Truncated cuboctahedron translucent cycle

I've shown the truncated cuboctahedron (TCO) before in the gear system, but for my Vorohedron technique I need the coordinates of the dual polyhedron, the disdyakis dodecahedron. I usually go to Wikipedia for these things, but the coordinates weren't there. So I spent some quality time with pencil and paper and derived the coordinates myself, starting with the basic pictorial definition of TCO.

It turned out rather simple in retrospect, just a few iterations of the Pythagorean theorem. Of course, I had to add the results to the Wikipedia article as well. It's been quite a while since I've contributed anything to Wikipedia, but thankfully my old account from the 00s was still there.

There is a particular challenge with the definition of TCO itself, and this may be a reason for the lack of the dual coordinates in the first place. The actual truncation of a cuboctahedron makes rectangles instead of squares. But as an Archimedean solid, TCO only has regular polygonal faces. So its name only approximates the truncation process.

For the dual polyhedron, this means that the Kleetope approach won't work. In fact I went down that path first, playing with a compound of the rhombic dodecahedron and the cuboctahedron using various multipliers, but the dual always showed those ugly rectangles. So I went back to basics and derived the dual of TCO from its Archimedean definition. In essence, I had to find the distance of each face from the origin. And this distance is essential in my Vorohedron approach to ray-marching these shapes in realtime.

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