Schymura, MatthiasYuan, Liping2019-12-262019-12-262019-12-262019-12-0110.1007/s13366-019-00446-xhttps://infoscience.epfl.ch/handle/20.500.14299/164188WOS:000502041300012Cao and Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that the vertex set of every Archimedean tiling is the union of translates of a fixed lattice, we take a more general viewpoint and investigate basic questions for such point sets about the homogeneous and inhomogeneous problem in the geometry of numbers. The Archimedean tilings nicely exemplify our results.Mathematicsdiscrete lattice-periodic setslatticesarchimedean tilingsblichfeldt-type theoremstheoremtext::journal::journal article::research article