On the Five-Pointed Snowflake

There’s a fun letter in the latest issue of Nature from Thomas Koop at the University of Bielefeld pointing out how often snowflakes in festive decorations, greetings and wrapping paper are misdrawn with fewer or more than six points. Above is a particularly fine example that I discovered this year, in which some of my presents were (ironically) wrapped (available at Sainsbury’s, no doubt now at a reduced price). It never ceases to amaze me that designers have failed to assimilate this very basic fact about the six-pointed snowflake, though it’s been generally known for centuries. Indeed, the knowledge goes much further back than Kepler’s seventeenth-century treatise, as I pointed out here and in the ‘Branches’ volume of my recent trilogy Nature’s Patterns.

(I’m amused too to see that Nature’s marketing folk are still managing to embarrass the scientific staff. I could tell other tales, but it would be cruel.)

Yet these pentagonal snowflakes set me thinking. As is widely known, the only way ‘crystals’ can display growth habits with fivefold (or indeed eightfold) symmetry is if they are in fact quasicrystals. But could water form quasicrystals? Certainly, in the liquid state it is much more congenial for water molecules to form fivefold rings than the sixfold ones present in ice, because the bond angles are then much closer to that preferred in the tetrahedral coordination geometry. And these pentagonal rings are a general feature of the crystal structures of clathrate hydrates, in which water is frozen around nonpolar solutes such as methane. Now, I’m no crystallographer but I have the impression that it would be naïve to imagine that a local pentagonal packing symmetry is all it takes to make quasicrystallinity feasible. But on the other hand, it’s a good start; our current understanding of quasicrystals grew partly out of Charles Frank’s early work on icosahedral clustering in simple liquids. And large icosahedral structures for water have certainly been postulated. In fact, I’m very puzzled that I can seem to find no discussion in the literature of the possibility of quasicrystallinity in water – either I’m failing badly to understand something (quite possible) or I’m somehow looking in the wrong places (also possible). But I will ask my water structure gurus about this, and if anything comes of that, watch this space.

Incidentally, strict twelvefold symmetry is also forbidden in true crystals but known in quasicrystals. Yet a sort of pseudo-twelvefold symmetry has been seen in snowflakes, due to the coalescence of two snowflakes.