Hexagonal ice crystal anisotropy ($\gamma (\varphi +\pi /3)=\gamma (\varphi )$)

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.