As noted by earlier researchers studying polytopal rearrangements, vibrational atomic motions correspond to the beginning of rearrangement reaction coordinates. For example, the geometric reflection ("inversion") of trigonal pyramidal TPY-3 NH3 involves the umbrella vibrational mode of a1 symmetry, and the Berry pseudorotation mechanism in trigonal bipyramidal TBPY-5 PF5 is affected by a vibrational mode of eʹ symmetry. In this work, a mathematically-rigorous method that we developed for describing ABn configuration spaces and based upon the above principle, is applied to the AB4 tetrahedral (T-4) system, focusing on angular atom displacements that have "e generic symmetry" (the E-mode).