“Simplify, simplify, simplify.” — Thoreau

“One ‘simplify’ would have sufficed.” — Emerson

With a nifty construction method settled upon, it was time to decide on a polygonal shape for our “new year’s disco ball.” This seemed like a solved problem — geodesic domes are sufficiently popular that you can find kits and calculators all over the internet — but we soon hit a snag: while at first glance these domes appear to be comprised of many identical triangles, it turns out there are actually very subtle variations throughout. This is not a technical problem at all; it could certainly be done, but it fails our Annoying Test. Each piece must be aligned with exactly the right neighbors and turned exactly the right way. Now repeat the process dozens or hundreds of times without a single mistake. No.

So, Plan B, we looked at Archimedian solids. Many of these polyhedra achieve a nice ball-like shape while being comprised of just two or three types of regular polygons. The truncated icosahedron (colloquially sometimes labeled a “soccer ball” or “Buckyball”) was especially pleasing:

On its own, the shape is now pretty easy to build. But when it came time to think about lighting this up, even this shape proved just a bit too complex. Here’s why:

If we just wanted to jam LEDs in there and blink them at random, that would be simple and we could call it done. But that’s…just…lacking something. We’d really like to be able to address these LEDs with order and purpose…top to bottom, around the circumference, you name it. And again, there’s nothing technically barring us from doing that with this shape. It’s simply a matter of not wanting to alienate readers and kit-builders with limited patience. You see, to keep track of their positions, every single LED would need to be installed in a specific place, in a specific sequence, somewhere on this map:

Not fun to try to explain…or read…in instructions. So we’ll back off one more step and consider the Platonic solids, which are each comprised of a single repeating regular polygon. Gamers are well familiar with them:

(Please ignore the d10 and imagine a d6 in its place!)

The dodecahedron (in blue) and icosahedron (red) are both vaguely round…ish. We settled on the icosahedron, comprised of 20 equilateral triangles, because the math is simpler, and it spreads out nicely as a flat map:

Much easier for indicating where will LEDs go! And a quick ugly prototype confirms that the LEDs will fit:

So, after that whole digression, we’ve come full circle to use one of the original cable-tie assembly shapes we had already looked at!

We’ll make the finished ball (yes, we’re still calling it a “ball,” despite its obvious polygonality) in mirrored acrylic for added bling factor. With 20 faces, and six LEDs per face, that’s 120 LED pixels total. We’ll need those figures later when coming up with a power supply…