  We propose theoretically a reconfigurable two-dimensional (2D) hexagonal
sonic crystal with higher-order topology protected by the six-fold, $C_6$,
rotation symmetry. The acoustic band gap and band topology can be controlled by
rotating the triangular scatterers in each unit-cell. In the nontrivial phase,
the sonic crystal realizes the topological spin Hall effect in a higher-order
fashion: (i) The edge states emerging in the bulk band gap exhibits partial
spin-momentum locking and are gapped due to the reduced spatial symmetry at the
edges. (ii) The gapped edge states, on the other hand, stabilize the
topological corner states emerging in the edge band gap. The partial
spin-momentum locking is manifested as pseudo-spin-polarization of edge states
away from the time-reversal invariant momenta, where the pseudospin is emulated
by the acoustic orbital angular momentum. We reveal the underlying topological
mechanism using a corner topological index based on the symmetry representation
of the acoustic Bloch bands.
