You've probably heard it before: Every snowflake that falls from the sky is different in some way from every other one — or from any other flake that has ever fallen.

You've probably heard it before: Every snowflake that falls from the sky is different in some way from every other one — or from any other flake that has ever fallen.

Considering how many snowflakes actually fall, that seems incredible. But snow experts say it really is true.

Let's start with the basics.

Snowflakes are made up of ice, but they are not frozen raindrops. (That's sleet, which is water that freezes as it falls.)

Instead, snowflakes are created inside clouds when a tiny droplet of cloud — which is water vapor — freezes into what is called an ice crystal. These crystals are mostly simple hexagons, or six-sided shapes.

But as more water vapor condenses, more crystals stick together and the six sides can grow. "Branches" or "arms" sprout on each of the sides.

Shapes are partly determined by the temperature and humidity in the air in which the snowflake is created. As the flakes fall, collisions and partial melting can create other shapes — or take away a shape.

From those complex snowflakes comes the notion that no two are the same.

Here is one way of looking at the mathematical possibilities of that, according to Kenneth Libbrecht, a snowflake expert (what a great job that must be!) and physics professor at the California Institute of Technology.

Let's say you have 15 books on a shelf. If you had the time to arrange them in as many different possible ways as existed, you would find that there are more than 1 trillion combinations! Just for 15 books.

If you have 100 books to play with, the number of possible ways you could put them on the shelf would go up to this number: a "1" followed by 158 zeroes.

So experts say that it is virtually impossible for two complex snowflakes with many molecules to be identical. They may look that way to you if you can get a good enough-look, but they aren't.

On the Net: www.its.caltech.edu/~atomic/snowcrystals.