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Modular Problem, Part II

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It works!

20131207-111831.jpg
yes, it looks the same as the previous pictures, but trust me, the pesky doubled-up pieces are gone.

I started with assembling ten equal, symmetric pieces:

20131207-112012.jpg
Now I want to play Space Invaders…

I figured if I could keep the pieces sorta “facing” the same way, it would work itself out. And then:

20131207-112221.jpg

Right. Duh. Five-sided holes are hard to construct from pre-assembled three-pieced things.

So, I took a few of my pre-constructs apart, but only as many as I had to. And it worked!

In other words, I had a semi-correct sorta kinda plan than didn’t really work as I thought, but did get the results I wanted.

So, I’ve answered half of my question (although I don’t know of a way to sorta “calculate” it beforehand, I’m inclined to think it’s something along the lines of the four-color problem), and it is possible to construct the model so that you only use three colors without similar-colored neighbors. But the other question still remains: is there a way to guarantee that this works? How about for other models?

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