Snowflakes are symmetrical because they reflect the internal order of the water molecules as they arrange themselves in the solid state (the process of crystallization). Water molecules in the solid state, such as in ice and snow, form weak bonds (called hydrogen bonds) to one another. These ordered arrangements result in the basic symmetrical, hexagonal shape of the snowflake. In reality, there are many different types of snowflakes (as in the clich that 'no two snowflakes are alike'); this differentiation occurs because each snowflake is a separate crystal that is subject to the specific atmospheric conditions, notably temperature and humidity, under which it is formed.
The second question has to do with the way in which snowflakes are formed. The growth of snowflakes (or of any substance changing from a liquid to a solid state) is known as crystallization. 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. Water molecules simply arrange themselves to fit the spaces and maintain symmetry; in this way, the different arms of the snowflake are formed.
Howard T. Evans, Jr., an x-ray crystallographer who is now scientist emeritus at the U.S. Geological Survey, adds a few details:
Snowflakes are mysterious things. Their fundamental form derives from the arrangement of the water molecules in the ice crystal. When a liquid freezes, the molecules tend to settle in the lowest-energy state, and that almost always involves some form of symmetry. The higher the symmetry, the more stable the crystal is.
Water molecules floating freely in a vapor begin to arrange themselves into a crystalline solid when the temperature drops below freezing. The two hydrogen atoms of the molecules tend to attract neighboring water molecules. When the temperature (thermal motion) is low enough, the molecules link together to form a solid, open framework that has a strict hexagonal symmetry.
But why are snowflake shapes so elaborate? Nobody has a good answer for that. The general explanation is that snowflakes form in the atmosphere where conditions are very complex and variable. A crystal might begin to grow in one manner and then minutes or even seconds later something changes (temperature or humidity), so it starts to grow in another manner. The hexagonal symmetry is maintained, but the ice crystal may branch off in new directions. The changes in environmental conditions take place over a large area compared with the size of a single snowflake, so all regions of the flake are similarly affected. In the end, there are all kinds of forms that can arise: everything from prisms and needles to the familiar lacy snowflakes. Water is an amazing substance!
Answer originally posted October 21, 1999.