[Die Symmetrie von Spiralketten].

In crystals, polymeric chain molecules often adopt helical structures. Neglecting small distortions possibly caused by an anisotropic environment within the crystal, the symmetry of the single helix can be described by a rod group, which has translational symmetry in one dimension. The rod groups have Hermann-Mauguin symbols similar to space groups, beginning with a script style \scr p followed by a screw-axis symbol; the order of the screw axis can adopt any value. In a crystal, the rod-site symmetry, the so-called penetration rod group, must be a common crystallographic rod subgroup of the molecular rod group and the space group. Instructions are given for the derivation of the rod subgroups in question for a molecular helical rod group of any order. In polymer chemistry, a helix is designated by a (chemical) symbol like 7/2, which means 7 repeating units in 2 coil turns of covalent bonds per translational period. The corresponding Hermann-Mauguin screw-axis symbol is easily derived with a simple formula from this chemical symbol; for a 7/2 helix it is 73 or 74 , depending on chirality. However, it is not possible to deduce the chemical symbol from the Hermann-Mauguin symbol, because it depends on where the covalent bonds are assumed to exist. Covalent bonds are irrelevant for symmetry considerations; a symmetry symbol does not depend on them. A chemically right-handed helix can have a left-handed screw axis. The derivation of the Hermann-Mauguin symbol of a multiple helix is not that easy, as it depends on the mutual position of the interlocked helices; conversion formulae for simpler cases are presented. Instead of covalent bonds, other kinds of linking can serve to define the chemical helix, for example, edge- or face-sharing coordination polyhedra.