In the two posts right before this one, I’ve been exploring simple structures made of modified rhombicosidodecahedra, and today I’m going to post a much larger, more complex one. Here’s the rhombicosidodecahedron — the original Archimedean solid which started all of this:

The modified forms of this polyhedron which I’m using as building-blocks are all among the 92 Johnson solids. Here are the two which have already appeared in the last two posts on this blog: the diminished rhombicosidodecahedron (J76) and the parabidiminished rhombicosidodecahedron (J80).

For this new, more ambitious construction, I’m going to need some more pieces, starting with the metabidiminished rhombicosidodecahedron (J81), which will be useful to make angles.

The Johnson solid called the tridiminished rhombicosidodecahedron (J83) can be used to make three-valent vertices.

Finally, here’s the more complex structure for which I needed all these pieces. It could be extended outwards indefinitely, in a manner similar to the tessellation of the plane with regular hexagons.

To make these polyhedral images, I use a program called Stella 4d. If you’d like to give it a try, for free, please visit this website.