Each snow crystal forms when water vapor in the clouds condenses into ice. The molecules of H2O join together in a hexagonal lattice, and those molecules begin to clump together. The small core of a crystal has "rough" patches with many dangling chemical bonds as well as "smooth" areas; a crystal grows into a six-sided prism because the incoming molecules attach to the rough patches at six distinct spots. Those areas grow faster than the "smooth" patches, and soon a basic hexagonal shape with six points and six facets has formed.
"The geometry of the molecule gets transformed to geometry of the snowflake," Libbrecht says, "so you can see it."