(I don’t know if this is a chemistry or a physics question)
In: Chemistry
Water molecules are made up with an oxygen atom joined to two hydrogen atoms. But they don’t join in a straight line. Instead, they form a sort of angled L shape. When snow crystals form, the oxygen in one molecule gets attracted to one of the hydrogens in another molecule. All these angles together end up being at 120°, i.e. a third of a circle. This is the same angle you get between two sides of a hexagon. So, as the crystals grow, the hexagonal pattern emerges.
Water molecules look [something like this](https://useruploads.socratic.org/RzH7TE7JRESZMgoYLTe3_books.jpg). They’re kind of bent and they have a more positive electric charge near the hydrogens and a more negative charge near the oxygens.
Positive charges attract negative charges, and like charges repel. So when you put a bunch of water molecules together and get them cold enough that they aren’t just bouncing around everywhere, they like to arrange themselves so that the positive charges on the hydrogens are close to the negative charges on the oxygens. This tends to produce little flat hexagons, like [this](https://upload.wikimedia.org/wikipedia/commons/3/31/Cryst_struct_ice.png). The solid lines are the molecular bonds that hold the oxygens to its own hydrogens inside a single water molecule, while the dashed lines represent the attraction between one molecule’s oxygen and another molecule’s hydrogen.
Because all the little building blocks of ice are hexagonal, ice likes to form hexagons if it can grow in any direction it wants freely (so, in your ice maker, where the ice is grown in a solid container, it generally will just take on the shape of the container). In a cloud, though, the ice will grow floating in the air, so it can just add more molecules and build more hexagons on the ones that already exist, making larger and larger hexagonal structures.
As conditions on each part of the hexagon tend to be similar at any given time, we expect the crystal to grow very symmetrically. That is, we expect it to add a very similar number of hexagons in similar places around the ice crystal as it grows, so it doesn’t get too lopsided most of the time. Small changes in the conditions (different temperatures, different amounts of water in the air, etc.) mean that it adds these in slightly different ways, [leading to different shapes of snow crystals](https://www.researchgate.net/figure/The-Nakaya-snow-crystal-morphology-diagram-showing-different-types-of-snow-crystals-that_fig1_233753190).
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