# A Space-Filling Arrangement of Polyhedra Using Truncated Cubes, Rhombcuboctahedra, Cubes, and Octagonal Prisms

This image above has only one polyhedron-type hidden from view, in the center:  a red truncated cube. Next, more of this pattern I just found will be added.

The next step will be to add another layer of blue octagonal prisms.

And now, more yellow cubes.

This was an accidental discovery I made, just messing around with Stella 4d, a program you may try for yourself at http://www.software3d.com/Stella.php. The next cells added will be red truncated cubes.

Next up, I’ll add a set of pink rhombcuboctahedra.

The next set of polyhedra added: some yellow cubes, and blue octagonal prisms.

Now I’ll add more of the red truncated cubes.

At this point, more yellow cubes are needed.

The next polyhedra added will be pink rhombcuboctahedra.

And now, more of the blue octagonal prisms.

As long as this pattern is followed, this may be continued without limit, filling space, without leaving any gaps.

## 6 thoughts on “A Space-Filling Arrangement of Polyhedra Using Truncated Cubes, Rhombcuboctahedra, Cubes, and Octagonal Prisms”

• Thanks for letting me know, Tom. Once again, as with so many things I independently find, I learn a short time later that others beat me to the punch. *Sigh*

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1. How do you determine the speed of rotation? I like this pace.

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• It’s entered into “Stella 4d” when I make these .gif files. Just before you started following my blog, another reader asked me to slow the rotation of models I post, and I recognized this as a good idea. I now use a rotational period of six to eight seconds for each model — eight for the more complex ones.

For some, like these, I can save memory by only making ,gif files for a fraction of a rotation, when the fraction chosen makes things appear to rotate smoothly. For this post, I made two-second, looping .gifs of 1/4-rotation, which appear identical to a full-rotation .gif with a period of eight seconds.

WordPress only gives us 3 GB for free, and I’ve exceeded that recently, so keeping the file size small does matter to me. 🙂

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