  It is commonly assumed that the long-wavelength limit of a metamaterial can
always be described in terms of effective permeability and permittivity
tensors. This assumption holds true in all metamaterials considered up to now.
Here we report that this assumption is false--there exist an entirely new class
of metamaterials consisting of multiple interlocking disconnected metal
networks, for which the effective long-wavelength theory is local, but the
effective field is non-Maxwellian, and possesses much more internal degrees of
freedom than effective Maxwellian fields in a homogeneous medium.
