Convex pentagons and convex hexagons that can form rotationally symmetric tilings

In this study, the properties of convex hexagons that can generate rotationally symmetric edge-to-edge tilings are discussed. Since the convex hexagons are equilateral convex parallelohexagons, convex pentagons generated by bisecting the hexagons can form rotationally symmetric non-edge-to-edge tilings. In addition, under certain circumstances, tiling-like patterns with an equilateral convex polygonal hole at the center can be formed using these convex hexagons or pentagons.Comment: 23 pages, 28 figures. arXiv admin note: text overlap with arXiv:2005.0847

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