The image on the faces of these polyhedra appeared, in black and white form, in the last post here. I used Geometer’s Sketchpad and MS-Paint to make it. It took a third program, Stella 4d, to project the image onto each face of a rhombic dodecahedron (as seen above), as well as the rhombic dodecahedron’s first stellation (below), and then generate these rotating .gif images. You can try Stella for free, as a trial download, at www.software3d.com/Stella.php.
The smaller one may be enlarged with a single click.
I made these using Stella 4d, which you can find at http://www.software3d.com/Stella.php.
Above is this polyhedral stellation in three colors. If every face is given its own color, though, except for parallel faces, it looks like this (click to enlarge):
I made both images using Stella 4d, a program you can find at http://www.software3d.com/Stella.php.
Geometer’s Sketchpad and MS-Paint were both used to make the images on the faces of this polyhedron, and then Stella 4d was used to put it all together and create this rotating image. Stella may be bought, and/or tried for free, at www.software3d.com/Stella.php.
This is not the only truncated form of the rhombic dodecahedron. In this polyhedron, square-based pyramids have been “truncated away” from the rhombic dodecahedron’s four-valent vertices, but the three-valent vertices remain untouched.
If this truncation is done in such a way as to leave the hexagonal faces equilateral (which is not done here), so that all edges of the polyhedron have the same length, the result is called a “chamfered cube.” This closely-related figure may be seen at https://en.wikipedia.org/wiki/Chamfered_cube.
[Image credit: this rotating model was created using Stella 4d, software you can find right here, with a free trial download available.]
The decorations on each face were created using the design, made using Geometer’s Sketchpad and MS_Paint, shown here. I then used Stella 4d, available at this website, to project this flat image onto each face of this polyhedron, and make this rotating image.
I created this using Stella 4d, which is available (including a free trial download) at http://www.software3d.com/Stella.php. It can also be viewed as a compound of the rhombic dodecahedron and another polyhedron, but I haven’t been able to identify that second polyhedron — at least, not yet. If you know what the orange polyhedron is, please leave a comment with its name.
I’ve been asked by a reader of this blog to post nets for this polyhedral compound. Printing nets with Stella 4d is easy, and I’m happy to post them here, in response to that request. Warning, though: there are many nets needed for this compound.
Each of these smaller images may be enlarged with a single click.
Here’s the first net type needed (above). You’ll need thirty copies of this net. The gray parts show, and the white parts are tabs to help put it together. Below is the second type needed, of which you need sixty copies.
There’s also a third type of net, and these last two types may need to be rescaled before you print them, to fit the net of the first type, also. You’ll need sixty copies of this third net (below) as well, It’s the mirror-image of the net of the second type.
Finally, here’s a non-rotating image of the completed polyhedron, to help with the construction:
I recommend using card stock or posterboard, and trying to get as much tape as possible on the inside of the model, making an uncolored version — and then painting it with five different colors of your choice, after the model is assembled. Happy building!
[Software credit: I used Stella 4d: Polyhedron Navigator to create all these images. It’s available at http://www.software3d.com/Stella.php. Downloading and trying a trial version is free, but you have to buy the fully-functioning version to print nets, or to make these rotating .gif files I post all over this blog.]
This compound is unusual in that it is most attractive as a ball-and-stick model, with the faces rendered invisible, rather than the traditional coloring for compounds. In the traditional coloring, no faces are hidden, and each component of the compound is given faces of a different color. Here’s the same compound, rendered in the traditional manner:
Of course, matters of aesthetics are not subject to mathematical proof. Some might prefer the second version to the first.
Software credit: please see www.software3d.com/Stella.php to try or buy Stella 4d, the software I use to make these polyhedral images.
Several recent posts here have been of tessellations I have made using Geometer’s Sketchpad and MS-Paint. To create this rotating polyhedron, I selected one of these tessellations, and projected it onto each face of a rhombic dodecahedron, using another program called Stella 4d. Unlike in the last, similar post, though, I set these tessellation-images to keep their orientation, from the point of view of a stationary observer watching the entire polyhedron rotate, from a distance. Since the polyhedron itself is rotating, this creates a rotation-effect for the tessellation-image on each face.
You can try Stella 4d for yourself, right here, for free: http://www.software3d.com.stella.php.
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