  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.
