Investigating dispersion surface morphology of sonic metamaterials is crucial in providing information on related phenomena as inertial coupling, acoustic transparency, polarisation, and absorption. In the present study, we look into frequency surface morphology of two-dimensional (2D) metamaterials of K3,3 and K6 topologies. The elastic structures under consideration consist of the same substratum lattice points and form a pair of sublattices with hexagonal symmetry. We show that, through introducing universal localised mass-in-mass phononic microstructures at lattice points, six single optical frequency-surfaces can be formed with required properties including negative group velocity. Splitting the frequency-surfaces is based on the classical analog of the quantum phenomenon of ‘energy-level repulsion’, which can be achieved only through internal anisotropy of the nodes and allows us to obtain different frequency band gaps.