First, not all snowflakes are perfectly symmetrical. In fact, the vast majority of snowflakes are asymmetrical. However they appear to be because on a microscopic scale, each side of a crystal being is such close proximity to the other will produce similar results because each molecule was formed under the same environmental conditions simultaneously.
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All snowflakes are six-sided crystals
snowflakes are shaped like stars
No, they are not!
Symmetrical. See http://www.orbitals.com for pictures of all the orbitals
No. Socks are not symmetrical.