plassgruppe

Plassgruppe, in crystallography, refers to the symmetry group that describes all symmetry operations leaving a crystal lattice invariant in three-dimensional space. In English, the term is space group. A plassgruppe combines the translational symmetry of the crystal lattice with point-group operations such as rotations, reflections, inversion, as well as glide reflections and screw axes that couple translation to rotation or reflection. The space-group symmetry constrains the arrangement of atoms in the crystal and determines many physical properties as well as the patterns seen in X-ray, neutron, or electron diffraction.

There are 230 distinct plassgrupper in three dimensions. They are categorized according to the seven crystal systems and the 14 Bravais lattice types, and they encode both the lattice translations and the additional symmetry elements. Each plassgruppe is given a Hermann–Mauguin (international) symbol, such as Pm3m for a highly symmetric cubic lattice or P2_1/c for a monoclinic lattice, and tools such as the International Tables for Crystallography provide formal descriptions of their symmetry operations and Wyckoff positions.

In practice, knowing the plassgruppe of a crystal helps in solving and refining crystal structures, interpreting diffraction data, and predicting possible atomic arrangements. The term is standard in Norwegian crystallography, while researchers worldwide refer to the same concept as a space group.