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In the window approach to quasicrystals, the atomic position space E_parallelis embedded into a space E^n = E_parallel + E_perp. Windows are attached topoints of a lattice Lambda \in E^n. For standard 5fold and icosahedral tilingmodels, the windows are perpendicular projections of dual Voronoi and Delonecells from Lambda. Their cuts by the position space E_parallel mark tiles andatomic positions. In the alternative covering approach, the position space iscovered by overlapping copies of a quasi-unit cell which carries a fixed atomicconfiguration. The covering and window approach to quasicrystals are shown tobe dual projects: D- and V- clusters are defined as projections to positionspace E_parallel of Delone or Voronoi cells. Decagonal V-clusters in thePenrose tiling, related to the decagon covering, and two types of pentagonalD-clusters in the triangle tiling of 5fold point symmetry with their windowsare analyzed. They are linked, cover position space and have definite windows.For functions compatible with the tilings they form domains of definition. Foricosahedral tilings the V-clusters are Kepler triacontahedra, the D-clustersare two icosahedra and one dodecahedron.

Quasicrystals: atomic coverings and windows are dual projects