  The paper presents the study of waves in a structured geometrically chiral
solid. A special attention is given to the analysis of the Bloch-Floquet waves
in a doubly periodic high-contrast lattice containing tilted resonators.
Dirac-like dispersion of Bloch waves in the structure is identified, studied
and applied to wave-guiding and wave-defect interaction problems. The work is
extended to the transmission problems and models of fracture, where
localisation and edge waves occur. The theoretical derivations are accompanied
with numerical simulations and illustrations.
