Why are snowflakes symmetrical?

Snowflakes, more or less, are symmetrical.

Now, I understand how the crystal pattern is related to the angles between the Oxygen and Hydrogen atoms. What I don’t know is how the snowflake “arm” on one side of the snowflake is influenced by the snowflake arm on the other side.

If I have a bunch of tinkertoy pieces with 104.5 degree angle in them, I’ve got lots of ways to assemble them that aren’t symmetrical. Why do snowflakes form, seemingly, to be pretty.

I read once that it’s not “one side influencing the other” or anything like that, but that the ambient temperature and humidity affects all arms of the flake the same way. So any slight fluctuation will cause (mostly) identical growth and crystallization on each arm.

This is from “snow” on Wikipedia:

There are, broadly, two possible explanations for the symmetry of snowflakes. First, there could be communication or information transfer between the arms, such that growth in each arm affects the growth in each other arm. Surface tension or phonons are among the ways that such communication could occur. The other explanation, which appears to be the prevalent view, is that the arms of a snowflake grow independently in an environment that is believed to be rapidly varying in temperature, humidity and other atmospheric conditions. This environment is believed to be relatively spatially homogeneous on the scale of a single flake, leading to the arms growing to a high level of visual similarity by responding in identical ways to identical conditions, much in the same way that unrelated trees respond to environmental changes by growing near-identical sets of tree rings. The difference in the environment in scales larger than a snowflake leads to the observed lack of correlation between the shapes of different snowflakes. The sixfold symmetry happens because of the basic hexagonal crystalline structure from which the snowflake grows. The exact reason for the threefold symmetry of triangular snowflakes is still a mystery[citation needed] although trigonal symmetry is a subsymmetry of hexagonal.