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Meaning
  1. 1
    English · JMdict
    mathematics point group
  2. 2
    computing point cloud
  3. 3
    English · Wikipedia

    In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y: y = Mx where the origin is the fixed point. Point-group elements can either be rotations (determinant of M = 1) or else reflections, or improper rotations (determinant of M = −1). Discrete point groups in more than one dimension come in infinite families, but from the crystallographic restriction theorem and one of Bieberbach's theorems, each number of dimensions has only a finite number of point groups that are symmetric over some lattice or grid with that number. These are the crystallographic point groups.

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