| 单词 | point group |
| 释义 | ˈpoint group Math. and Cryst.
[f. point n.1 + group n.]
†a. [tr. G. punktgruppe (Brill & Noether 1873, in Nachrichten von der K. Ges. der Wiss. zu Göttingen 117).] A set of points. Obs.
1895Proc. London Math. Soc. XXVI. 495 The following paper deals with the properties of point-groups in relation to algebraic curves drawn through them. 1900Rep. Brit. Assoc. Adv. Sci. 1900 121 (heading) Report on the present state of the theory of point-groups. 1900K. Fink Hist. Math. 240 This theorem..introduced point groups, or systems of points of intersection of two curves, into geometry.
b. Any subgroup of the symmetry group of a sphere; esp. any of the thirty-two sets of symmetry operations which are used to classify crystal types.
[1896Amer. Jrnl. Math. XVIII. 172 We mark on the faces of the regular bodies a general point group.] 1903H. Hilton Math. Crystallogr. iv. 48 Finite groups whose operations all leave one point unmoved are called point⁓groups. 1924R. W. G. Wyckoff Structure of 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. 1950W. 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. 1973T. Janssen Crystallographic Groups iii. 72 Each subgroup of O(3) is called a point group, because it leaves the origin invariant. Point groups occur as symmetry groups of molecules and of atoms in a crystal. |
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