Advancements in materials design and manufacturing have allowed for the production of ordered and disordered metamaterials with diverse properties. Hyperuniform two-phase heterogeneous materials, which anomalously suppress density fluctuations on large length scales compared to typical disordered systems, and network materials are two classes of metamaterials that have desirable physical properties. Recent focus has been placed on the design of disordered hyperuniform network metamaterials that inherit the desirable properties of both of these metamaterial classes. In this work, we focus on determining the extent to which network structures derived from the spatial tessellations of hyperuniform point patterns inherit the hyperuniformity of the progenitor point patterns. In particular, we examine the Delaunay, Voronoi, Delaunay-centroidal, and Gabriel tessellations of nonhyperuniform and hyperuniform point patterns in two- and three-dimensional Euclidean space. We use the spectral density to characterize the density fluctuations of two-phase media created by thickening the edges of these tessellations in two dimensions and introduce a variance-based measurement to characterize the network structures directly in two and three dimensions. We find that, while none of the tessellations completely inherit the hyperuniformity of the progenitor point pattern, the degree to which the hyperuniformity is inherited is sensitive to the tessellation scheme and the short- and long-range translational disorder in the point pattern, but not to the choice of beam shape when mapping the networks into two-phase media.

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• Disordered systems