point groupn.

1887 Amer. Jrnl. Math. 9 186 The four points of the corresponding latter point-group must also lie two and two on each line, so that the theorem holds where the conics degenerate.

1895 Proc. London Math. Soc. 26 495 The following paper deals with the properties of point-groups in relation to algebraic curves drawn through them.

1949 Trans. Amer. Math. Soc. 65 138 This condition of quasi-equivalence between the point groups..can also be expressed as an algebraic condition between the coordinates..of the two corresponding points.

1983 Amer. Math. Monthly 90 141 The point groups of interest for the discussion of plane curves are those which are contained in the intersection of the curve with a second curve.

1896 Amer. Jrnl. Math. 18 172 We mark on the faces of the regular bodies a general point group. This means we choose arbitrarily, say in the vicinity of one of the vertices a point, and let the regular body undergo all the N rotations of the corresponding group.]

1903 H. Hilton Math. Crystallogr. iv. 48 Finite groups whose operations all leave one point unmoved are called point-groups.

1924 R. W. G. Wyckoff Struct. Crystals i. 21 The point groups, or classes of crystal symmetry, thus formed may be uniquely defined either by stating their symmetry properties or, more analytically, by giving the coördinates of the equivalent points which arise from any arbitrarily chosen point by the operation of each of their elements of symmetry.

1950 W. J. Moore Physical Chem. xiii. 364 The possible combinations of these symmetry elements that can occur in crystals have been shown to number exactly 32. These define the 32 crystallographic point groups, which determine the 32 crystal classes.

1986 P. W. Atkins Physical Chem. (ed. 3) xvii. 409 As soon as the point group of a molecule has been identified, it is possible to make some statements about its properties. For instance, only molecules belonging to the groups C_n, C_nv, and C_s may have an electric dipole monent.