299 research outputs found
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
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
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