To make this symmetrohedron, I augmented the faces of a rhombic dodecahedron with prisms, then formed the convex hull of the result. All faces except for the red rhombi are regular. This was made using Stella 4d, which you can try for free here.
This was created using Stella 4d: Polyhedron Navigator. You may try this program for free at this website.
This is the cuboctahedron, one of the Archimedean solids. Its dual, shown below, is the rhombic dodecahedron.
The rhombic dodecahedron has a property which sets it apart from most other polyhedra: it can fill space with copies of itself, leaving no gaps. The next stage of such growth is shown below.
The next step is to add more rhombic dodecahedra on each face.
One more set added, and the edge-length of the cluster reaches four rhombic dodecahedra.
This could be continued without limit. As is does, the overall shape of the cluster becomes more and more shaped like a cuboctahedron, which is back where we started. You can easily see this in the convex hull of the last cluster.
All of these rotating images were created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
To make this, I used Stella 4d: Polyhedron Navigator to take the image I blogged here, and then project it onto the faces of a rhombic dodecahedron. Next, I put that polyhedron into motion for the .gif shown below.
If you’d like to give Stella a free try, the site to visit is http://www.software3d.com/Stella.php.
I made these using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
This is the compound of five rhombic dodecahedra, with each component shown in a different color. This is one of the few well-known polyhedral compounds which is actually more attractive with the faces hidden, and that’s what’s shown in the next image.
I made these images using Stella 4d: Polyehdron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
The patterns on the faces are from the last post here, immediately before this one. I used Stella 4d: Polyhedron Navigator to make this, and you can try this software for free at this website.
The image of Saturn was taken by NASA, and I put it on the faces of a rhombic dodecahedron, and created this image, with a program called Stella 4d. You can try this program for free at http://www.software3d.com/Stella.php.
The truncated octahedron is well-known as the only Archimedean solid which can fill space, by itself, without leaving any gaps. The cluster below shows this, and has the overall shape of a rhombic dodecahedron.
It’s easier to see the rhombic dodecahedral shape of this cluster when looking at its convex hull:
Both images here were made using Stella 4d, which you can try for free right here.
Programs used to make this included Geometer’s Sketchpad, MS-Paint, and Stella 4d: Polyhedron Navigator, which was used to assemble everything else into what you see here. You may try Stella for free at http://www.software3d.com/Stella.php.
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