In this paper, we study the transitive action of the fundamental group of the space of normal planes of a transnormal manifold on the set of isometries of the generating frame of the manifold itself. We use dihedral groups as a tool to describe the generating polytopes of transnormal tori in \(\textbf{R}^{4}\) . We, algebraically, show that the generating polytope of a transnormal torus in \(\textbf{R}^{4}\) is a rectangle.