Further, what constrains snowflakes to be so thin and so planar? When we do see a snowflake that has a sharp “bend”, why are the two portions of the snowflake individually almost planar?

Concerning the SA article, I think it is reasonable for it to state that temperature and humidity are the main factors in determining the pattern of a snowflake (although the best known explanation does omit humidity). But, concerning the global perfection of snowflake symmetry, this article is just as vague as all the other explanations I’ve seen.

It’s as though these professors want to prove that physics has a simple explanation for every phenomenon in nature, so they make up something that sounds plausible. On close inspection, all the explanations fall apart due to “hand waving” (a lack of rigor). They focus on supposedly relevant principles but omit a sufficient amount of actual explanation.

The part of this article that I believe is the statement that hydrogen bonds (proton-electron cloud attraction) cause a sixfold symmetry. The part I don’t believe is that they also explain the fact that each of the six arms are identical (except for minor dislocations, which are always corrected).

The question remains: why is each arm virtually identical?
The answer to this specific question at http://www.scientificamerican.com/article.cfm?id=why-are-snowflakes-symmet isn’t science. It basically says “during formation of a snowflake, each adsorbed molecule of water must go in one and only one place due to electrical attraction and repulsion.” This begs the question entirely. I’m shocked to see such a pseudoscientific statement published by SA.

I admit that crystalline structures have been well understood for many years. But the familiar case of solid crystals growing in liquid don’t make “arms” like snowflakes. Can all crystals growing by adsorption in a cold fog make arm patterns, or is this restricted to water?

And what causes the corrections of dislocations?

Maybe it’s time for physicists to admit that they don’t really know and are unwilling to experiment sufficiently to discover the reason?

During this process, the molecules (in this case, water molecules) align themselves to maximize attractive forces and minimize repulsive ones. As a result, the water molecules arrange themselves in predetermined spaces and in a specific arrangement. This process is much like tiling a floor in accordance with a specific pattern: once the pattern is chosen and the first tiles are placed, then all the other tiles must go in predetermined spaces in order to maintain the pattern of symmetry.

The rest of the article is here.

As for the 3D aspect, I have seen some photos in 3D that look columnar, but when we have a snowfall that has these big six-sided ones, to the naked eye they do look flat. I think they’re essentially planar, and I suspect that photographing them from the side would be quite tricky indeed [though it wouldn't surprise me if someone, somewhere, had done it].

If the entire pattern of a snowflake were determined by the first few molecules of water, then accidental dislocations should occur all along each spike, massively spoiling the symmetry.

Also, this bonding-angle explanation fails to explain the good approximation to circles that can appear (there is one in the video at http://www.metacafe.com/watch/793880/snowflakes_under_a_microscope/).

And, continuing my ranting, why is it that almost all snowflake micrographs, from the 1800s until now, show two-dimensional objects? None of the snowflakes are at an angle that would display their three-dimensional form. Thus, we have the common description “six-sided symmetry”. Only a two-dimensional snowflake would have only six sides. If snowflakes actually are two-dimensional, I think that would be quite remarkable. There must be some detail in the third dimension. So, what keeps most of each snowflake in one plane? Bond angles don’t explain that. Bond angles would imply a three-dimensional crystal, like that of salt. Something else must be going on.

Consider the rings of Saturn, Uranus, etc. They actually are (approximately) in one plane. Physicists tell us that “shepherd moons” (see http://en.wikipedia.org/wiki/Shepherd_satellite) may help create the intricate structure of planetary rings. But is this an adquate explanation? Not really; it’s just a conjecture without a proof. Why are planetary rings always (approximately) in one plane? Is it because any rock in a tilted orbit would be eliminated by collisions with the others? Maybe. But there are other theories (see http://en.wikipedia.org/wiki/Rings_of_Saturn#Formation and http://www.efluxmedia.com/news_Saturn_Has_Moonlets_in_Its_Belts_from_Collisions_09936.html).

The reason I’m raising these questions is to encourage critical thinking. Few schools teach critical thinking to our young children. As a result, they believe that guesses like these are complete explanations. Even adult scientists don’t question them and don’t embark on more serious and long-term research (until the exceptional scientist comes along to find out why objects rise in shaking sand, or why each type of lightning always has the same fractal shape. Our children also believe that Coca-Cola and Pepsi-Cola are good to drink, and that, while tabacco and alcohol are bad for you, it’s perfectly okay to smoke and drink with your buddies after school.

Anyway, thanks for all the lovely photos of snowflakes, even though they show no detail in the third dimension. It’s not your fault .