AbstractPropagation behaviors of electromagnetic waves are governed by the equifrequency surface of the medium. Up to now, ordinary materials, including the medium exist in nature and the man-made metamaterials, always have an equifrequency surface (ellipsoid or hyperboloid) centered at zero k-point. Here we propose a new type of metamaterial possessing multiple index ellipsoids centered at arbitrary nonzero k-points. Their locations in momentum space are determined by the connectivity of a set of interpenetrating metallic scaffolds, whereas the group velocities of the modes are determined by the geometrical details. Such system is a new class of metamaterial whose properties arise from global connectivity and hence can have broadband functionality in applications such as negative refraction, orientation-dependent coupling effect, and cavity without walls, and they are fundamentally different from ordinary resonant metamaterials that are inherently bandwidth limited. We perform microwave experiments to confirm our findings.