Pentagons and rhombuses that can form rotationally symmetric tilings

In this study, various rotationally symmetric tilings that can be formed using pentagons that are related to rhombus are discussed. The pentagons can be convex or concave and can be degenerated into a trapezoid. If the pentagons are convex, they belong to the Type 2 family. Since the properties of pentagons correspond to those of rhombuses, the study also explains the correspondence between pentagons and various rhombic tilings.Comment: 50 pages, 42 figure

Rotationally symmetric tilings with convex pentagons belonging to both the Type 1 and Type 7

Rotationally symmetric tilings by a convex pentagonal tile belonging to both the Type 1 and Type 7 families are introduced. Among them are spiral tilings with two- and four-fold rotational symmetry. Those rotationally symmetric tilings are connected edge-to-edge and have no axis of reflection symmetry.Comment: 13 pages, 16 figures. arXiv admin note: text overlap with arXiv:2005.08470, arXiv:2005.1270