Why is every snowflake different (and yet symmetrical)?

In 1611 Johannes Kepler wrote a paper explained the structure of snow flakes by suggesting that each snow flake begins with a hexagonal symmetric seed which grows as it falls through the atmosphere. Changing conditions of temperature and moisture ensure that each snow flake is unique, and yet the snowflake is small enough that the conditions determining the pattern of growth are the same on each of the six faces (and corners depending on your viewpoint).

Kepler's interest in how matter arranges itself was stimulated, and he went on to look at the ways particles can arrange themselves to occupy the least possible volume. Assuming that particles of matter are spherical it is obvious that however they are arranged there will always be space between them.

Kepler studied a whole variety of configurations and noted in this paper that it was the the face-centred cubic lattice for which 'the packing will be the tightest possible'. Although generally accepted as true, no mathematical proof that the face centred cubic structure is indeed the optimum packing strategy was found till at least 2006 when Hales and Ferguson proposed a computational method.

Snowflake Links

An ice crystal