I’ve been interested in the rhombic dodecahedron (RD for short) ever since I learned that it is a space-filling polyhedron (i.e., they can be packed together with no wasted space), and that all faces are identical, like the rhombus below. Here’s a rotating 3d picture, and the relative dimensions of one face.
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The angles of the rhombus are approximately 70.53 and 109.47 degrees.
My first thought was that a modular building, such as house, could be made from a collection of them, with suitable openings and infrastructure. I made a couple of them out of thin plywood. Later, when I started thinking about modular spacecraft for the Two Years at the Hot End story, I decided to make several of them and see how well they could be used. By this time, I was using Shapeways to 3D-print my designs, so I designed a rhombus with flanges to connect them at their edges, and clips toehold them together. I designed a large hole in the rhombus, to provide access to the interior, as if for a door or airlock.
The cost of ordering two faces was too high at the original size (10 cm along the long diagonal), so I reduced it to half-size. At this size, the thickness of the clips and the indentations to hold them didn’t meet Shapeways’s design rules, but they provide a “print it anyway” feature, which I used. The first two faces worked pretty well, so I ordered 10 more to make full RD. This worked fine, as in the figure below, but was too expensive to make very many.
Next I designed a set of twelve of the faces connected into a single “part” by way of two bars of clips. By printing as a single part, the cost was reduced by about 70%. The images below show the 3D model and the part as received. Apparently for packing, Shapeways separated the faces into pairs.
To have a reasonable number of RDs to try various arrangements, I next designed a complete RD only 2cm across, with clips to hold them together and again with holes for access. I made a grid of 25 of these, with thin wires strung between them, and rows of clips attached. This still counted as a single part for pricing purposes, and was affordable. The picture below shows five of the RDs and a couple of clips, and the rest still strung on their wires. Unfortunately, the size of the holes was a bit too small to allow tweezers inside to attach the clips. I might end up using water-soluble glue to arrange the RDs into various configurations.