Famously, each snow flake is unique, no two are the same. This is really true. As the crystal lattice of ice has six-fold symmetry, so do snow flakes, which are ice crystals. But this symmetry is never perfect. If you rotate the crystal above by 60 degrees then it would look different, just not as different as if you rotated it by say 45 degrees. If you rotate it by 60 degrees, then you rotate each arm into the position of the next arm and as the arms are roughly similar the crystal will not look very different, bit it will look different.
The snow flake is imperfect, and every snow flake is imperfect in its own unique way. I guess if I were Brian Cox, I would just wonder in awe at this. But I am not Brian Cox, and I just got back from a conference in Leeds, where there was some grumbling about crystals all being imperfect in their unique way.
Unique snow flakes are cool, a hopper full of trillions of wildly varying shapes and sizes of crystals is a pain in the arse – if you want to make 10,000 almost identical uniform drug tablets from them. And we do, most drugs are crystalline, and nobody wants each and every paracetamol tablet to be unique. This would turn taking a painkiller into a lottery, and medicine can do without that excitement.
Crystals have defects in them that break the crystal symmetry, these defects are of all sizes, from the size of a single molecules less than the millionths of a millimetre, to the imperfections around a millimetre across in the six arms above. Again, this is a beautiful set of puzzles, but boy is it tough to deal with.
For example, my student is studying crystals of a molecule called glycine. Every crystal is unique and so grows at a unique rate, some zoom up to a few millimetres in size in half an hour, others are in much less of a hurry. This is kind of fun but it does rather complicate matters.