Tanguy Chouard at Nature has pointed out to me Google’s tribute to the snowflake today:
Nine Lessons and Carols for Godless People just before Christmas. Eight-pointed flakes like this are relatively common, because they are easier to draw than six-pointed ones:
More rarely one sees five-pointed examples like this from some wrapping paper in 2010:
possible sighting of quasicrystalline ice should make us hesitant to be too dismissive of these inventive geometries. What’s more, there do exist claims of pentagonal flakes having been observed, though this seems extremely hard to credit. Of course, in truth quasicrystal ice, even if it exists in very rare circumstances, hardly has five- or eightfold snowflakes as its inevitable corollary. But it’s fun to think about it, especially near the quadricentenary [?] of Kepler’s classic treatise on the snowflake, De nive sexangula.