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We provide a new construction of the modes of the Poincare dodecahedral spaceS^3/I*. The construction uses the Hopf map, Maxwell's multipole vectors andorbifolds. In particular, the *235-orbifold serves as a parameter space for themodes of S^3/I* shedding new light on the geometrical significance of thedimension of each space of $k$-modes, as well as on the modes themselves.

Orbifold construction of the modes of the Poincare dodecahedral space