Reflections on the ambivalent helix

The helix is nature's favourite shape. Because of its elementary geometry and distinctive appearance it is also the clearest instance of an enantiomorphic object--a helix and its mirror image are identical in all respects except their screw sense. This is a distinction that can be ignored from the points of view of pure geometry and pure group theory but any helical structure is actually available as either or both hands. Whether in nature helices do occur as just one hand, or both, is one of the best--perhaps the best--puzzles of the science of form. In this short review I look at a few examples of naturally occurring helices, some where only one hand is found, some where both are commonly found, and perhaps the most interesting examples in biological terms--those where both are found but one hand is very much rarer than the other. I review what mechanisms--physico-chemical, genetic, evolutionary--underlie the different manifestations of left- and right-handedness.