In the first Section of this work, we establish fundamental principles and theory, and describe a physically inspired ("polytopal rearrangements" ), mathematical method for describing complete ABn stereoisomeric configuration spaces and their subspaces using purely angle-changing vibrational normal modes as bases to span the spaces. Though the resulting configuration spaces are uncountable and of high dimension, we describe how some ABn configuration spaces, or subspaces thereof, can be compactified closed or compact manifolds such as the 2-dimensional sphere or torus.