I'm pretty sure snowflakes are six pointed symmetrical ice crystals, almost by definition; and are almost always depicted that way.
And although it's impossible "to prove a negative" it is extremely unlikely that any two snowflakes would be completely identical. However, "matching" or substantially similar snowflakes have been found in similar environments.
Wikipedia - Snowflake |
A non-aggregated snowflake often exhibits six-fold "radial" symmetry. The initial symmetry can occur 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 can grow in nearly the same way. However, being in the same micro-environment does not guarantee that each arm grows the same; indeed, for some crystal forms it does not because the underlying crystal growth mechanism also affects how fast each surface region of a crystal grows.
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... It is more likely that two snowflakes could become virtually identical if their environments were similar enough. Matching snow crystals were discovered in Wisconsin in 1988. The crystals were not flakes in the usual sense but rather hollow hexagonal prisms.