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.


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….

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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