The existence of crystals with their regular appearance reveals properties that are characterized by the word symmetry, which has been adapted from the Greek term for "evenness". Circles are symmetrical, mirror images are symmetrical, the letter A is symmetrical (unlike G), and when science uses such an expression, it means that an object is symmetrical if it can be changed (i.e. transformed by an operation) in such a way that it then appears unchanged.
A circle is therefore called rotationally symmetrical and the letter A correspondingly mirror-symmetrical. Crystals have many different symmetries, and it goes without saying that people associate symmetries with the impression of beauty. In science, we feel the same way, but we also want to distinguish symmetries and separate a continuous one, as in the rotation of a circle, from a discrete one, as in the mirror image of a letter. One classifies a continuous symmetry higher than a graduated one, which allows one to assign the beautiful ice crystals a reduced symmetry compared to homogeneous water. In physics, there is merciless talk of symmetry breaking, even if nothing is broken, but the destructive-sounding word is introduced because it leads to a paradoxical situation that is highly relevant to the discipline known as condensed matter physics. This refers to substances in solid or liquid form, and one of the greatest (unnoticed) insights of recent decades is that they all acquire their properties through symmetry breaking - broken symmetry in English. And this explains the paradox of crystals. The crystals themselves become understandable through the symmetry they exhibit in the shape of their lattice. However, they only acquire their quality when this symmetry is reduced - or broken. A quartz crystal lacks mirror symmetry, and this gives it its optical quality, with which the plane of polarization of the light is rotated. Crystals that lack inversion symmetry become piezoelectric, which means that they produce a voltage and with it a spark when struck, which is realized in a lighter. Breaking symmetry, as unpleasant as the term sounds, ensures the quality you want. You always need the opposite of what you have.
