Building Rhombic Dodecahedra Resonators

hypercubeBuilding this shape can be challenging if you do not know the right geometry.

In conventional language, the shape is a truncated rhombic dodecahedron. It is made of 8 rhombuses (rhombi), 4 triangles, and 1 square.

The basic rhombus can be made from joining four triangles together. Each triangle has sides proportional to one, the square root of two, and the square root of three. Put simply, the small angles of the rhombus are both approximately 70.5 degrees and the large angles are both about 109.5 degrees.

rhombusIf you want more accuracy, the angles are 70.5287 degrees and 109.4712 degrees. This is generally accurate enough for most CAD/CAM systems.

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trianglesThe triangles (whose bases meet the square where you cut a whole for the woofer) are actually half-rhombi — that is, they come from slicing the rhombus down the middle of the two big angles, making two triangles whose angles areĀ 70.5287 degrees and 54.73565 degrees and 54.73565 degrees.
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trianglesThe easiest way to proceed is to take three rhombi, lay them outer-face-up and tape them together like so.

Repeat this process to get two groups of 3 panels taped togetherĀ (tripanels). Now apply a strip of tape to close up each tripanel and flip them over so you are looking at the insides or concave view.

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Putting a rubber glove on your hand, get some glue on the end of your gloved index finger and trace down the Y of the three internal seams so that they are glued. Do the same for the other tripanel, and then set them to dry for an hour.
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rhombus
Now take these two tripanels and tape them together to make a pyramidal point corner like this. Glue the seams on the inside as before. Looking at this “hexpanel” assembly, you will see two spaces for rhombi. Tape and glue rhombi into these spaces and you will see where to add the four triangles and the square.

—MRK

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