagonal faces.

Rhombicosidodeca -StelDiag for twelve face-planes

For the planes of the twenty triangular faces, this is the stellation-diagram:

Rhombicosidodeca -StelDiag for twenty face-planes-StelDiagFinally, there are the the planes of the thirty square faces.

Rhombicosidodeca -StelDiag for thirty face-planes-StelDiag

The following survey of the first hundred stellations is not intended to be exhaustive; I’m including all those I find worthy of inclusion on subjective aesthetic grounds. The first stellation shown here is actually the 25th stellation of the rhombicosidodecahedron:

Rhombicosidodeca 25th stellation

Next, the 30th stellation:

Rhombicosidodeca 30th stellation

The next one is the 33rd stellation.

Rhombicosidodeca 33rd stellation

And next, the 38th stellation.

Rhombicosidodeca 38th stellation

Here is the 46th stellation:

Rhombicosidodeca 46th stellation

And the 48th stellation:

Rhombicosidodeca 48th stellation

Next, the 58th stellation:

Rhombicosidodeca 58th stellation

And now, the 62nd stellation.

Rhombicosidodeca 62nd stellation

Next is the 85th stellation; it’s also a compound of an icosahedron (blue), and a yellow polyhedron I have not yet identified, except as the nth stellation of something. This I know: I have seen the yellow polyhedron before. If you happen to know what it is, the identify it in a comment.

Rhombicosidodeca 85th stellation might also be a compound

The next stellation shown is the next one in the series, the 86th. It demonstrates a phenomenon I have observed, but cannot explain, and that is the tendency, in sequences of stellations, to have a large number of similar stellations in a row, followed by a sudden, much more extreme change in appearance, from one stellation to the next, as seen here. It’s a phenomenon which I would like to better understand.

Rhombicosidodeca 86th stellation

To be continued, with selections from the next hundred stellations….