New families of moment-angle manifolds diffeomorphic to connected sums of products of spheres

We prove that the moment-angle manifold ${\mathcal{Z}}_{\mathcal{K}}$ is diffeomorphic to a connected sum of products of spheres when $\mathcal{K}$ is a starshaped (in particular, polytopal) 3-dimensional simplicial sphere with exactly two missing edges that are not adjacent to each other. One of the summands of the connected sum is a product of three spheres. For neighbourly starshaped simplicial spheres $\mathcal{K}$ of odd dimension, we prove the diffeomorphism ${\mathcal{Z}}_{\mathcal{K}}\cong M_1\mathrm{\#}\cdots \mathrm{\#}{M}_k$, where each $M_i$ is a product of two spheres. We give an explicit description of the moment-angle manifolds corresponding to non-polytopal Barnette and Brückner spheres.