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 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 table for one of these objects. Examples of these objects like C-sub-infinity and T-sub-d respectively (10[1])describe linear and tetrahedral molecules, and are built up from elements like axes of rotation and planes of reflection. For 10 points, “space” and “point” examples of what algebraic objects describe symmetries of crystals and molecules? ■END■