Decagonal motifs found in the traditional tile designs of Islamic art and architecture can, with a little refinement, be arranged according to the fundamental quasiperiodic structure of the Penrose tiling. A simple tessellation is applied to six traditional motifs to create analogues to the pentagonal Penrose tiles. Substitution rules guiding hierarchical assembly of these Penrose tiling arrangements are then applied, mediated by the tessellation tiles. I then explore how the artist may include hints to the viewer about the mathematical characteristics of Penrose tilings that these designs represent, including their correct arrangement, substitution rules, quasiperiodicity, and other features.