Five More Clusters of Rhombicosidodecahedra

Making the four different clusters of rhombicosidodecahedra seen in the post right before this one was fun, so I decided to make more of them.

Tetrahedra 20 A augmented with 80 RIDs

There are two different forms of the compound of twenty tetrahedra. To make the polyhedral cluster above, I chose one of them, and then augmented each of its 20(4) = 80 triangular faces with a rhombicosidodecahedron.

For the next of these clusters, I decided to move away from using compounds for the central, hidden figure. Instead, I chose a snub cube, and augmented each of its 32 triangular faces with a rhombicosidodecahedron. Since the snub cube is chiral, this cluster is chiral as well.

Augmented Snub Cube the 32 triangles are augmented by RIDs

Any chiral polyhedron can be combined with its mirror-image to produce a new compound, and that’s what I did to make this next cluster, which is composed of 64 rhombicosidodecahedra: I simply added the cluster above to its own reflection.

Compound of enantiomorphic pair of snub cubes with RIDs augmenting the 64 triangles

Next, I turned to the snub dodecahedron, also chiral, and with 80 triangular faces. Augmentation of all 80 produced this chiral cluster of 80 rhombicosidodecahedra:

Augmented Snub Dodeca with 80 RIDs on triangular faces it is chiral

Finally, I added this last cluster to its own mirror-image, producing this symmetrical cluster of 160 rhombicosidodecahedra.

160 RIDs augmenting the triangular faces of snub dod enan pair compound

Each of these was created using a program called Stella 4d: Polyhedron Navigator, software you can try for free right here.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things 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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