Crystal interface anisotropy ($\gamma (\mathbf{n}),M(\mathbf{n})$)

A crystal's interfacial free energy and attachment kinetics depend on the interface normal $\mathbf{n}$. The orientation-dependent energy $\gamma$ and mobility $M$ select directions even when bulk diffusion is isotropic. This supplements the transport mechanism of crystal dendrites; isotropic transport alone does not specify the number of preferred arms.

Ordinary atmospheric snow crystals are predominantly hexagonal ice Ih. Rotating by sixty degrees around its crystallographic axis leaves the equilibrium orientation dependence unchanged, giving six equivalent basal-plane directions. Temperature and supersaturation determine whether plates, columns or crystal dendrites develop. Dendritic growth of a snowflake needs this crystal symmetry as well as the diffusion instability.