Morphological possibilities in general crystallography. Snow crystals.
Morphological features of snow crystals are analyzed on the basis of concepts of a general crystallography, where point groups of infinite order are possible. The observations are first formulated in a set of rules, leading to a macroscopic growth lattice and to continuous growth boundaries. Both are brought in connection with two-dimensional integral invertible transformations. Families of boundaries are considered, labeled by a set of indices restricted by selection rules and generalizing the law of rational indices. These properties are indicated graphically on a sample of 12 natural snow crystals. Their geometric and arithmetic properties are summarized in a table.
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Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands. alo@sci.kun.nl