For anyone who knows me, it will come as no great surprise to hear that I am a weak-willed man when it comes to flashing tricolor light-emitting diodes (LEDs). As I often say, “Show me a flashing LED and I’ll show you a man drooling.”

The reality-bending Morph LED Ball (Click image to see a larger version — Image source:

I’ve created and documented numerous LED-based projects over the years. Since I’m a huge fan of the anachronistic retro-futuristic steampunk aesthetic, many of these little beauties have a hint of a sniff of a whiff of a steampunk look and feel about them. Currently, I’m working with friends Recreating Retro-Futuristic 21-Segment Victorian Displays, for example.

The term “mechatronics” refers to an interdisciplinary branch of engineering that focuses on systems that combine electronic, electrical, and mechanical elements. Sad to relate, although I’ve occasionally dabbled with relays and solenoids and servos and motors, I’ve never really done more than dip my toes into the mechatronic waters, but all that may be about to change.

I just saw an article about the reality-bending Morph LED Ball that features 486 stepper motors and 86,000 LEDs. As noted in the article:

The result is an artistic assault on reality, as the highly coordinated combinations of light, sound, and motion make this feel alive, otherwordly, or simply a glitch in the matrix.

I really do urge you to visit this article, scroll down the page until you reach the videos, and then feast your orbs on this magnificent mechatronic marvel. I’ll wait here for your return…

…Oh! You’re back sooner than I expected. Well, what did you think? Personally, I’m drooling with desire all over my keyboard. Seeing this bodacious beauty has whipped my mechatronic juices into a frenzy (I’ll wipe everything down and mop everything up later).

Did you notice anything odd about the hexagonal panels adorning the Morph Ball? How about the fact that some of these “hexagonal” panels are actually pentagonal (if you see what I mean)? This set me to wondering how one would set about mapping hexagonal tiles onto a sphere, which led me to this column, which notes:

If you try to tile with hexagons (by subdividing an icosahedron), you end up with twelve pentagons left over […] even in a map with millions of tiles, you will still have those twelve pentagons hiding among millions of hexagons.

That’s interesting. I didn’t know that. I’m still wondering how this works. Say you have a sphere 100 cm in diameter, for example, surely you can’t arbitrarily map polygons (hexagons and associated pentagons) of any arbitrary size onto it. Won’t there be “magic numbers” for the permissible sizes of the polygons (e.g., 1.5 cm, 2.7 cm, 3.9 cm, etc.)?

Mapping hexagons onto a sphere (Click image to see a larger version — Image source: Wikipedia and Max)

Speaking of which, to what did my example numbers refer? Is there a particular — or favored — way of specifying the size of a hexagon?

Do you just specify the length of one side, or the length of the perimeter (six sides), or the length of a long diagonal (two sides — linking two of the vertices passing through the center), or the length of a short diagonal (the square root of 3 multiplied by the length of one of the sides — linking two vertices with one between them), or the area, or…? (You might want to check out the Omnivision Hexagon Calculator for more details.)

The reason I ask is that I’m thinking it would be an interesting project to start with say a 50 cm diameter sphere constructed out of 3D printed polygons (hexagons and associated pentagons), where we just print the outsize edges of the polygons, cover them with diffusers, and mount circuit boards with LEDs behind them (a bit like the 21-Segment Victorian Displays). What I laughingly call what’s left of my mind is currently mulling this conundrum furiously. What say you? Do you have any thoughts you’d care to share?