De Nive Sexangula Stellata

Scaling symmetry is observed in snow crystals as a relation between hexagons inscribing and circumscribing hexagonal star polygons. These patterns are revealed by a characteristic distribution of clear spots (pores) and of dark lines. The new symmetry demonstrates the possible relevance of non-Euclidean (multimetrical) crystallography for crystals in nature. The multimetrical space group of the (ideal) ice structure is derived and the morphology of snow crystals is interpreted on the basis of the corresponding crystallographic point group of infinite order. The morphological importance of a set of basic structural sites, indexed according to points of a macroscopic hexagonal lattice, is discussed. Rules are formulated for the growth forms of snow crystals of the dendritic and of the facet type.