Let's see how we can create a snowflake using the Blender geometry editor 2.6.

A snowflake, as we have used to create a wallpaper, is a fractal (self-similar) with six axes of symmetry. Its structure is therefore based on models which are essentially hexagonal, as shown in the attached image. Each arm hence repeated six times on each of the flakes, although there are different configurations depending on the crystallization conditions such as temperature and humidity.