Why is snow six-cornered (hexagonal symmetry of snowflakes)

Partly settled. Some of it is understood, some is still argued about.

Johannes Kepler's 1611 essay first posed the puzzle of why snow crystals consistently show six-fold symmetry, without access to any atomic theory of matter. The basic answer, that ice's crystal lattice itself has hexagonal symmetry, was established once X-ray crystallography revealed ice's atomic structure in the 20th century. However, explaining and predicting the enormous variety of complex branching, plate, and column morphologies observed in real snowflakes, and how they depend sensitively on temperature and humidity during growth, remained an open and actively developed problem; Kenneth Libbrecht's 2005 review and subsequent laboratory growth experiments substantially advanced quantitative, predictive models of these patterns, though fully first-principles prediction of arbitrary snow-crystal morphology remains an active research area.

Every snowflake obeys the same six-fold rule set by ice's crystal lattice, yet the huge variety of paths a crystal can take through changing temperature and humidity means virtually no two ever look exactly alike.

Explanations that circulated

• The folk claim that 'no two snowflakes are ever alike' is sometimes stated as a proven physical law in its own right; it is better understood as an extremely high-probability statistical consequence of the enormous number of distinct temperature/humidity growth histories a crystal can experience, not a separate physical principle
• Early explanations attributing six-fold symmetry simply to 'water molecules being hexagonal' conflate the individual water molecule's geometry with the larger-scale hexagonal symmetry of the ice crystal lattice that actually governs facet growth

References

• The physics of snow crystals, Kenneth G. Libbrecht, Reports on Progress in Physics, 2005