The complete group of spatial symmetry operations of a periodic crystal, including translations and combinations such as screw axes and glide planes.
A space group whose point-group operations cannot all be represented without essential fractional translations for any origin. screw axes and glide planes are characteristic examples. Its point group alone omits these translational data.
A space group for which an origin can be chosen so that representatives of all point-group operations have zero translation part. It is a semidirect product of its lattice translations and point group. Presence of centring translations in a conventional cell does not alone make a group nonsymmorphic.
Write a Euclidean isometry as , acting by . Composition is . The translation subgroup is normal; the quotient is the crystallographic point group.
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A space group is a mathematical classification used in crystallography that describes the symmetries of a crystal structure. Specifically, it combines the symmetries of both the lattice (the periodic arrangement of points in space) and the motif (the group of atoms associated with each lattice point). In other words, a space group encapsulates how a crystal can be transformed into itself through operations like translations, rotations, reflections, and inversions.
All possible repetitive crystal structures!
219 of them.