  Mirror symmetry of a wave system imposes corresponding even or odd parity on
its eigenmodes. For a discrete system, eigenmode parity on a specific subset of
sites may also originate from so-called latent symmetry. This symmetry is
hidden, but can be revealed in an effective model upon reduction of the
original system onto the latently symmetric sites. Here we show how latent
symmetries can be leveraged for continuous wave setups in the form of acoustic
networks. These are systematically designed to have point-wise amplitude parity
between selected waveguide junctions for all low frequency eigenmodes. We
further develop a modular principle: latently symmetric networks can be
interconnected to feature multiple latently symmetric junction pairs, allowing
the design of arbitrarily large latently symmetric networks. By connecting such
networks to a mirror symmetric subsystem, we design asymmetric setups featuring
eigenmodes with domain-wise parity. Bridging the gap between discrete and
continuous models, our work takes a pivotal step towards exploiting hidden
geometrical symmetries in realistic wave setups.
