Orbifold construction of the modes of the Poincaré dodecahedral space

We provide a newconstruction of the modes of the Poincare dodecahedral space S(3)/I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S(3)/I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.