Structural insights into a rhombic Penrose tiling variant abundant in five-petaled flower motifs

We present a novel variant of a planar quasiperiodic tiling with ten-fold symmetry, utilising thick and thin rhombuses akin to the well-known rhombic Penrose tiling. It is shown that this new tiling shares several key characteristics with its predecessor, including similar vertex environments, polygonal acceptance domains exhibiting five-fold symmetry and a self-similarity tied to the golden mean, which serves as the fundamental scaling ratio. Nonetheless, it presents a fundamentally distinct structure. The new tiling introduces additional complexity through an increased number of prototiles and a dual grid pattern that incorporates both folded and straight lines. Most notably, it is characterized by a high density of two-tiered, five-petaled flower motifs, which occupy a significant portion of the tiling. Based on this prominent characteristic, we refer to the new tiling as the "Pentas tiling". We also observe a slightly enhanced degree of hyperuniform order compared to the standard rhombic Penrose tiling.