Tag Archives: octahedra

Honeycomb Made of Cuboctahedra and Octahedra

This is the three-dimensional version of what is called a tessellation in two dimensions. It fills space, and can be continued in all directions. Software used: Stella 4d, available here.

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Augmenting the Octahedron with Octahedra, Repeatedly.

This is an octahedron. If you augment each face of an octahedron with more octahedra, you end up with this. One can then augment each triangular face of this with yet more octahedra. Here’s the next iteration: This could, of … Continue reading

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The Compounds of Five Octahedra and Five Cubes, and Related Polyhedra

This is the compound of five octahedra, each a different color. Since the cube is dual to the octahedron, the compound of five cubes, below, is dual to the compound above. Here are five cubes and five octahedra, compounded together, … Continue reading

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A Compound of Ten Elongated Octahedra Which Is Also a Particular Faceting of the Rhombicosidodecahedron, Together with Its Dual

Thinking about the post immediately before this one led me to see if I could connect opposite triangular faces of a rhombicosidodecahedron to form a ten-part compound — and it worked with Stella 4d just as it had when I … Continue reading

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Two Different Forty-Part Polyhedral Compounds

The polyhedron above is a compound of twenty cubes and twenty octahedra, colored by symmetry-based face-type. If the same compound is viewed in “rainbow color mode,” it looks like this: With this particular compound, though, there are two versions — … Continue reading

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“Fractured” Octahedra

These are variations of the octahedron. I made them all with Stella 4d, which is available here. “Fractured” isn’t an official term, as “truncated or stellated” are, but I can’t come up with a better description, at least not yet. … Continue reading

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A Cluster of Nine Octahedra, and Related Polyhedra

If one starts with a central octahedron, then augments each of its eight triangular faces with identical octahedra, this is the result. It is then possible to augment each visible triangle of this cluster with yet more octahedra, which produces … Continue reading

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