Almanac For Moderns: The Symmetry of Snow
That about snow crystals which confounds all understanding is how so many variations–millions perhaps–can be schemed upon the unvarying fundamental plan of six. Be it etched out to elaborations as fine feathered as a whole pane covered with frost designs, still there are always six rays to each delicate star, and one can still make out in the finest, the ultimate details of attenuated ornamentation, the same fundamental symmetry. There can be no chance about this; some cause underlies it, and I am no crystallographer to explain the details of a snowflake’s fine-wrought surfaces, its internal tensions and stresses, it perfect equilibria and balanced strains that distend each fairy tracery of give to these flowers of the winter air their gossamer strength.
But one may hazard the guess that the six-sidedness of the snow crystal is in reality a doubling of three, just as the symmetry of the lily and the amaryllis is. Of all the magic numbers in old necromancy and modern science, three is the first. Three dimensions has matter; three is the least number of straight sides that will just enclose a space. Three legs is the smallest number that will just support the equilibrium and stresses of a stool. Two would not do; four are superfluous; and twice three points are required, and just required, to keep intact the frailest of all solids–a flake of snow.
[More information on our Almanac For Moderns project and the work of Donald Culross Peattie can be found here.]