Some hyperbolic 4-manifolds with low volume and number of cusps

We construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume vm=4π2/3vm=4π2/3 and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic 4-manifolds. The second has volume 2⋅vm2⋅vm and one cusp. It has lowest volume among known one-cusped hyperbolic 4-manifolds.