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3 articles on this topic.
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Fold a square of paper four times, make three straight snips, and unfold a six-pointed star. Every fold is a mirror, so every snip gets copied once for each layer, and a kid can watch exactly how that happens one unfold at a time.
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It started with two rules: bonds have a length, and things attached to the same atom push each other away. That got methane its tetrahedron and benzene its hexagon. Then water needed lone pairs, ethene needed a reason not to fold in half, ethane needed a reason to stagger, and copper needed to be told. Here is what each rule bought, and what the ones I tried and threw away did not.
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Drop charged vertices into a 3D workspace, join them, and let them settle. Every Platonic solid comes out with its edges equal to within a thousandth, from an energy that has no notion of an angle and no rest length. The Archimedean solids come out wrong, and the reason why turns out to be the interesting part.