The Maxwell-Garnett (MG) effective medium model has a pure resonance controlled by volume fraction f, but is usually invalid at high density. I present special 2D structures that match quasistatic MG over the entire range 0 < f < 1, in several regular and semi-regular arrays, expanding the applicability of MG. Optimal contours depend on both lattice and fill-factor, transforming from circular at low f to nearly polygonal at high f. A key insight is the direct relationship between optimal surface polarization and surface position. Electrodynamic calculations underline the effect of constituent permittivity on spatial dispersion and required sizes for quasistatic response in various materials.