Symmetry, crystallography, and art

Abstract

Crystallography, a scientific discipline about the properties and structure of crystals, and the arts seem to be two different areas of human endeavor. There are, indeed, many differences between them – however, there are also similarities. The concept of symmetry can be used as a bridge to recognize such similarities. Symmetry is everywhere, in the hard sciences, in the arts, in nature, and in our everyday life; therefore it seems to be a natural choice for connecting the seemingly disparate fields of crystallography and the arts. In the following, first we look at science and the arts through one of the simplest symmetries, reflection. This is followed by considerations of chirality, which is related to reflection in a special way. Further, space groups will be discussed, the one-, two-, and three-dimensional space groups with examples from both the sciences and the arts. The symmetries of crystal structures belong to the three-dimensional space groups.