  The research field of magnetic frustration is dominated by triangle-based
lattices but exotic phenomena can also be observed in pentagonal networks. A
peculiar noncollinear magnetic order is indeed known to be stabilized in
Bi2Fe4O9 materializing a Cairo pentagonal lattice. We present the spin wave
excitations in the magnetically ordered state, obtained by inelastic neutron
scattering. They reveal an unconventional excited state related to local
precession of pairs of spins. The magnetic excitations are then modeled to
determine the superexchange interactions for which the frustration is indeed at
the origin of the spin arrangement. This analysis unveils a hierarchy in the
interactions, leading to a paramagnetic state (close to the N\'eel temperature)
constituted of strongly coupled dimers separated by much less correlated spins.
This produces two types of response to an applied magnetic field associated
with the two nonequivalent Fe sites, as observed in the magnetization
distributions obtained using polarized neutrons.
