We study the poloidal modes (modes whose variations are strictly along the direction of the torus axis) of toroidal nanoparticles. We show that the modes may be understood in terms of the symmetry breaking that occurs when an infinite cylinder is folded to form a torus. This symmetry breaking results in the splitting of the transverse cylinder modes into two distinct sets of modes on a torus. One set of these modes was known to exist already. We show the existence of the second set and also analytically derive the surface charge structure for that set of modes. We also consolidate recent advances made in studying the modal structure on torus particles and complete our understanding of the plasmonic modes of a torus.