Selections from the Second Hundred Stellations of the Rhombicosidodecahedron

This survey began in the last post, with selections from the first hundred stellations of this Archimedean solid. In this survey of the second hundred stellations, the first one I find noteworthy enough for inclusion here is the 102nd stellation.

Rhombicosidodeca 102nd stellation

A similar figure is the 111th stellation:

Rhombicosidodeca 111th stellation

There followed a long “desert” when I did not find any that really “grabbed” me . . . and then I came to the 174th stellation.

Rhombicosidodeca 174th stellation

The fact that it is monocolored, the way I had Stella 4d set, told me immediately that this stellation (the one above) has only one face-type. There are twenty of these faces; they are each equilateral hexagons which “circumscibe,” in a way, the triangular faces of an icosahedron. For this reason, I suspect this is also one of the stellations of the icosahedron; I’m making a mental note to do exactly that.

I also make a second virtual model of the 174th stellation of the rhombicosidodecahedron, with the faces colored in such a way as to make the interpenetrating equilateral hexagons more obvious.

Stellated Rhombicosidodeca

After that interesting stellation, the next one to caught my attention is the 179th stellation.

Rhombicosidodeca 179th stellation

Next of note, the 182nd stellation is similar to the icosahedron/dodecahedron compound, but with the dodecaheron larger than it is in that compound, so that edges, one from each component polyhedron, do not intersect, but are instead skew. Another way to view it is that the dodecahedron is encasing the icoahedron, but with enough room left for portions of the icosahedron to protrude from the faces of the “dodecahedral cage.”

Rhombicosidodeca 182nd stellation

Next is the 183rd stellation.

Rhombicosidodeca 183rd stellation

Here is the 187th stellation, which is quite similar to the last one shown. The pulsating effect, first seen in the last post above, is an accident, and not discovered until after these images were already made, using Stella 4d, which may be tried here. Why didn’t I re-create the .gifs? Simple: I don’t feel like taking the ~10 minutes each to do so.

Rhombicosidodeca 187th stellation

The 190th stellation may also be viewed as a dodecahedron, augmented with variations of pentagonal pyramids on each face:

Rhombicosidodeca 190th stellation

Next, the 191st stellation:

Rhombicosidodeca 191st stellation

And, after that, the 192nd stellation.

Rhombicosidodeca 192nd stellation

The next stellation which grabbed by attention: the 198th.

Rhombicosidodeca 198th stellation

Finally, I’ll close this set of highlights from this part of the rhombicosidodecahedron’s stellation-series with that solid’s 199th stellation.

Rhombicosidodeca 199th stellation

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. 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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