Normal modes can be computed by stepping through a descending sequence of one type 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. Mulliken symbols like A1 and B2 are used to label the rows of 2D diagrams whose columns correspond to elements of these objects. (-5[1])S·A·L·Cs transform with the irreps of these objects. 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 describe linear and tetrahedral molecules, and are built up from elements like axes of rotation and planes of reflection. For 10 points, “point” examples of what (10[1])algebraic objects describe (10[1])the symmetries of molecules? ■END■