  Disordered hyperuniform dispersions are exotic amorphous two-phase materials
characterized by an anomalous suppression of long-wavelength volume-fraction
fluctuations, endowing them with novel physical properties. While such unusual
materials have received considerable attention, a stumbling block has been an
inability to create large samples that are truly hyperuniform due to current
computational and experimental limitations. To overcome such barriers, we
introduce a new, simple construction procedure that guarantees perfect
hyperuniformity for very large sample sizes. It involves tessellating space
into cells and then inserting a particle into each cell such that the
local-cell particle packing fractions are identical to the global packing
fraction. We analytically prove that such dispersions are perfectly
hyperuniform in the infinite-sample-size limit. Our methodology enables a
remarkable mapping that converts a very large nonhyperuniform disordered
dispersion into a perfectly hyperuniform one, which we numerically demonstrate
in two and three dimensions. A similar analysis also establishes the
hyperuniformity of the famous Hashin-Shtrikman multiscale dispersions, which
possess optimal transport and elastic properties. Our hyperuniform designs can
be readily fabricated using modern photolithographic and 3D printing
technologies. The exploration of the enormous class of hyperuniform dispersions
that can be designed and tuned by our tessellation-based methodology paves the
way for accelerating the discovery of novel hyperuniform materials.
