Orientable hyperbolic 4-manifolds over the 120-cell.

Since there is no hyperbolic Dehn filling theorem in higher dimensions, it is difficult to construct concrete hyperbolic manifolds of small volume in dimension at least four. We build up a census of closed hyperbolic 4-manifolds of volume $\frac{34\pi^2}{3}\cdot 16$ by using small cover theory over the right-angled 120-cell. In particular, we classify all the orientable 4-dimensional small covers over the 120-cell and obtain exactly 56 many up to homeomorphism. Moreover, we calculate the homologies of the obtained orientable closed hyperbolic 4-manifolds and all of them have even intersection forms.