Space-Filling Octagonal Prisms and Great Rhombcuboctahedra

This is a continuation of the process shown in the last post here, but with a different coloring-scheme.

I made this using Stella 4d, which you can try for free at this website.

Packing Space with Great Rhombcuboctahedra and Octagonal Prisms

…And so on….

[Software credit: I made these images using Stella 4d, which you can try for free right here.]

Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube

To start building this space-filling honeycomb of three Archimedean solids, I begin with a great rhombcuboctahedron. This polyhedron is also called the great rhombicuboctahedron, as well as the truncated cuboctahedron.

Trunc Cubocta honeycomb core

Next, I augment the hexagonal faces with truncated tetrahedra.

Trunc Cubocta honeycomb core plus 1.gif

The next polyhedra to be added are truncated cubes.

Trunc Cubocta honeycomb core plus 2

Now it’s time for another layer of great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 3

Now more truncated tetrahedra are added.

Trunc Cubocta honeycomb core plus 4

Now it’s time for a few more great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 5

Next come more truncated cubes.

Trunc Cubocta honeycomb core plus 6

More great rhombcuboctahedra come next.

Trunc Cubocta honeycomb core plus 7

More augmentations using these three Archimedean solids can be continued, in this manner, indefinitely. The images above were created with Stella 4d: Polyhedron Navigator, a program you may try for yourself at http://www.software3d.com/Stella.php.

ZigZag: A Faceting of the Great Rhombcuboctahedron

Faceted Great Rhombcuboctahedron

I made this using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

494 Circles, Each, Adorning Two Great Rhombcuboctahedra, with Different (Apparent) Levels of Anxiety

 

Trunc Cubocta

The design on each face of these great rhombcuboctahedra is made from 19 circles, and was created using both Geometer’s Sketchpad and MS-Paint. I then used a third program, Stella 4d (available here), to project this image on each of a great rhombcuboctahedron’s 26 faces, creating the image above.

If you watch carefully, you should notice an odd “jumping” effect on the red, octagonal faces in the polyhedron above, almost as if this polyhedron is suffering from an anxiety disorder, but trying to conceal it. Since I like that effect, I’m leaving it in the picture above, and then creating a new image, below, with no “jumpiness.” Bragging rights go to the first person who, in a comment to this post, figures out how I eliminated this anxiety-mimicking effect, and what caused it in the first place. 

Trunc Cubocta

Your first hint is that no anti-anxiety medications were used. After all, these polyhedra do not have prescriptions for anything. How does one “calm down” an “anxious” great rhombcuboctahedron, then?

On a related note, it is amazing, to me, that simply writing about anxiety serves the purpose of reducing my own anxiety-levels. It is an effect I’ve noticed before, so I call it “therapeutic writing.” That helped me, as it has helped me before. (It is, of course, no substitute for getting therapy from a licensed therapist, and following that therapist.) However, therapeutic writing can’t explain how this “anxious polyhedron” was helped, for polyhedra can’t write.

For a second hint, see below.

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[Scroll down….]

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Second hint: the second image uses approximately twice as much memory-storage space as the first image used.

A Great Rhombcuboctahedron, Decorated with Circles and Hexagons

Trunc Cubocta

The images on the faces of this polyhedron were created with Geometer’s Sketchpad and MS-Paint. Projecting these images onto these faces, and then creating this rotating image, was accomplished using Stella 4d: Polyhedron Navigator— a program you can try for yourself, for free, at http://www.software3d.com/Stella.php.