Space-Filling Truncated Octahedra in a Rhombic Dodecahedral Cluster

The truncated octahedron is well-known as the only Archimedean solid which can fill space, by itself, without leaving any gaps. The cluster below shows this, and has the overall shape of a rhombic dodecahedron.

Augmented Trunc Octa.gif

It’s easier to see the rhombic dodecahedral shape of this cluster when looking at its convex hull:

Convex hull.gif

Both images here were made using Stella 4d, which you can try for free right here.

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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