We all know that every snowflake is unique because they all grow in slightly different ways. However, the unique six-pointed shape cannot be escaped from the ever-changing appearance. This single structure has been shaped into a snowball fight, and it is still for people to watch and dodge when moving. 
In the three-dimensional space we are in, these crystals could have grown in any direction. Why are they always flat hexagons? Why are snowflakes basically two-dimensional?
It all comes down to the way ice crystals are formed at the molecular level.
The most important condition that determines the shape of a snowflake is temperature. Different temperatures generally correspond to different shapes. Between about -10 and -22 degrees Celsius, you're most likely to see a feathery hexapod shape called dendrites.
Snowflakes are not always flat at this point. Depending on the atmospheric conditions, such as temperature and humidity, they can form a column, rose, needle, or any number of shapes. Between -3 and -10 degrees, they may form hollow columns or narrow needles.
But in any case, over a wide range of temperatures, the most basic structure of a snowflake is a flat hexagonal shape, not an ornate dendrite.
We don't know why temperature has such a drastic effect on the shape of tiny crystals. But what is certain is that they are relatively two-dimensional. Why is that?
The answer is that the six sides of these simple planes are symmetrical to the structure of water, i.e., the direct result of the molecular structure.
Water molecules have what chemists call curved geometry. Because it looks like it's bent in half. As shown in the figure below:
Water is also polar, which means that one end of the curved molecule – oxygen – has a negative charge, while two hydrogens have a positive charge.
This means that when water molecules come together to form a solid, they are arranged in a positive and negative charge – oxygen to chlorine, and when all the bonds are aligned, chlorine naturally forms a hexagonal shape.
This characteristic of crystal growth, i.e., the availability of chemical bonds, determines a larger structure, known as faceting.
Depending on the conditions, it may be easier for a water molecule to grasp the edge of a hexagon – forming the shape of a thin plate – or the surface, meaning it will grow into the shape of a column. This strange effect is known as sharpening.
That's why all snowflakes have a hexagonal structure.
But when the conditions are right, these hexagons can start to expand. That's another of our most important conditions: humidity.
As the snowflake grows, the water around it is incorporated into the crystals. This means that in that tiny environment, there is less water and the water molecules have to travel farther to join the snowflakes.
But near the edge, the water molecules don't need to travel that far. So it's easier for them to connect the edges faster, and sharpening again results in smaller structures closer to the edge of the snowflake.
As the crystal gets bigger, it also starts to grow faster because these molecules are attached to the edges.
Whenever conditions allow, the crystals grow faster at the edges than at the surface, and the edges become very fine – producing those dendrite structures. The conditions have to be just right, but it's not just the water to do that. Even table salt can form a dendrite structure under the right circumstances.
So we're lucky that when it snows, it's all right in the right place. This is why we can appreciate the various beautiful shapes of this "hexagonal princess".