  We demonstrate that a bianisotropic response associated with a broken mirror
symmetry of a dielectric resonator allows opening the bandgap in simple square
lattice arrays of such resonators. Realizing the proposed system as an array of
high-index ceramic resonators working at GHz frequencies, we numerically and
experimentally demonstrate the presence of edge states at the interface between
two domains with opposite orientations of the bianisotropic resonators as well
as at the boundary between a single domain and free space. For both cases, we
characterize the dispersion of edge states, examine their propagation along
sharp bends, their resilience towards various types of geometrical defects, and
a spin-momentum locked unidirectional propagation in the case of circularly
polarized excitation. The considered design opens novel possibilities in
constructing optical and microwave structures simultaneously featuring edge
states at the interfaces between distinct resonator domains or a resonator
domain and free space.
