Hyperuniformity variation with quasicrystal local isomorphism class

Hyperuniformity is the suppression of long-wavelength density fluctuations, relative to typical structurally disordered systems. In this paper, we examine how the degree of hyperuniformity [[Formula: see text]] in quasicrystals depends on the local isomorphism class. By studying the continuum of pentagonal quasicrystal tilings obtained by direct projection from a five-dimensional hypercubic lattice, we find that [Formula: see text] is dominantly determined by the local distribution of vertex environments (e.g. as measured by Voronoi cells) but also exhibits a non-negligible dependence on the restorability. We show that the highest degree of hyperuniformity [smallest [Formula: see text]] corresponds to the Penrose local isomorphism class. The difference in the degree of hyperuniformity is expected to affect physical characteristics, such as transport properties.