Cyclic generalizations of two hyperbolic icosahedral manifolds

We study two families of closed orientable three-dimensional manifolds, which are defined as cyclic generalizations of two hyperbolic icosahedral manifolds, which were described first by Richardson and Rubinstein and then by Everitt. Results about covering properties, fundamental groups and hyperbolic volumes are proved for the manifolds belonging to these families. In particular, we show that they are cyclic coverings of the lens space L3,1 branched over some 2- or 3-component links. In some cases our results correct those announced in Cavicchioli, Spaggiari and Telloni (2010) [5].