  In the article "Construction of the continuous hull for the combinatorics of
a regular pentagonal tiling of the plane" we constructed a compact topological
space for the combinatorics of "A regular pentagonal tiling of the plane",
which we call the continuous hull. We also constructed a substitution map on
the space which turns out to be a homeomorphism, and so the pair given by the
continuous hull and the substitution map yields a dynamical system. In this
paper we show how we can write this dynamical system as another dynamical
system given by an inverse limit and a right shift map.
