chirality
/ ky-RAL-it-ee /
Chirality is handedness. Your left and right hands are mirror images, yet no matter how you rotate one, you can never lay it exactly on top of the other, a left glove will not fit a right hand. An object is chiral when it and its mirror image cannot be superimposed by any rotation. The word comes from the Greek kheir, meaning hand.
In crystals, chirality has a sharp symmetry test: a structure is chiral if and only if its point group contains no improper operation, no mirror plane, no inversion centre, no rotoinversion axis. Only proper rotations are allowed. Exactly 11 of the 32 crystal classes pass this test (1, 2, 222, 4, 422, 3, 32, 6, 622, 23, 432); they are the enantiomorphic classes, and a crystal in one of them comes in distinct left-handed and right-handed forms. Quartz is the classic example: left- and right-handed quartz rotate polarised light in opposite directions.
Chirality is central to life and to technology. Most biological molecules, sugars, amino acids, DNA, are chiral, and living things use almost exclusively one hand, so a drug's 'wrong' mirror-image can be useless or harmful. In crystals, handedness controls optical activity and some nonlinear-optical behaviour. A mirror plane or inversion centre in the point group instantly forbids chirality.
Right-handed and left-handed quartz are enantiomorphs: same chemistry (SiO2), same energy, but mirror-image atomic arrangements that twist light clockwise versus counterclockwise.
A chiral object cannot be superimposed on its mirror image, like a left and right hand.
Chirality is about the absence of improper symmetry, not the presence of a rotation. A shape can have plenty of rotation axes and still be chiral, as long as it has no mirror, inversion, or rotoinversion.