Abstract
Observational data hint at a finite universe, with spherical manifolds such as the Poincaré dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present paper provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincaré dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D*m and the lens spaces L(p, 1).
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