The term centrosymmetric, as generally used in crystallography, refers to a space group which contains an inversion center as one of its symmetry elements. In such a space group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Crystals with an inversion center cannot display certain properties, such as the piezoelectric effect. Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... Sphere symmetry group o. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... Piezoelectricity is the ability of certain crystals to produce a voltage when subjected to mechanical stress. ...

Space groups lacking an inversion center (non-centrosymmetric) are further divided into polar and chiral types. A chiral space group is one without any rotoinversion symmetry elements. Rotoinversion (also called an 'inversion axis') is rotation followed by inversion; for example, a mirror reflection corresponds to a two-fold rotoinversion. Chiral space groups must therefore only contain (purely) rotational and translational symmetry. These arise from the crystal point groups 1, 2, 3, 4, 6, 222, 422, 622, 32, 23, and 432. Chiral molecules such as proteins crystallize in chiral space groups. ... In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... Sphere symmetry group o. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... The term chiral (pronounced ) is used to describe an object which is non-superimposable on its mirror image. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...

The term polar is often used for those space groups which are neither centrosymmetric nor chiral. However, the term is more correctly used for any space group containing a unique anisotropic axis. These occur in crystal point groups 1, 2, 3, 4, 6, m, mm2, 3 m, 4 mm, and 6 mm. Thus some chiral space groups are also polar. The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ...

See also

Centrosymmetric matrix