https://phys.org/news/2018-07-classification-symmetry-groups-crystal-space.html

Each of the 230 symmetry space groups is characterized by specific limitations on the atomic arrangement in crystal space, which are determined by the set of elements of space group symmetry, as well as the unit-cell sizes. This means that some regular systems of points of these groups cannot exist in nature for purely geometric reasons. The set of these points forms "forbidden regions" in crystal space, and the existence of such regions was demonstrated by the outstanding chemist and crystallographer, laureate of the Chugaev Prize Mikhail Porai-Koshits.

"We have determined the symmetry of forbidden regions for packing solid circles in a two-dimensional space, whose symmetry is described by one of two-dimensional space symmetry groups. It was also established that, depending on the symmetry of forbidden regions, two-dimensional space symmetry groups can be divided into seven classes," says Nikolai Somov, associate professor of the UNN Department of Crystallography and Experimental Physics.