  A relaxed version of Gummelt's covering rules for the aperiodic decagon is
considered, which produces certain random-tiling-type structures. These
structures are precisely characterized, along with their relationships to
various other random tiling ensembles. The relaxed covering rule has a natural
realization in terms of a vertex cluster in the Penrose pentagon tiling. Using
Monte Carlo simulations, it is shown that the structures obtained by maximizing
the density of this cluster are the same as those produced by the corresponding
covering rules. The entropy density of the covering ensemble is determined
using the entropic sampling algorithm. If the model is extended by an
additional coupling between neighboring clusters, perfectly ordered structures
are obtained, like those produced by Gummelt's perfect covering rules.
