  It is shown that the covering approach with a single decagonal prototile can
be transformed into a hexagon, boat and star tiling. Particularly, the atomic
decoration recently proposed by Cockayne and Widom (Phys. Rev. Lett. 81, 598
(1998)) as a structure model for the decagonal phase is investigated. There,
conflicts with the prototile approach arise which are due to specific
peculiarities of the decoration. The above model is compared with recent
experimental images which give strong support to its main features, but
contradict competing structure proposals. The implications for the
stabilization mechanism are discussed.
