It’s just one equilateral triangle and then two pairs. The specific slots the opposing pairs are in don’t matter. You can see that each sample of the triangle has a gap of 7 slots between each other.
There isn’t much math to do really. Take as axioms that the obvious way to balance 2 or 3 tubes is in fact balanced, and that if you add a balanced arrangement of tubes to an already balanced arrangement, the result is still balanced.
Centrifuge spins really fast so you need to balance where you put the samples, or else it will vibrate. The trick is to put them on the opposite side or equally spaced apart from each other.
Think of it like a tilt-a-whirl. When you don’t distribute the load as best as possible and it starts spinning at an angle, someone (a test tube) will puke.
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