Snow crystals growing from water vapor occasionally exhibit morphologies with three-fold (trigonal) symmetry, even though the ice crystal lattice has a molecular structure with six-fold symmetry. In extreme cases, thin platelike snow crystals can grow into faceted forms that resemble simple equilateral triangles. Although far less common than hexagonal forms, trigonal snow crystals have long been observed both in nature and in laboratory studies, and their origin has been an enduring scientific puzzle. In this paper I describe how platelike trigonal structures can be grown on the ends of slender ice needles in air with high reliability at -14 C. I further suggest a physical model that describes how such structures can self-assemble and develop, facilitated by an edge-sharpening instability that turns on at a specific combination of temperature and water-vapor supersaturation. The results generally support a comprehensive model of structure-dependent attachment kinetics in ice growth that has been found to explain many of the overarching behaviors seen in the Nakaya diagram of snow crystal morphologies.
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