  We systematically engineer a series of square and rectangular phononic
crystals to create experimental realisations of complex topological phononic
circuits. The exotic topological transport observed is wholly reliant upon the
underlying structure which must belong to either a square or rectangular
lattice system and not to any hexagonal-based structure. The phononic system
chosen consists of a periodic array of square steel bars which partitions
acoustic waves in water over a broadband range of frequencies (~0.5 MHz). An
ultrasonic transducer launches an acoustic pulse which propagates along a
domain wall, before encountering a nodal point, from which the acoustic signal
partitions towards three exit ports. Numerical simulations are performed to
clearly illustrate the highly resolved edge states as well as corroborate our
experimental findings. To achieve complete control over the flow of energy,
power division and redirection devices are required. The tunability afforded by
our designs, in conjunction with the topological robustness of the modes, will
result in their assimilation into acoustical devices.
