Dodecahedral L-spaces and hyperbolic 4-manifolds

We prove that exactly 6 out of the 29 rational homology 3-spheres tessellated by four or less right-angled hyperbolic dodecahedra are L spaces. The algorithm used is based on the L-space census provided by Dunfield in [12], and relies on a result by Rasmussen-Rasmussen [37]. We use the existence of these manifolds together with a result of Martelli [30] to construct explicit examples of hyperbolic 4-manifolds containing separating L-spaces, and therefore having vanishing Seiberg-Witten invariants. This answers a question asked by Agol and Lin in [1].