With Lie-algebraic methods we obtain the set of orthogonal harmonic polynomials on the Poincaré dodecahedral three-manifold. The expansion in these polynomials of temperature fluctuations of the cosmic micro wave background tests this manifold as a candidate for cosmic topology.
"Harmonic Polynomials on the Poincaré Dodecahedral Three-Manifold." J. Geom. Symmetry Phys. 6 55 - 66, 2006. https://doi.org/10.7546/jgsp-6-2006-55-66