Symmetry in Snowflakes

Snowflakes are symmetrical because they reflect the internal order of the water molecules as they arrange themselves during crystallization. When a minute cloud droplet first freezes into a tiny particle of ice, water vapor starts condensing on its surface, the ice particle quickly develops facets, becoming a small hexagonal prism. As the crystal becomes larger, branches begin to sprout from the six corners of the hexagon.

While it grows, the crystal is blown to and fro inside the clouds, so the temperature it sees changes randomly with time. Since the crystal growth depends strongly on temperature, thus the six arms of the snow crystal each change their growth with time. And because all six arms see similar conditions at the same times, they all grow about the same way. The end result is a complex, branched structure that is also six-fold symmetric.

Sources:
https://www.scientificamerican.com/article/why-are-snowflakes-symmet/
http://www.its.caltech.edu/~atomic/snowcrystals/faqs/faqs.htm

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