Normal modes can be computed by stepping through a decreasing sequence of these objects via successive atom substitutions, and reading a correlation table. Volume A of the International Tables for Crystallography is a list of one type of these objects, along with each one’s associated Wyckoff positions. SALCs transform with the irreps of (-5[1])these objects, which are labeled with Mulliken symbols like A1 and B2. Whether a molecule is IR or Raman-active can be read from the (*) character (15[1])table for one (-5[1])of these objects. (10[4])Examples (10[1])of (10[4])these (10[1])objects like (10[1])C-sub-infinity and T-sub-d respectively (10[1])describe linear and tetrahedral molecules, and are built up from elements (10[1])like axes of rotation and planes of reflection. For 10 points, “space” and (10[1])“point” examples of what algebraic objects describe symmetries of crystals and molecules? ■END■