Cosmic topology of polyhedral double-action manifolds

Aspecial class of non-trivial topologies of the spherical space S-3 is investigated with respect to their cosmic microwave background (CMB) anisotropies. The observed correlations of the anisotropies on the CMB sky possess on large separation angles surprising low amplitudes which might be naturally be explained by models of the Universe having a multiconnected spatial space. We analysed in Aurich and Lustig (2012 Class. Quantum Grav. 29 215005) the CMB properties of prism double-action manifolds that are generated by a binary dihedral group D-p* and a cyclic group Z(n) up to a group order of 180. Here we extend the CMB analysis to polyhedral double-action manifolds which are generated by the three binary polyhedral groups (T*, O*, I*) and a cyclic group Zn up to a group order of 1000. There are 20 such polyhedral double-action manifolds. Some of them turn out to have even lower CMB correlations on large angles than the Poincare dodecahedron.