
To get started packing space with cuboctahedra and octahedra, I started with a single octahedron, then augmented its square faces with additional cuboctahedra.

Next, I augmented each triangular face with a blue octahedron.

Next, I augmented each square face with a cuboctahedron.

Next, I added still more cuboctahedra.

The next step was to augment the yellow triangular faces with blue octahedra.

I next added more cuboctahedra.

This process may be continued without limit. I used a program called Stella 4d to make these models, and you can try this software yourself, for free, at this website.
The more you go the more the while thing resembles an octahedron. Last image you can see eight triangular faces. Although obviously not smooth.
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Wonderful! Thanks so much Robert. I teach this principle, but have never seen such excellent graphics to illustrate it before.
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Very nice.
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