Just about all snowflakes start off as a few basic shapes. Snowflakes in those groups are mostly the same, with only a few variations. But that all changes on the way down. By the time they reach the ground, snowflakes are unique marvels. It seems like no two are ever exactly alike.
Why all snowflakes have six sides
Every snowflake starts its life as a single supercooled liquid water molecule suspended in midair. In spite of temperatures well below freezing, it stays liquid right up until the moment it is jostled. Only supercooled water can freeze quickly enough to form a delicate, six-sided snowflake. If the water freezes normally, all you get is a glob of ice.
The instant that supercooled water molecule encounters even a tiny speck of dust, it will instantly freeze around it. Other supercooled water molecules will freeze around this tiny nucleus and start building an ice crystal.
Every water molecule crystallizes at a fixed angle based on its H-O-H molecular structure. That's why snowflakes always have six sides. The only place you'll ever see an eight-sided snowflake is when it's made of paper!
Taking shape on the way down
The temperature and humidity determine what initial form the snowflake's six-sided structure will take. Tiny needle-like crystals form where the temperature is only a few degrees below freezing. Flat six-sided plates don't form unless the temperature is a lot colder. Those delicate, feather-like arms don't start growing until the snowflake starts falling.
As more supercooled water molecules bump into the tiny ice crystal, they each find their own place in the delicate crystalline structure. With each addition, the future snowflake grows heavier and heavier.
As first, the strong winds at high altitudes are enough to keep these tiny crystals aloft. However, they'll keep growing heavier until they're heavy enough for gravity to take over. At this point, they start to fall.
There are a lot of things that can happen to a snowflake on the way down. A snowflake gains its own unique character during this stage. It can also die at this stage.
Many snowflakes partly melt and refreeze as they pass through warmer and colder parts of the atmosphere. These changes in temperature are the second thing which determines a snowflake's final shape.
Some snowflakes split apart completely, but still remain connected to each other. Others collide with separate snowflakes and freeze together. These changes determine a snowflake's final shape.
You'd think the most solid shapes, the solid prisms and columns, would have the best chance of surviving. However, it's the delicate stellar dentrites which we know best. These beautiful ice stars are the largest ice crystals which reach the ground. They're so big that when they land on your coat, you can clearly see their structure just by looking at them.
By the time they reach the ground, each snowflake has gone through so many individual events that it's extremely unlikely that any two snowflakes are exactly alike. It could happen! However, you'd have better odds of winning the lottery than of finding two identical snowflakes.
When a snowflake doesn't make it all the way down
Snowflakes which melt completely on the way down turn into rain. Snowflakes which melt and then refreeze lose all their delicate structure and turn into sleet. They've lost their crystal structure at this point, so they're no longer snowflakes.
Sometimes a weird thing happens when a snowflake manages to hang onto part of its crystal structure through the melt. When only the edges of the snowflake melt together and rime builds up on it, the result looks a lot like a fuzzy snowflake. It's called graupel. It's also sometimes called 'soft hail' because the ice builds up gently on something delicate instead of something hard.