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A note on discrete lattice-periodic sets with an application to Archimedean tilings

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arxiv 1710.02552 v1 pith:XMGVK23X submitted 2017-10-06 math.CO math.MG

Matthias Schymura , Liping Yuan This is my paper · ORCID
classification math.COmath.MG
keywords archimedeansetstilingtilingsapplicationbasicblichfeldt-typediscrete
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Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that 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.

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