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Number Theory puzzle: What is the significance of these number sets?
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A friend recently sent me this video taken from MoMath in NYC. I have been determining each of the meanings of the symbols attached to the numbers, but am stuck on only two: the tetrahedral molecule symbol, and the geometer's compass symbol.

What I've noticed is that the symbols have to do with the number sets, e.g. the pizza symbol is placed on all numbers pertaining to the lazy caterer's sequence.

For brevity, here are the two sets, up to a few numbers:

Tetrahedral molecule set: 4, 6, 12, 24, 36, 48, 60...

Compass set: 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20...

So... why are these two sets of numbers grouped together? What's their significance? Any thoughts or wisdom is so greatly appreciated. TIA!

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6 months ago