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I checked out the wikipedia site. Unfortunately it isn't very helpful. Here is another one I found at work today:
http://www.its.caltech.edu/~atomic/snowcrystals/primer/primer.htm
This is a little better:
``The six-fold symmetry of a snow crystal ultimately derives from the
hexagonal geometry of the ice crystal lattice. But the lattice has
molecular dimensions, so it's not trivial how this nano-scale symmetry
is transferred to the structure of a large snow crystal. The way it
works is through faceting. No long-range forces are necessary to form
facets; they appear simply because of how the molecules hook up
locally in the lattice (see Crystal Faceting for how this works).
>From faceting we get hexagonal prisms, which are large structures with
six-fold symmetry.''
This suggests that the six fold symmetry is the consequence of EM forces on the surface of the generating molecules that link together as a planar tessellation, with secondary perpendicular linkages that create another plane either above or below the inital lattice.
But such sheet like constructions have no intrinsic center. I would suggest (I would like to believe) that some how the gravitational vector acts as an axial center, which despite all the variations of shape, all these shapes have in common.
Further down in the physics section under branching:
``The growth of snow crystals depends on a balance between faceting (see Crystal Faceting) and branching. Faceting tends to make simple flat surfaces, while branching tends to make more complex structures. The interplay between faceting and branching is a delicate one, depending strongly on things like temperature and humidity. This means snow crystals can grow in many different ways, resulting in the great diversity we see in snow crystal forms.''
All well and good. But why don't the global results of these interplays resemble feathers for example, instead of radially symetric shapes?
I've played a lot with hexagonal tesselations, and I discovered that they tend to gobally resemble parallograms, rhomboids, trapizoids, large hexagons or large triangles, all depending on how you generate the tessellation from its source tile.
cg