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