  We obtain full moduli parameters for generic non-planar BPS networks of
domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields,
and exhaust all exact solutions in the corresponding $\mathbb{C}P^{N -1}$
model. We develop a convenient description by grid diagrams which are polytopes
determined by mass parameters of the model. To illustrate the validity of our
method, we work out non-planar domain wall networks for lower $N$ in $3+1$
dimensions. In general, the networks can have compact vacuum bubbles, which are
finite vacuum regions surrounded by domain walls, when the polytopes of the
grid diagrams have inner vertices, and the size of bubbles can be controlled by
moduli parameters. We also construct domain wall networks with bubbles in the
shapes of the Platonic, Archimedean, Catalan, and Kepler-Poinsot solids.
