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Investigating dispersion surface morphology of sonic metamaterials is crucialin providing information on related phenomena as inertial coupling, acoustictransparency, polarisation, and absorption. In the present study, we look intofrequency surface morphology of two-dimensional metamaterials of K3,3 and K6topologies. The elastic structures under consideration consist of the samesubstratum lattice points and form a pair of sublattices with hexagonalsymmetry. We show that, through introducing universal localised mass-in-massphononic microstructures at lattice points, six single opticalfrequency-surfaces can be formed with required properties including negativegroup velocity. Splitting the frequency-surfaces is based on the classicalanalog of the quantum phenomenon of "energy-level repulsion", which can beachieved only through internal anisotropy of the nodes and allows us to obtaindifferent frequency band gaps.

Sonic metamaterials: reflection on the role of topology on dispersion surface morphology