Platonic polyhedra tune the three-sphere: II. Harmonic analysis on cubic spherical three-manifolds

From the homotopy groups of two distinct cubic spherical three-manifolds, we construct the isomorphic groups of deck transformations acting on the three-sphere. These groups become the cyclic group of order eight and the quaternion group, respectively. By reduction of representations from the orthogonal group to the identity representation of these subgroups we provide two subgroup-periodic bases for the harmonic analysis on the three-manifolds, which have applications to cosmic topology.