symmetry of snow flake

A non-aggregated snowflake often exhibits six-fold "radial" symmetry. The initial symmetry occurs because the crystalline structure of ice is six-fold. The six "arms" of the snowflake then grow independently, and each side of each arm grows independently. Most snowflakes are not completely symmetric. The micro-environment in which the snowflake grows changes dynamically as the snowflake falls through the cloud, and tiny changes in temperature and humidity affect the way in which water molecules attach to the snowflake. Since the micro-environment (and its changes) are very nearly identical around the snowflake, each arm grows in nearly the same way. Since the micro-environment of one snowflake is not the same as the micro-environment of a different snowflake, it is very unlikely that two snowflakes will be identical.