This is my latest creation with my newest polyhedron-building tool, Lux Blox. The orange and blue “Lux squares” differ only in color, and here they represent the square faces of a rhombicuboctahedron. The triangular gaps represent that polyhedron’s triangular faces.
If you’d like to try Lux Blox yourself, the website to visit to buy them is www.luxblox.com. The last picture includes my hand to give a sense of scale to these models.
This particular faceting of the rhombcuboctahedron can also be viewed as a cluster of stella octangulae. I made it using Stella 4d, polyhedron-manipulating software you can try, for yourself, at http://www.software3d.com/Stella.php.
Some prefer to call the great rhombcuboctahedron the “truncated cuboctahedron,” instead. Whichever term you prefer, this is a faceted version of that Archimedean solid. I made it using Stella 4d: Polyhedron Navigator, software you may find here.
I noticed that I could arrange eight great rhombcuboctahedra into a ring, but that ring, rather than being regular, resembled an ellipse.
I then made a ring of four of these elliptical rings.
After that, I added a few more great rhombcuboctahedra to make a meta-rhombcuboctahedron — that is, a great rhombcuboctahedron made of rhombcuboctahedra. However, it’s squashed. (I believe the official term for this is “oblate,” but “squashed” also works, at least for me.)
So now I’m wondering if I can make this more regular. In other words, can I “unsquash” it? I notice that even this squashed metapolyhedron has regular rings on two opposite sides, so I make such a ring, and start anew.
I then make a ring of those . . .
. . . And, with two more ring-additions, I complete the now-unsquashed meta-great-rhombcuboctahedron. Success!
To celebrate my victory, I make one more picture, in “rainbow color mode.”
[All images made using Stella 4d, available here: http://www.software3d.com/Stella.php.]
All four of these rotating images were created using software called Stella 4d: Polyhedron Navigator. You can buy this program, or try it for free, at this website. Faceting is the inverse function of stellation, and involves connecting the vertices of an already-established polyhedron in new ways, to create different polyhedra from the one with which one started. For each of these, the convex hull is the great rhombcuboctahedron, itself.
I just ordered a crystal rhombcuboctahedron on eBay because I like its geometrical properties, despite the mystical claims in the item listing. I did so with the full knowledge and expectation that these claims are almost certainly false, because, well, they’re mystical claims.
Here’s my ethical dilemma: would it be ethical to lab-test those claims, then post the results in the feedback I leave?
[Image created using Stella 4d, available at http://www.software3d.com/Stella.php. This isn’t a picture of the crystal on eBay; it is made of quartz, and not rainbow-colored. It is of the same shape, however.]
This faceting was created using Stella 4d, available here.
I created this using Stella 4d, available at http://www.software3d.com/Stella.php.
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.
I used Stella 4d, available at http://www.software3d.com/Stella.php, to make this.
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