  We construct new families of smooth Fano fourfolds with Picard rank 1, which
contain cylinders, i.e., Zariski open subsets of form $Z\times A^1$, where $Z$
is a quasiprojective variety. The affine cones over such a fourfold admit
effective $G_a$-actions. Similar constructions of cylindrical Fano threefolds
and fourfolds were done previously in [KPZ11, KPZ14, PZ15].
