Cohomology of the continuous hull of a combinatorial pentagonal tiling

In the article “Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane” we constructed the continuous hull for the combinatorics of “A regular pentagonal tiling of the plane”, and in the article “Continuous hull of a combinatorial pentagonal tiling as an inverse limit” we showed how we could write this hull as an inverse limit. In this paper we show how to compute the cohomology of the hull and its topological K-theory.