Orientable hyperbolic 4-manifolds over the 120-cell

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it challenging to construct explicit manifolds of small volume in dimension at least four. Here, we build up closed 4-manifolds 34 π 2 3 ⋅ 16 \frac {34\pi ^2}{3}\cdot 16 by using the cover theory. In particular, classify all orientable four-dimensional covers over right-angled 120-cell homeomorphism; these are with even intersection forms.