In the crystallography of quasicrystals,the space for the structure description is taken as a subspace E_||,embedded irrationally in an N-dimensional space equipped with a lattice A.Quasiperiodic dual canonical tilings (tau,LAMBDA)tau*,LAMBDA) arise from the geometry and approach to quasicrystals,tiles are replaced by a few covering clusters.As a typical example,the tiling (LAMBDA*,A_4) of fivefold symmetry is covered by two Deloneclusters.This constructionis called a covering presentation compatible with the tiling.We show that any given tile in the tiling can be uniiquely associated with a specific overlap of Delone clusters.Each specific overlap is called a color for this tile.Te range of colors and their relative frequencies are explicitly determined.
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