Tag Archives: octahedra

Octahedra and Truncated Cubes Can Fill Space Without Leaving Any Gaps

I created this using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

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Octahedra and Cuboctahedra Can Fill Space Without Leaving Any Gaps

I created this image using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

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Some Ten-Part Polyhedral Compounds

While examining different facetings of the dodecahedron, I stumbled across one which is also a compound of ten elongated octahedra. Here’s what this compound looks like with the edges and vertices hidden: Next, I’ll put the edges and vertices back, … Continue reading

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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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