To form the cluster-polyhedron above, I started with one truncated octahedron in the center, and then augmented each of its fourteen faces with another truncated octahedron. Since the truncated octahedron is a space-filling polyhedron, this cluster-polyhedron has no gaps, nor overlaps. The same cluster-polyhedron is below, but colored differently: each set of parallel faces gets a color of its own.

This is the cluster-polyhedron’s sixth stellation, using the same coloring-scheme as in the last image:

Here’s the sixth stellation again, but with the coloring scheme that* Stella 4d: Polyhedron Navigator* (the program I use to make these images) calls “color by face type.” If you’d like to try *Stella* for yourself, you can do so here.

Also colored by face-type, here are the 12th, 19th, and 86th stellations.

Leaving stellations now, and returning to the original cluster-polyhedron, here is its dual.

This image reveals little about this dual, however, for much of its structure is internal. So that this internal structure may be seen, here is the same polyhedron, but with only its edges visible.

Finally, here is an edge-rendering of the original cluster-polyhedron, but with vertices shown as well — just not the faces.

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This one actually looks edible. Yum!

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